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Effective Field Theory of Random Quantum Circuits. ENTROPY 2022; 24:e24060823. [PMID: 35741543 PMCID: PMC9223178 DOI: 10.3390/e24060823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 06/09/2022] [Accepted: 06/10/2022] [Indexed: 11/23/2022]
Abstract
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.
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2
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Nakaharai S, Iwasaki T, Morita Y, Moriyama S, Ogawa S. Electron Transport Tuning of Graphene by Helium Ion Irradiation. NANO EXPRESS 2022. [DOI: 10.1088/2632-959x/ac73ad] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
Abstract
This article reviews charge carrier transport phenomena in single-layer graphene, which generates crystalline defects through helium-ion-beam irradiation using a helium-ion microscope. Crystalline defects act as electron scatterers, and the conductivity decays drastically with increase in ion dose. Real-time conductivity monitoring during ion beam scans over the graphene surface is also presented. Negative magnetoresistance is observed in defective graphene in cryogenic measurements under magnetic fields, suggesting that strong localisation occurred in this two-dimensional electron system, which survived even at room temperature. The localised state also contributes to inducing a transport gap around the Dirac point, where the density of states is at its minimum, and it enables field-effect control of the carrier transport by tuning the carrier density. The fabrication and operation of field-effect transistors with defective graphene channels are also demonstrated.
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Quantum Diffusion in the Lowest Landau Level of Disordered Graphene. NANOMATERIALS 2022; 12:nano12101675. [PMID: 35630897 PMCID: PMC9145546 DOI: 10.3390/nano12101675] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 03/30/2022] [Accepted: 05/11/2022] [Indexed: 11/17/2022]
Abstract
Electronic transport in the lowest Landau level of disordered graphene sheets placed in a homogeneous perpendicular magnetic field is a long-standing and cumbersome problem which defies a conclusive solution for several years. Because the modeled system lacks an intrinsic small parameter, the theoretical picture is infested with singularities and anomalies. We propose an analytical approach to the conductivity based on the analysis of the diffusive processes, and we calculate the density of states, the diffusion coefficient and the static conductivity. The obtained results are not only interesting from the purely theoretical point of view but have a practical significance as well, especially for the development of the novel high-precision calibration devices.
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4
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Kirkpatrick TR, Belitz D, Dorfman JR. Nonhydrodynamic initial conditions are not soon forgotten. Phys Rev E 2021; 104:024111. [PMID: 34525645 DOI: 10.1103/physreve.104.024111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Accepted: 07/28/2021] [Indexed: 11/07/2022]
Abstract
Solutions to hydrodynamic equations, which are used for a vast variety of physical problems, are assumed to be specified by boundary conditions and initial conditions on the hydrodynamic variables only. Initial values of other variables are assumed to be irrelevant for a hydrodynamic description. We show that this assumption is not correct because of the existence of long-time-tail effects that are ubiquitous in systems governed by hydrodynamic equations. We illustrate this breakdown of a hydrodynamic description by means of the simple example of diffusion in a disordered electron system.
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Affiliation(s)
- T R Kirkpatrick
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| | - D Belitz
- Department of Physics and Institute for Fundamental Science, University of Oregon, Eugene, Oregon 97403, USA.,Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA
| | - J R Dorfman
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
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Zhao PL, Lu HZ, Xie XC. Theory for Magnetic-Field-Driven 3D Metal-Insulator Transitions in the Quantum Limit. PHYSICAL REVIEW LETTERS 2021; 127:046602. [PMID: 34355953 DOI: 10.1103/physrevlett.127.046602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Revised: 04/07/2021] [Accepted: 06/17/2021] [Indexed: 06/13/2023]
Abstract
Metal-insulator transitions driven by magnetic fields have been extensively studied in 2D, but a 3D theory is still lacking. Motivated by recent experiments, we develop a scaling theory for the metal-insulator transitions in the strong-magnetic-field quantum limit of a 3D system. By using a renormalization-group calculation to treat electron-electron interactions, electron-phonon interactions, and disorder on the same footing, we obtain the critical exponent that characterizes the scaling relations of the resistivity to temperature and magnetic field. By comparing the critical exponent with those in a recent experiment [F. Tang et al., Nature (London) 569, 537 (2019)NATUAS0028-083610.1038/s41586-019-1180-9], we conclude that the insulating ground state was not only a charge-density wave driven by electron-phonon interactions but also coexisting with strong electron-electron interactions and backscattering disorder. We also propose a current-scaling experiment for further verification. Our theory will be helpful for exploring the emergent territory of 3D metal-insulator transitions under strong magnetic fields.
