1
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Bernaschi M, González-Adalid Pemartín I, Martín-Mayor V, Parisi G. The quantum transition of the two-dimensional Ising spin glass. Nature 2024; 631:749-754. [PMID: 38987607 PMCID: PMC11269196 DOI: 10.1038/s41586-024-07647-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 06/03/2024] [Indexed: 07/12/2024]
Abstract
Quantum annealers are commercial devices that aim to solve very hard computational problems1, typically those involving spin glasses2,3. Just as in metallurgic annealing, in which a ferrous metal is slowly cooled4, quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. Removing the field diminishes the quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, compared to classical computers, rest on the assumption that the gap will close algebraically with the number of spins5-9. However, renormalization group calculations predict instead that there is an infinite-randomness fixed point10. Here we solve this debate through extreme-scale numerical simulations, finding that both parties have grasped parts of the truth. Although the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. As this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the quantum annealing paradigm11-13.
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Affiliation(s)
| | | | - Víctor Martín-Mayor
- Departamento de Física Teórica, Universidad Complutense de Madrid, Madrid, Spain
| | - Giorgio Parisi
- Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy
- Nanotec-Rome unit, CNR, Rome, Italy
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2
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King AD, Raymond J, Lanting T, Harris R, Zucca A, Altomare F, Berkley AJ, Boothby K, Ejtemaee S, Enderud C, Hoskinson E, Huang S, Ladizinsky E, MacDonald AJR, Marsden G, Molavi R, Oh T, Poulin-Lamarre G, Reis M, Rich C, Sato Y, Tsai N, Volkmann M, Whittaker JD, Yao J, Sandvik AW, Amin MH. Quantum critical dynamics in a 5,000-qubit programmable spin glass. Nature 2023; 617:61-66. [PMID: 37076625 DOI: 10.1038/s41586-023-05867-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 02/20/2023] [Indexed: 04/21/2023]
Abstract
Experiments on disordered alloys1-3 suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Owing to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization4-13. Here we achieve this goal by realizing quantum-critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and time evolution of the Schrödinger equation in small spin glasses. We then measure dynamics in three-dimensional spin glasses on thousands of qubits, for which classical simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for large-scale quantum simulation and a scaling advantage in energy optimization.
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Affiliation(s)
- Andrew D King
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada.
| | - Jack Raymond
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | | | - Alex Zucca
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | | | - Kelly Boothby
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Sara Ejtemaee
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Colin Enderud
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | | | | | | | | | - Reza Molavi
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Travis Oh
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | - Mauricio Reis
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Chris Rich
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Yuki Sato
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Nicholas Tsai
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Mark Volkmann
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | - Jason Yao
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | - Mohammad H Amin
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada.
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada.
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3
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Sinha A. Development of research network on Quantum Annealing Computation and Information using Google Scholar data. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210413. [PMID: 36463919 DOI: 10.1098/rsta.2021.0413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2022] [Accepted: 09/08/2022] [Indexed: 06/17/2023]
Abstract
We build and analyse the network of 100 top-cited nodes (research papers and books from Google Scholar; the strength or citation of the nodes range from about 44 000 up to 100) starting in early 1980 until last year. These searched publications (papers and books) are based on Quantum Annealing Computation and Information categorized into four different sets: (A) Quantum/Transverse Field Spin Glass Model, (B) Quantum Annealing, (C) Quantum Adiabatic Computation and (D) Quantum Computation Information in the title or abstract of the searched publications. We fitted the growth in the annual number of publication ([Formula: see text]) in each of these four categories, A-D, to the form [Formula: see text] where [Formula: see text] denotes the time in years. We found the scaling time [Formula: see text] to be of the order of about 10 years for categories A and C, whereas [Formula: see text] is of the order of about 5 years for categories B and D. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Antika Sinha
- Department of Computer Science, Asutosh College, Kolkata, West Bengal 700026, India
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4
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Mukherjee S. Role of quantum fluctuation in inducing ergodicity in the spin glass phase and its effect in quantum annealing. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210406. [PMID: 36463924 DOI: 10.1098/rsta.2021.0406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 09/30/2022] [Indexed: 06/17/2023]
Abstract
