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Abstract
The simplest possible structural transition that an electronic system can undergo is Wigner crystallization. The aim of this short review is to discuss the main aspects of three recent experimets on the one-dimensional Wigner molecule, starting from scratch. To achieve this task, the Luttinger liquid theory of weakly and strongly interacting fermions is briefly addressed, together with the basic properties of carbon nanotubes that are required. Then, the most relevant properties of Wigner molecules are addressed, and finally the experiments are described. The main physical points that are addressed are the suppression of the energy scales related to the spin and isospin sectors of the Hamiltonian, and the peculiar structure that the electron density acquires in the Wigner molecule regime.
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Porta S, Cavaliere F, Sassetti M, Traverso Ziani N. Topological classification of dynamical quantum phase transitions in the xy chain. Sci Rep 2020; 10:12766. [PMID: 32728056 PMCID: PMC7391734 DOI: 10.1038/s41598-020-69621-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2019] [Accepted: 05/26/2020] [Indexed: 11/23/2022] Open
Abstract
Understanding the properties of far-from-equilibrium quantum systems is becoming a major challenge of both fundamental and applied physics. For instance, the lack of thermalization in integrable and (many body) localized systems provides new insights in the understanding of the relaxation dynamics of quantum phases. On a more applicative side, the possibility of exploiting the properties of far-from-equilibrium states, for example in pump-probe experiments, opens unprecedented scenarios. The effort in providing a classification of far-from-equilibrium phases, in terms of local or topological order parameters, is hence intense. In this context, the concept of Dynamical Quantum Phase Transition (DQPT) has been introduced. A DQPT is (roughly) defined as a zero of the Loschmidt-Echo as a function of time and represents a natural non-equilibrium counterpart of a thermal phase transition. Here, we investigate the DQPTs occurring in the quantum xy chain subject to a quantum quench of finite duration. We show that the number of distinct DQPTs can vary as the duration of the quantum quench is varied. However, the parity of such number only depends on the pre-quench and post-quench Hamiltonians and is related to a topological invariant.
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Affiliation(s)
- Sergio Porta
- Dipartimento di Fisica, Università di Genova, 16146, Genova, Italy.,SPIN-CNR, 16146, Genova, Italy
| | - Fabio Cavaliere
- Dipartimento di Fisica, Università di Genova, 16146, Genova, Italy.,SPIN-CNR, 16146, Genova, Italy
| | - Maura Sassetti
- Dipartimento di Fisica, Università di Genova, 16146, Genova, Italy.,SPIN-CNR, 16146, Genova, Italy
| | - Niccolò Traverso Ziani
- Dipartimento di Fisica, Università di Genova, 16146, Genova, Italy. .,SPIN-CNR, 16146, Genova, Italy.
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Dóra B, Moca CP. Quantum Quench in PT-Symmetric Luttinger Liquid. PHYSICAL REVIEW LETTERS 2020; 124:136802. [PMID: 32302175 DOI: 10.1103/physrevlett.124.136802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 03/11/2020] [Indexed: 06/11/2023]
Abstract
A Luttinger liquid (LL) describes low energy excitations of many interacting one dimensional systems, and exhibits universal response both in and out of equilibrium. We analyze its behavior in the non-Hermitian realm after quantum quenching to a PT-symmetric LL by focusing on the fermionic single particle density matrix. For short times, we demonstrate the emergence of unique phenomena, characteristic to non-Hermitian systems, that correlations propagate faster than the conventional maximal speed, known as the Lieb-Robinson bound. These emergent supersonic modes travel with velocities that are multiples of the conventional light cone velocity. This behavior is argued to be generic for correlators in non-Hermitian systems. In the long time limit, we find typical LL behavior, extending the LL universality to the nonequilibrium, non-Hermitian case. Our analytical results are benchmarked numerically and indicate that the dispersal of quantum information is much faster in non-Hermitian systems.
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Affiliation(s)
- Balázs Dóra
- Department of Theoretical Physics and MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
| | - Cătălin Paşcu Moca
- MTA-BME Quantum Dynamics and Correlations Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary
- Department of Physics, University of Oradea, 410087 Oradea, Romania
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Bastianello A, Alba V, Caux JS. Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions. PHYSICAL REVIEW LETTERS 2019; 123:130602. [PMID: 31697554 DOI: 10.1103/physrevlett.123.130602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Indexed: 06/10/2023]
Abstract
We provide a new hydrodynamic framework to describe out-of-equilibrium integrable systems with space-time inhomogeneous interactions. Our result builds up on the recently introduced generalized hydrodynamics (GHD). The method allows us to analytically describe the dynamics during generic space-time-dependent smooth modulations of the interactions. As a proof of concept, we study experimentally motivated interaction quenches in the trapped interacting Bose gas, which cannot be treated with current analytical or numerical methods. We also benchmark our results in the XXZ spin chain and in the classical sinh-Gordon model.