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Affiliation(s)
- Peng-Lu Zhao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, West Building 3, No. 10, Xibeiwang East Road, Haidian District, Beijing 100193, China
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6
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Garratt SJ, Chalker JT. Many-Body Delocalization as Symmetry Breaking. PHYSICAL REVIEW LETTERS 2021; 127:026802. [PMID: 34296927 DOI: 10.1103/physrevlett.127.026802] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
We present a framework in which the transition between a many-body localized (MBL) phase and an ergodic one is symmetry breaking. We consider random Floquet spin chains, expressing their averaged spectral form factor (SFF) as a function of time in terms of a transfer matrix that acts in the space direction. The SFF is determined by the leading eigenvalues of this transfer matrix. In the MBL phase, the leading eigenvalue is unique, as in a symmetry-unbroken phase, while in the ergodic phase and at late times the leading eigenvalues are asymptotically degenerate, as in a system with degenerate symmetry-breaking phases. We identify the broken symmetry of the transfer matrix, introduce a local order parameter for the transition, and show that the associated correlation functions are long-ranged only in the ergodic phase.
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Affiliation(s)
- S J Garratt
- Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - J T Chalker
- Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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7
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Abstract
It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.
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Antinucci G, Fresta L, Porta M. A Supersymmetric Hierarchical Model for Weakly Disordered 3 d Semimetals. ANNALES HENRI POINCARE 2020; 21:3499-3574. [PMID: 33088211 PMCID: PMC7567744 DOI: 10.1007/s00023-020-00909-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Accepted: 04/04/2020] [Indexed: 06/11/2023]
Abstract
In this paper, we study a hierarchical supersymmetric model for a class of gapless, three-dimensional, weakly disordered quantum systems, displaying pointlike Fermi surface and conical intersections of the energy bands in the absence of disorder. We use rigorous renormalization group methods and supersymmetry to compute the correlation functions of the system. We prove algebraic decay of the two-point correlation function, compatible with delocalization. A main technical ingredient is the multiscale analysis of massless bosonic Gaussian integrations with purely imaginary covariances, performed via iterative stationary phase expansions.
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Affiliation(s)
- Giovanni Antinucci
- Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Luca Fresta
- Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Marcello Porta
- Mathematics Area, SISSA, Via Bonomea 265, 34136 Trieste, Italy
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Micklitz T, Monteiro F, Altland A. Nonergodic Extended States in the Sachdev-Ye-Kitaev Model. PHYSICAL REVIEW LETTERS 2019; 123:125701. [PMID: 31633962 DOI: 10.1103/physrevlett.123.125701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2019] [Revised: 04/28/2019] [Indexed: 06/10/2023]
Abstract
We analytically study spectral correlations and many body wave functions of a Sachdev-Ye-Kitaev model deformed by a random Hamiltonian diagonal in Fock space. Our main result is the identification of a wide range of intermediate coupling strengths where the spectral statistics is of Wigner-Dyson type, while wave functions are nonuniformly distributed over Fock space. The structure of the theory suggests that such manifestations of nonergodic extendedness may be a prevalent phenomenon in many body chaotic quantum systems.
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Affiliation(s)
- T Micklitz
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
| | - Felipe Monteiro
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
| | - Alexander Altland
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937 Cologne, Germany
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Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2018. [DOI: 10.3390/mca24010001] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, we present a modified auxiliary equation method. We harness this modification in three fundamental models in the biological branch of science. These models are the biological population model, equal width model and modified equal width equation. The three models represent the population density occurring as a result of population supply, a lengthy wave propagating in the positive x-direction, and the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes, respectively. We discuss these models in nonlinear fractional partial differential equation formulas. We used the conformable derivative properties to convert them into nonlinear ordinary differential equations with integer order. After adapting, we applied our new modification to these models to obtain solitary solutions of them. We obtained many novel solutions of these models, which serve to understand more about their properties. All obtained solutions were verified by putting them back into the original equations via computer software such as Maple, Mathematica, and Matlab.
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11
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Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems. APPLIED SCIENCES-BASEL 2018. [DOI: 10.3390/app8122401] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.