We review the numerical studies on the critical behaviour of the quantum Sherrington-Kirkpatrick (SK) spin glass model, which indicate that a quantum critical behaviour is observed up to a low but non-zero value of temperature. We revisit the numerical investigations on the spin glass order parameter distributions, which identify a low temperature along with high transverse field spin glass phase where the order parameter distribution becomes a delta function in the thermodynamic limit indicating the restoration of replica symmetry and ergodic nature of the system. In the remaining spin glass phase associated with high temperature and low transverse field, the observed distribution is broad akin to the Parisi order parameter distribution. This essentially indicates the non-ergodic behaviour of the system. We further discuss the annealing dynamics studies on the quantum SK model. Such investigations reveal the system size independence of annealing time when the annealing paths go through the ergodic spin glass region. Interestingly, when such dynamics are performed in the non-ergodic spin glass phase the annealing time becomes an increasing function of the system size. Spin autocorrelation shows faster relaxation in the ergodic spin glass region compared with that found in the non-ergodic spin glass region. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Sudip Mukherjee
- Department of Physics, Barasat Government College, Kolkata 700124, India
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5
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Rajak A, Suzuki S, Dutta A, Chakrabarti BK. Quantum annealing: an overview. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210417. [PMID: 36463923 DOI: 10.1098/rsta.2021.0417] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 08/22/2022] [Indexed: 06/17/2023]
Abstract
In this review, after providing the basic physical concept behind quantum annealing (or adiabatic quantum computation), we present an overview of some recent theoretical as well as experimental developments pointing to the issues which are still debated. With a brief discussion on the fundamental ideas of continuous and discontinuous quantum phase transitions, we discuss the Kibble-Zurek scaling of defect generation following a ramping of a quantum many body system across a quantum critical point. In the process, we discuss associated models, both pure and disordered, and shed light on implementations and some recent applications of the quantum annealing protocols. Furthermore, we discuss the effect of environmental coupling on quantum annealing. Some possible ways to speed up the annealing protocol in closed systems are elaborated upon: we especially focus on the recipes to avoid discontinuous quantum phase transitions occurring in some models where energy gaps vanish exponentially with the system size. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Atanu Rajak
- Department of Physics, Presidency University, Kolkata 700073, India
| | - Sei Suzuki
- Department of Liberal Arts, Saitama Medical University, Moroyama, Saitama 350-0495, Japan
| | - Amit Dutta
- Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Bikas K Chakrabarti
- Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
- Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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6
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Agrawal U, Gopalakrishnan S, Vasseur R. Quantum Criticality in the 2D Quasiperiodic Potts Model. PHYSICAL REVIEW LETTERS 2020; 125:265702. [PMID: 33449710 DOI: 10.1103/physrevlett.125.265702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2020] [Accepted: 11/19/2020] [Indexed: 06/12/2023]
Abstract
Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic q-state Potts model in 2+1D. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of q, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be ν=1, saturating a modified version of the Harris-Luck criterion.
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Affiliation(s)
- Utkarsh Agrawal
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Sarang Gopalakrishnan
- Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314; Physics Program and Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10016, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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7
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Puschmann M, Crewse J, Hoyos JA, Vojta T. Collective Modes at a Disordered Quantum Phase Transition. PHYSICAL REVIEW LETTERS 2020; 125:027002. [PMID: 32701338 DOI: 10.1103/physrevlett.125.027002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 06/23/2020] [Indexed: 06/11/2023]
Abstract
We study the collective excitations, i.e., the Goldstone (phase) mode and the Higgs (amplitude) mode, near the superfluid-Mott glass quantum phase transition in a two-dimensional system of disordered bosons. Using Monte Carlo simulations as well as an inhomogeneous quantum mean-field theory with Gaussian fluctuations, we show that the Higgs mode is strongly localized for all energies, leading to a noncritical scalar response. In contrast, the lowest-energy Goldstone mode undergoes a striking delocalization transition as the system enters the superfluid phase. We discuss the generality of these findings and experimental consequences, and we point out potential relations to many-body localization.
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Affiliation(s)
- Martin Puschmann
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - Jack Crewse
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
| | - José A Hoyos
- Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos, São Paulo 13560-970, Brazil
| | - Thomas Vojta
- Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
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8
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Thompson F, Singh RRP. Griffiths-McCoy singularities in the dilute transverse-field Ising model: A numerical linked cluster expansion study. Phys Rev E 2019; 99:032129. [PMID: 30999511 DOI: 10.1103/physreve.99.032129] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Indexed: 11/07/2022]
Abstract
We use numerical linked cluster expansions (NLCEs) to study the site-diluted transverse-field Ising model on the square lattice at T=0. NLCE with a self-consistent mean field on the boundary of the clusters is used to obtain the ground-state magnetization, susceptibility, and structure factor as a function of transverse field h and exchange constant J. Adding site dilution to the model turns NLCE into a series expansion in the dilution parameter p. Studying the divergence of the structure factor allows us to establish the phase diagram in the h/J and p plane. By studying the magnetization of the system in a longitudinal field, we investigate the Griffiths-McCoy singularities. We find that the magnetization develops nonlinearities in the Griffiths phase with exponents that vary continuously with h. Additionally, the probability distribution of the local susceptibility develops long tails in the Griffiths phase, which is studied in terms of its moments.