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Affiliation(s)
- Alvise Bastianello
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Vincenzo Alba
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Jean-Sébastien Caux
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
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Bernier JS, Citro R, Kollath C, Orignac E. Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas. PHYSICAL REVIEW LETTERS 2014; 112:065301. [PMID: 24580691 DOI: 10.1103/physrevlett.112.065301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2013] [Indexed: 06/03/2023]
Abstract
We investigate the response of a one-dimensional Bose gas to a slow increase of its interaction strength. We focus on the rich dynamics of equal-time single-particle correlations treating the Lieb-Liniger model within a bosonization approach and the Bose-Hubbard model using the time-dependent density-matrix renormalization group method. For short distances, correlations follow a power law with distance with an exponent given by the adiabatic approximation. In contrast, for long distances, correlations decay algebraically with an exponent understood within the sudden quench approximation. This long distance regime is separated from an intermediate distance one by a generalized Lieb-Robinson criterion. At long times, in this intermediate regime, bosonization predicts that single-particle correlations decay following a stretched exponential, an unconventional behavior. We develop here an intuitive understanding for the propagation of correlations, in terms of a generalized light cone, applicable to a large variety of systems and quench forms.
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Affiliation(s)
- Jean-Sébastien Bernier
- Department of Physics and Astronomy, University of British Columbia, Vancouver V6T 1Z1, Canada
| | - Roberta Citro
- Dipartimento di Fisica "E. R. Caianiello" and CNR-SPIN, Università degli Studi di Salerno, I-84084 Fisciano, Italy
| | - Corinna Kollath
- HISKP, University of Bonn, Nussallee 14-16, D-53115 Bonn, Germany
| | - Edmond Orignac
- Laboratoire de Physique de l'École Normale Supérieure de Lyon, CNRS UMR5672, 46 Allée d'Italie, F-69364 Lyon Cedex 7, France
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Otterbach J, Moos M, Muth D, Fleischhauer M. Wigner crystallization of single photons in cold Rydberg ensembles. PHYSICAL REVIEW LETTERS 2013; 111:113001. [PMID: 24074081 DOI: 10.1103/physrevlett.111.113001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2013] [Revised: 07/16/2013] [Indexed: 06/02/2023]
Abstract
The coupling of weak light fields to Rydberg states of atoms under conditions of electromagnetically induced transparency leads to the formation of Rydberg polaritons which are quasiparticles with tunable effective mass and nonlocal interactions. Confined to one spatial dimension their low energy physics is that of a moving-frame Luttinger liquid which, due to the nonlocal character of the repulsive interaction, can form a Wigner crystal of individual photons. We calculate the Luttinger K parameter using density-matrix renormalization group simulations and find that under typical slow-light conditions kinetic energy contributions are too strong for crystal formation. However, adiabatically increasing the polariton mass by turning a light pulse into stationary spin excitations allows us to generate true crystalline order over a finite length. The dynamics of this process and asymptotic correlations are analyzed in terms of a time-dependent Luttinger theory.
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Affiliation(s)
- Johannes Otterbach
- Physics Department, Harvard University, Cambridge, 02138 Massachusetts, USA
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Wang P, Xianlong G, Li H. Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022113. [PMID: 24032781 DOI: 10.1103/physreve.88.022113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2013] [Revised: 06/21/2013] [Indexed: 06/02/2023]
Abstract
It is demonstrated in many thermodynamic textbooks that the equivalence of the different ensembles is achieved in the thermodynamic limit. In this present work we discuss the inequivalence of microcanonical and canonical ensembles in a finite ultracold system at low energies. We calculate the microcanonical momentum distribution function (MDF) in a system of identical fermions (bosons). We find that the microcanonical MDF deviates from the canonical one, which is the Fermi-Dirac (Bose-Einstein) function, in a finite system at low energies where the single-particle density of states and its inverse are finite.
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Affiliation(s)
- Pei Wang
- Institute of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
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Mitra A. Time evolution and dynamical phase transitions at a critical time in a system of one-dimensional bosons after a quantum quench. PHYSICAL REVIEW LETTERS 2012; 109:260601. [PMID: 23368544 DOI: 10.1103/physrevlett.109.260601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2012] [Revised: 09/30/2012] [Indexed: 06/01/2023]
Abstract
A renormalization group approach is used to show that a one-dimensional system of bosons subject to a lattice quench exhibits a finite-time dynamical phase transition where an order parameter within a light cone increases as a nonanalytic function of time after a critical time. Such a transition is also found for a simultaneous lattice and interaction quench where the effective scaling dimension of the lattice becomes time dependent, crucially affecting the time evolution of the system. Explicit results are presented for the time evolution of the boson interaction parameter and the order parameter for the dynamical transition as well as for more general quenches.
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Affiliation(s)
- Aditi Mitra
- Department of Physics, New York University, 4 Washington Place, New York, New York 10003, USA
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Karrasch C, Rentrop J, Schuricht D, Meden V. Luttinger-liquid universality in the time evolution after an interaction quench. PHYSICAL REVIEW LETTERS 2012; 109:126406. [PMID: 23005968 DOI: 10.1103/physrevlett.109.126406] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2012] [Indexed: 06/01/2023]
Abstract
We provide evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: the leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our hypothesis of universality by considering spinless lattice fermions within the framework of the density-matrix renormalization group.
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Affiliation(s)
- C Karrasch
- Department of Physics, University of California, Berkeley, 95720, USA
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