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Schirmacher W, Abaie B, Mafi A, Ruocco G, Leonetti M. What is the Right Theory for Anderson Localization of Light? An Experimental Test. PHYSICAL REVIEW LETTERS 2018; 120:067401. [PMID: 29481270 DOI: 10.1103/physrevlett.120.067401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Indexed: 06/08/2023]
Abstract
Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description, the random potential depends on the wavelength of the incident light. For transverse Anderson localization, this leads to the prediction that the distribution of localization lengths-and, hence, its average-strongly depends on the wavelength. In an alternative description, in terms of a spatially fluctuating electric modulus, this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using optical samples exhibiting transverse Anderson localization. We do not find any dependence of the observed average localization radii on the light wavelength. We conclude that the modulus-type description is the correct one and not the potential-type one. We corroborate this by showing that in the derivation of the traditional potential-type theory, a term in the wave equation has been tacitly neglected. In our new modulus-type theory, the wave equation is exact. We check the consistency of the new theory with our data using the nonlinear sigma model. We comment on the consequences for the general case of three-dimensional disorder.
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Affiliation(s)
- Walter Schirmacher
- Center for Life Nano Science @ Sapienza, Isituto Italiano di Tecnologia, Viale Regina Elena, 291, I-00161 Roma, Italia
- Dipartimento di Fisica, Universitá "La Sapienza," Piazzale Aldo Moro, 5, I-00185 Roma, Italia
- Institut für Physik, Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany
| | - Behnam Abaie
- Department of Physics and Astronomy and Center for High Technology Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Arash Mafi
- Department of Physics and Astronomy and Center for High Technology Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Giancarlo Ruocco
- Center for Life Nano Science @ Sapienza, Isituto Italiano di Tecnologia, Viale Regina Elena, 291, I-00161 Roma, Italia
- Dipartimento di Fisica, Universitá "La Sapienza," Piazzale Aldo Moro, 5, I-00185 Roma, Italia
| | - Marco Leonetti
- Center for Life Nano Science @ Sapienza, Isituto Italiano di Tecnologia, Viale Regina Elena, 291, I-00161 Roma, Italia
- CNR NANOTEC, Istituto di Nanotechologia, I-73100 Lecce, Italia
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13
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Altland A, Micklitz T. Field Theory Approach to Many-Body Localization. PHYSICAL REVIEW LETTERS 2017; 118:127202. [PMID: 28388186 DOI: 10.1103/physrevlett.118.127202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 06/07/2023]
Abstract
We introduce an analytic approach to many-body localization (MBL) in random spin chains. We consider MBL within a first quantized framework where it becomes a localization phenomenon in the high-dimensional lattice defined by the Hilbert space of the clean system. Designed in analogy with the field-theory description of single particle localization, our approach describes wave package propagation on that lattice after a disorder average has been performed and the system is controlled by only a few universal parameters. We discuss the stability of an ergodic weak disorder and a localized strong disorder phase, respectively, and demonstrate that the latter is protected by mechanisms which put MBL outside the universality class of Anderson localization.
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Affiliation(s)
- Alexander Altland
- Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany
| | - Tobias Micklitz
- Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
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Sinner A, Ziegler K. Finite-size scaling in a 2D disordered electron gas with spectral nodes. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2016; 28:305701. [PMID: 27270084 DOI: 10.1088/0953-8984/28/30/305701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo-Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless (diffusion) modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmic divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near [Formula: see text].
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Affiliation(s)
- Andreas Sinner
- Institut für Physik, Universität Augsburg, D-86135 Augsburg, Germany
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15
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Zhang W, Wuttig M, Mazzarello R. Effects of stoichiometry on the transport properties of crystalline phase-change materials. Sci Rep 2015; 5:13496. [PMID: 26333869 PMCID: PMC4558572 DOI: 10.1038/srep13496] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2015] [Accepted: 07/21/2015] [Indexed: 11/17/2022] Open
Abstract
It has recently been shown that a metal-insulator transition due to disorder occurs in the crystalline state of the GeSb2Te4 phase-change compound. The transition is triggered by the ordering of the vacancies upon thermal annealing. In this work, we investigate the localization properties of the electronic states in selected crystalline (GeTe)x-(Sb2Te3)y compounds with varying GeTe content by large-scale density functional theory simulations. In our models, we also include excess vacancies, which are needed to account for the large carrier concentrations determined experimentally. We show that the models containing a high concentration of stoichiometric vacancies possess states at the Fermi energy localized inside vacancy clusters, as occurs for GeSb2Te4. On the other hand, the GeTe-rich models display metallic behavior, which stems from two facts: a) the tail of localized states shrinks due to the low probability of having sizable vacancy clusters, b) the excess vacancies shift the Fermi energy to the region of extended states. Hence, a stoichiometry-controlled metal-insulator transition occurs. In addition, we show that the localization properties obtained by scalar-relativistic calculations with gradient-corrected functionals are unaffected by the inclusion of spin-orbit coupling or the use of hybrid functionals.
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Affiliation(s)
- Wei Zhang
- Institute of Physics (IA), RWTH Aachen University, 52056 Aachen, Germany.,Institute for Theoretical Solid State Physics, RWTH Aachen University, 52056 Aachen, Germany
| | - Matthias Wuttig
- Institute of Physics (IA), RWTH Aachen University, 52056 Aachen, Germany.,JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
| | - Riccardo Mazzarello
- Institute for Theoretical Solid State Physics, RWTH Aachen University, 52056 Aachen, Germany.,JARA-FIT and JARA-HPC, RWTH Aachen University, 52056 Aachen, Germany
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16
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Zhao YX, Wang ZD. Disordered Weyl Semimetals and Their Topological Family. PHYSICAL REVIEW LETTERS 2015; 114:206602. [PMID: 26047246 DOI: 10.1103/physrevlett.114.206602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2014] [Indexed: 06/04/2023]
Abstract
We develop a topological theory for disordered Weyl semimetals in the framework of the gauge invariance of the replica formalism and boundary-bulk correspondence of Chern insulators. An anisotropic topological θ term is analytically derived for the effective nonlinear σ model. It is this nontrivial topological term that ensures that the bulk transverse transport of Weyl semimetals is robust against disorders. Moreover, we establish a general diagram that reveals the intrinsic relations among topological terms in the nonlinear σ models and gauge response theories, respectively, for (2n+2)-dimensional topological insulators, (2n+1)-dimensional chiral fermions, (2n+1)-dimensional chiral semimetals, and (2n)-dimensional topological insulators with n being a positive integer.
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Affiliation(s)
- Y X Zhao
- Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Z D Wang
- Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
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17
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Eichhorn A, Mesterházy D, Scherer MM. Multicritical behavior in models with two competing order parameters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042141. [PMID: 24229149 DOI: 10.1103/physreve.88.042141] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2013] [Indexed: 06/02/2023]
Abstract
We employ the nonperturbative functional renormalization group to study models with an O(N(1) ⊕O(N)(2)) symmetry. Here different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N(1),N(2) plane. We study the fate of nontrivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of noncanonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.
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Affiliation(s)
- Astrid Eichhorn
- Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, N2L 2Y5 Ontario, Canada
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18
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Vidal P, Kanzieper E. Integrability of zero-dimensional replica field theories at β=1. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:030101. [PMID: 24125199 DOI: 10.1103/physreve.88.030101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2013] [Indexed: 06/02/2023]
Abstract
Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica σ models derived in the context of real symmetric random matrices. Specifically, the fermionic and the bosonic replica partition functions are proven to form a single (supersymmetric) Pfaff-KP hierarchy whose replica limit is shown to reproduce the celebrated nonperturbative formula for the density-density eigenvalue correlation function in the infinite-dimensional Gaussian orthogonal ensemble. Implications of the formalism outlined are briefly discussed.
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Affiliation(s)
- Pedro Vidal
- Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 5810201, Israel and Fakultät für Physik, Universität Bielefeld, Bielefeld 33615, Germany
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19
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Kirkpatrick TR, Belitz D. Quantum phase transition in a clean two-dimensional electron system. PHYSICAL REVIEW LETTERS 2013; 110:035702. [PMID: 23373935 DOI: 10.1103/physrevlett.110.035702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2012] [Indexed: 06/01/2023]
Abstract
A quantum phase transition that was recently observed in a high-mobility silicon metal-oxide-semiconductor field-effect transistor is analyzed in terms of a scaling theory. The most striking characteristic of the transition is a divergence of the thermopower, according to an inverse linear law, as a critical value of the electron density is approached. A scaling description of this transition yields predictions about the critical behavior of other observables, e.g., the specific heat. We also explore the possibility that this transition realizes a recently predicted transition from a Fermi liquid to a non-Fermi-liquid state.
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Affiliation(s)
- T R Kirkpatrick
- Institute for Physical Science and Technology, and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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Fu L, Kane CL. Topology, delocalization via average symmetry and the symplectic Anderson transition. PHYSICAL REVIEW LETTERS 2012; 109:246605. [PMID: 23368359 DOI: 10.1103/physrevlett.109.246605] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2012] [Indexed: 06/01/2023]
Abstract
A field theory of the Anderson transition in two-dimensional disordered systems with spin-orbit interactions and time-reversal symmetry is developed, in which the proliferation of vortexlike topological defects is essential for localization. The sign of vortex fugacity determines the Z(2) topological class of the localized phase. There are two distinct fixed points with the same critical exponents, corresponding to transitions from a metal to an insulator and a topological insulator, respectively. The critical conductivity and correlation length exponent of these transitions are computed in an N=1-[symbol: see text] expansion in the number of replicas, where for small [symbol: see text] the critical points are perturbatively connected to the Kosterlitz-Thouless critical point. Delocalized states, which arise at the surface of weak topological insulators and topological crystalline insulators, occur because vortex proliferation is forbidden due to the presence of symmetries that are violated by disorder, but are restored by disorder averaging.
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Affiliation(s)
- Liang Fu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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21
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Zhang W, Thiess A, Zalden P, Zeller R, Dederichs PH, Raty JY, Wuttig M, Blügel S, Mazzarello R. Role of vacancies in metal-insulator transitions of crystalline phase-change materials. NATURE MATERIALS 2012; 11:952-6. [PMID: 23064498 DOI: 10.1038/nmat3456] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2012] [Accepted: 09/10/2012] [Indexed: 05/09/2023]
Abstract
The study of metal-insulator transitions (MITs) in crystalline solids is a subject of paramount importance, both from the fundamental point of view and for its relevance to the transport properties of materials. Recently, a MIT governed by disorder was observed in crystalline phase-change materials. Here we report on calculations employing density functional theory, which identify the microscopic mechanism that localizes the wavefunctions and is driving this transition. We show that, in the insulating phase, the electronic states responsible for charge transport are localized inside regions having large vacancy concentrations. The transition to the metallic state is driven by the dissolution of these vacancy clusters and the formation of ordered vacancy layers. These results provide important insights on controlling the wavefunction localization, which should help to develop conceptually new devices based on multiple resistance states.
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Affiliation(s)
- W Zhang
- Institut für Theoretische Festkörperphysik, RWTH Aachen University, D-52056 Aachen, Germany
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22
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Johri S, Bhatt RN. Singular behavior of eigenstates in Anderson's model of localization. PHYSICAL REVIEW LETTERS 2012; 109:076402. [PMID: 23006388 DOI: 10.1103/physrevlett.109.076402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2012] [Indexed: 06/01/2023]
Abstract
We observe an apparent singularity in the electronic properties of the Anderson model of localization with bounded diagonal disorder, which is clearly distinct from the well-established mobility edge (localization-delocalization transition) that occurs in dimensions d > 2. We present results of numerical calculations for Anderson's original uniform (box) distribution of on-site disorder in dimensions d = 1, 2, and 3. To establish this hitherto unreported behavior, and to understand its evolution with disorder, we contrast the behavior of two different measures of the localization length of the electronic wave functions-the averaged inverse participation ratio and the Lyapunov exponent. Our data suggest that Anderson's model exhibits richer behavior than has been established so far.
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Affiliation(s)
- S Johri
- Department of Electrical Engineering, Princeton University, New Jersey 08544, USA
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23
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Kirkpatrick TR, Belitz D. Theory of a Fermi-liquid to non-Fermi-liquid quantum phase transition in dimensions d>1. PHYSICAL REVIEW LETTERS 2012; 108:086404. [PMID: 22463549 DOI: 10.1103/physrevlett.108.086404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2011] [Indexed: 05/31/2023]
Abstract
We develop a theory for a generic instability of a Fermi liquid in dimension d>1 against the formation of a Luttinger-liquid-like state. The density of states at the Fermi level is the order parameter for the ensuing quantum phase transition, which is driven by the effective interaction strength. A scaling theory in conjunction with an effective field theory for clean electrons is used to obtain the critical behavior of observables. In the Fermi-liquid phase the order-parameter susceptibility, which is measurable by tunneling, is predicted to diverge for 1<d<3.
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Affiliation(s)
- T R Kirkpatrick
- Institute for Physical Science and Technology and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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24
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Kirkpatrick TR, Belitz D. Nature of the quantum phase transition to a spin-nematic phase. PHYSICAL REVIEW LETTERS 2011; 106:105701. [PMID: 21469808 DOI: 10.1103/physrevlett.106.105701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2011] [Revised: 02/01/2011] [Indexed: 05/30/2023]
Abstract
It is shown that the quantum phase transition in metallic non-s-wave ferromagnets, or spin nematics, is generically of first order. This is due to a coupling of the order parameter to soft electronic modes that play a role analogous to that of the electromagnetic vector potential in a superconductor, which leads to a fluctuation-induced first-order transition. A generalized mean-field theory for the p-wave case is constructed that explicitly shows this effect. Tricritical wings are predicted to appear in the phase diagram in a spatially varying magnetic field, but not in a homogeneous one.
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Affiliation(s)
- T R Kirkpatrick
- Institute for Physical Science and Technology and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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25
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26
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Osipov VA, Kanzieper E. Are bosonic replicas faulty? PHYSICAL REVIEW LETTERS 2007; 99:050602. [PMID: 17930738 DOI: 10.1103/physrevlett.99.050602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2007] [Indexed: 05/25/2023]
Abstract
Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to both fermionic and bosonic zero-dimensional replica field theories belonging to the broadly interpreted beta=2 Dyson symmetry class. We then utilize the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD-inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.
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Affiliation(s)
- Vladimir Al Osipov
- Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 58102, Israel.
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27
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Kaveh M. Effect of electron-electron interactions on critical exponents near the metal-insulator transition. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/13642818508243155] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- M. Kaveh
- a Department of Physics , Bar-Ilan University , Ramat-Gan , Israel
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28
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Affiliation(s)
- M. Kaveh
- a Department of Physics , Bar-Ilan University , Ramat-Gan , Israel
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29
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Affiliation(s)
- G. A. Thomas
- a AT&T Bell Laboratories , Murray Hill , New Jersey , 07974 , U.S.A
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30
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Affiliation(s)
- W. Götze
- a H. C. Ørsted Institute, University of Copenhagen , Copenhagen , Denmark
- b Physik-Department der Technischen Universität , D-8046 Garching and Max-Planck-Institut für Physik und Astrophysik, D-8000 , München , F. R. , Germany
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31
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Belitz D, Götze W. The temperature dependence of the d.c. conductivity near the Anderson transition in three-dimensional systems. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/01418638108222113] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- D. Belitz
- a Physik-Department der Technischen , Universität München , D-8046, Garching , F.R. , Germany
- b Max-Planck-Institut für Physik , D-8000, München, Föhringer Ring , F.R. , Germany
| | - W. Götze
- a Physik-Department der Technischen , Universität München , D-8046, Garching , F.R. , Germany
- b Max-Planck-Institut für Physik , D-8000, München, Föhringer Ring , F.R. , Germany
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32
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Affiliation(s)
- B. Movaghar
- a Queen Mary and Westfield College, Physics Department , University of London , Mile End Road, London , E4 1NS , England
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33
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Affiliation(s)
- N. F. Mott
- a Cavendish Laboratory , Madingley Road, Cambridge , CB3 0HE , England
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34
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Punnoose A, Finkel'stein AM. Spin relaxation in the presence of electron-electron interactions. PHYSICAL REVIEW LETTERS 2006; 96:057202. [PMID: 16486973 DOI: 10.1103/physrevlett.96.057202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2005] [Indexed: 05/06/2023]
Abstract
The D'yakonov-Perel' spin relaxation induced by the spin-orbit interaction is examined in disordered two-dimensional electron gas. It is shown that, because of the electron-electron interactions, substantially different spin relaxation rates may be observed depending on the technique used to extract them. It is demonstrated that the relaxation rate of a spin population is proportional to the spin-diffusion constant D(s), while the spin-orbit scattering rate controlling the weak-localization corrections is proportional to the diffusion constant D, i.e., the conductivity. The two diffusion constants get strongly renormalized by the electron-electron interactions, but in different ways. As a result, the corresponding relaxation rates are different, with the difference between the two being especially strong near a magnetic instability or near the metal-insulator transition.
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35
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Fyodorov YV, Savin DV, Sommers HJ. Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/0305-4470/38/49/017] [Citation(s) in RCA: 130] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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36
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Altland A, Kamenev A, Tian C. Anderson localization from the replica formalism. PHYSICAL REVIEW LETTERS 2005; 95:206601. [PMID: 16384077 DOI: 10.1103/physrevlett.95.206601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2005] [Indexed: 05/05/2023]
Abstract
We study Anderson localization in quasi-one-dimensional disordered wires within the framework of the replica sigma model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons, and Zirnbauer, we compute the exact density of transmission matrix eigenvalues of superconducting wires (of symmetry class CI.) For the unitary class of metallic systems (class A) we are able to obtain the density function, save for its large transmission tail.
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Affiliation(s)
- Alexander Altland
- Institut für Theoretische Physik, Universtät zu Köln, Köln, 50937, Germany
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37
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Müller S, Heusler S, Braun P, Haake F, Altland A. Periodic-orbit theory of universality in quantum chaos. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:046207. [PMID: 16383512 DOI: 10.1103/physreve.72.046207] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2005] [Indexed: 05/05/2023]
Abstract
We argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from all three Wigner-Dyson symmetry classes, we calculate the small-time spectral form factor K(tau) as power series in the time tau. Each term tau(n) of that series is provided by specific families of pairs of periodic orbits. The contributing pairs are classified in terms of close self-encounters in phase space. The frequency of occurrence of self-encounters is calculated by invoking ergodicity. Combinatorial rules for building pairs involve nontrivial properties of permutations. We show our series to be equivalent to perturbative implementations of the nonlinear sigma models for the Wigner-Dyson ensembles of random matrices and for disordered systems; our families of orbit pairs have a one-to-one relationship with Feynman diagrams known from the sigma model.
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Affiliation(s)
- Sebastian Müller
- Fachbereich Physik, Universität Duisburg-Essen, 45117 Essen, Germany
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38
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Phillips P, Chamon C. Breakdown of one-parameter scaling in quantum critical scenarios for high-temperature copper-oxide superconductors. PHYSICAL REVIEW LETTERS 2005; 95:107002. [PMID: 16196953 DOI: 10.1103/physrevlett.95.107002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2004] [Indexed: 05/04/2023]
Abstract
We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent z satisfies the unphysical constraint, z < 0. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single-correlation length scale is necessary to model transport in the cuprates.
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Affiliation(s)
- Philip Phillips
- Loomis Laboratory of Physics, University of Illinois at Urbana-Champaign, 61801-3080, USA
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39
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Comtet A, Desbois J, Texier C. Functionals of Brownian motion, localization and metric graphs. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/0305-4470/38/37/r01] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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40
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Shahbazi F, Bahraminasab A, Allaei SMV, Sahimi M, Tabar MRR. Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations. PHYSICAL REVIEW LETTERS 2005; 94:165505. [PMID: 15904243 DOI: 10.1103/physrevlett.94.165505] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2004] [Indexed: 05/02/2023]
Abstract
Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with nondecaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in any dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.
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Affiliation(s)
- F Shahbazi
- Department of Physics, Isfahan University of Technology, Isfahan 84156, Iran
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41
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Yudson VI. Field theory for the global density of states distribution function of disordered conductors. PHYSICAL REVIEW LETTERS 2005; 94:156601. [PMID: 15904171 DOI: 10.1103/physrevlett.94.156601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2004] [Indexed: 05/02/2023]
Abstract
A field-theoretical representation is suggested for the electron global density of states distribution function P(nu) in extended disordered conductors. This opens a way to study the complete statistics of fluctuations. The approach is based on a functional integration over bilocal functions Psir(1)(r(2)) instead of the integration over local functions in the usual functional representation for moments of physical quantities. The formalism allows one to perform the disorder averaging and to derive an analog of the usual nonlinear sigma model-a slow functional of a supermatrix field Qr(1)(r(2))(r) approximately Psi(rr(1)) composite functionPsi (r(2)r). As an application of the formalism, the long-tail asymptotics of P(nu) is derived.
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Affiliation(s)
- V I Yudson
- Institute for Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, 142190 Russia
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42
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Efetov KB, Schwiete G, Takahashi K. Bosonization for disordered and chaotic systems. PHYSICAL REVIEW LETTERS 2004; 92:026807. [PMID: 14753957 DOI: 10.1103/physrevlett.92.026807] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2003] [Indexed: 05/24/2023]
Abstract
Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems can be derived from our exact model using a coarse-graining procedure. As an example, we consider a model for a smooth disorder and demonstrate that using our approach does not lead to a "mode-locking" problem. As a new application, we consider scattering on strong impurities for which the Born approximation cannot be used. Our method provides a new calculational scheme for disordered and chaotic systems.
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Affiliation(s)
- K B Efetov
- Theoretische Physik III, Ruhr-Universität Bochum, 44780 Bochum, Germany
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43
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Kettemann S, Raikh ME. Localization length in anderson insulator with Kondo impurities. PHYSICAL REVIEW LETTERS 2003; 90:146601. [PMID: 12731935 DOI: 10.1103/physrevlett.90.146601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2002] [Indexed: 05/24/2023]
Abstract
The localization length, xi, in a two-dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, tau(-1)(s). For antiferromagnetic sign of the exchange, the time tau(s) is itself a function of xi, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, n(M), is smaller than a critical value, n(c). For n(M)>n(c), the dependence of xi on the dimensionless conductance, g, is reentrant, crossing over to unitary, and back to orthogonal behavior upon increasing g. Sensitivity of Kondo correlations to a weak parallel magnetic field results in a giant parallel magnetoresistance.
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Affiliation(s)
- S Kettemann
- I. Institut für Theoretische Physik, Universität Hamburg, Hamburg 20355, Germany
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44
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Evangelou SN, Katsanos DE. Spectral statistics in chiral-orthogonal disordered systems. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/12/322] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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45
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Kanzieper E. Replica field theories, painlevé transcendents, and exact correlation functions. PHYSICAL REVIEW LETTERS 2002; 89:250201. [PMID: 12484867 DOI: 10.1103/physrevlett.89.250201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2002] [Indexed: 05/24/2023]
Abstract
Exact solvability is claimed for nonlinear replica sigma models derived in the context of random matrix theories. Contrary to other approaches reported in the literature, the framework outlined does not rely on traditional "replica symmetry breaking" but rests on a previously unnoticed exact relation between replica partition functions and Painlevé transcendents. While expected to be applicable to matrix models of arbitrary symmetries, the method is used to treat fermionic replicas for the Gaussian unitary ensemble (GUE), chiral GUE (symmetry classes A and AIII in Cartan classification) and Ginibre's ensemble of complex non-Hermitian random matrices. Further applications are briefly discussed.
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Affiliation(s)
- Eugene Kanzieper
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
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46
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Mohanty P, Webb RA. Anomalous conductance distribution in quasi-one-dimensional gold wires: possible violation of the one-parameter scaling hypothesis. PHYSICAL REVIEW LETTERS 2002; 88:146601. [PMID: 11955164 DOI: 10.1103/physrevlett.88.146601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2001] [Indexed: 05/23/2023]
Abstract
We report measurements of conductance distribution in a set of quasi-one-dimensional gold wires. The distribution includes the second cumulant or the variance which describes the universal conductance fluctuations, and the third cumulant which denotes the leading deviation. We have observed an asymmetric contribution--or, a nonvanishing third cumulant--contrary to the expectation for quasi-one-dimensional systems in the noninteracting theories in the one-parameter scaling framework, which include the perturbative diagrammatic calculations and the random matrix theory.
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Affiliation(s)
- Pritiraj Mohanty
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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47
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48
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Denteneer PJ, Scalettar RT, Trivedi N. Particle-hole symmetry and the effect of disorder on the Mott-Hubbard insulator. PHYSICAL REVIEW LETTERS 2001; 87:146401. [PMID: 11580663 DOI: 10.1103/physrevlett.87.146401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2001] [Indexed: 05/23/2023]
Abstract
The understanding of the interplay of electron correlations and randomness in solids is enhanced by demonstrating that particle-hole ( p-h) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when p-h symmetry is preserved, and shows the opposite behavior, i.e., conductivity increases with increasing disorder, when p-h symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is p-h symmetry, whereas in its absence the gap diminishes with increasing disorder.
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Affiliation(s)
- P J Denteneer
- Lorentz Institute, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
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49
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Altland A, Kamenev A. Wigner-Dyson statistics from the Keldysh sigma-model. PHYSICAL REVIEW LETTERS 2000; 85:5615-5618. [PMID: 11136060 DOI: 10.1103/physrevlett.85.5615] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2000] [Indexed: 05/23/2023]
Abstract
The level statistics of disordered metallic grains with broken time reversal invariance is obtained from the Keldysh nonlinear sigma-model. The basic strategy of the approach--a nonperturbative integration over all saddle points of the sigma-model manifold--might prove useful in the analysis of problems involving disorder and interactions.
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Affiliation(s)
- A Altland
- Theoretische Physik III, Ruhr-Universität Bochum, 44780, Germany
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50
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