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Affiliation(s)
- Foster Thompson
- Department of Physics, Case Western Reserve University, Ohio 44106, USA
| | - Rajiv R P Singh
- Department of Physics, University of California Davis, California 95616, USA
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9
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Harris R, Sato Y, Berkley AJ, Reis M, Altomare F, Amin MH, Boothby K, Bunyk P, Deng C, Enderud C, Huang S, Hoskinson E, Johnson MW, Ladizinsky E, Ladizinsky N, Lanting T, Li R, Medina T, Molavi R, Neufeld R, Oh T, Pavlov I, Perminov I, Poulin-Lamarre G, Rich C, Smirnov A, Swenson L, Tsai N, Volkmann M, Whittaker J, Yao J. Phase transitions in a programmable quantum spin glass simulator. Science 2018; 361:162-165. [PMID: 30002250 DOI: 10.1126/science.aat2025] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2018] [Accepted: 05/15/2018] [Indexed: 11/02/2022]
Abstract
Understanding magnetic phases in quantum mechanical systems is one of the essential goals in condensed matter physics, and the advent of prototype quantum simulation hardware has provided new tools for experimentally probing such systems. We report on the experimental realization of a quantum simulation of interacting Ising spins on three-dimensional cubic lattices up to dimensions 8 × 8 × 8 on a D-Wave processor (D-Wave Systems, Burnaby, Canada). The ability to control and read out the state of individual spins provides direct access to several order parameters, which we used to determine the lattice's magnetic phases as well as critical disorder and one of its universal exponents. By tuning the degree of disorder and effective transverse magnetic field, we observed phase transitions between a paramagnetic, an antiferromagnetic, and a spin-glass phase.
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Affiliation(s)
- R Harris
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada.
| | - Y Sato
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - A J Berkley
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - M Reis
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - F Altomare
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - M H Amin
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada.,Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
| | - K Boothby
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - P Bunyk
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - C Deng
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - C Enderud
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - S Huang
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - E Hoskinson
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - M W Johnson
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - E Ladizinsky
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - N Ladizinsky
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - T Lanting
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - R Li
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - T Medina
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - R Molavi
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada.,Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
| | - R Neufeld
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - T Oh
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - I Pavlov
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - I Perminov
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | | | - C Rich
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - A Smirnov
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - L Swenson
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - N Tsai
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - M Volkmann
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - J Whittaker
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
| | - J Yao
- D-Wave Systems, 3033 Beta Avenue, Burnaby, BC V5G 4M9, Canada
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10
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King AD, Carrasquilla J, Raymond J, Ozfidan I, Andriyash E, Berkley A, Reis M, Lanting T, Harris R, Altomare F, Boothby K, Bunyk PI, Enderud C, Fréchette A, Hoskinson E, Ladizinsky N, Oh T, Poulin-Lamarre G, Rich C, Sato Y, Smirnov AY, Swenson LJ, Volkmann MH, Whittaker J, Yao J, Ladizinsky E, Johnson MW, Hilton J, Amin MH. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 2018; 560:456-460. [DOI: 10.1038/s41586-018-0410-x] [Citation(s) in RCA: 176] [Impact Index Per Article: 29.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Accepted: 06/22/2018] [Indexed: 11/09/2022]
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11
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Singh RRP, Young AP. Critical and Griffiths-McCoy singularities in quantum Ising spin glasses on d-dimensional hypercubic lattices: A series expansion study. Phys Rev E 2017; 96:022139. [PMID: 28950636 DOI: 10.1103/physreve.96.022139] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2017] [Indexed: 06/07/2023]
Abstract
We study the ±J transverse-field Ising spin-glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong-field limit. In the SK model and in high dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension d=6, which is below the upper critical dimension of d=8. In contrast, at lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power moments of the local susceptibility become singular in the paramagnetic phase before the critical point. Griffiths-McCoy singularities are very strong in two dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.
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Affiliation(s)
- R R P Singh
- Department of Physics, University of California, Davis, Davis, California 95616, USA
| | - A P Young
- Department of Physics, University of California, Santa Cruz, Santa Cruz, California 95064, USA
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12
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Mukherjee S, Rajak A, Chakrabarti BK. Classical-to-quantum crossover in the critical behavior of the transverse-field Sherrington-Kirkpatrick spin glass model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042107. [PMID: 26565168 DOI: 10.1103/physreve.92.042107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2015] [Indexed: 06/05/2023]
Abstract
We study the critical behavior of the Sherrington-Kirkpatrick model in transverse field (at finite temperature) using Monte Carlo simulation and exact diagonalization (at zero temperature). We determine the phase diagram of the model by estimating the Binder cumulant. We also determine the correlation length exponent from the collapse of the scaled data. Our numerical studies here indicate that critical Binder cumulant (indicating the universality class of the transition behavior) and the correlation length exponent cross over from their "classical" to "quantum" values at a finite temperature (unlike the cases of pure systems, where such crossovers occur at zero temperature). We propose a qualitative argument supporting such an observation, employing a simple tunneling picture.
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Affiliation(s)
- Sudip Mukherjee
- Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
| | - Atanu Rajak
- Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
| | - Bikas K Chakrabarti
- Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
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13
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Mydosh JA. Spin glasses: redux: an updated experimental/materials survey. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:052501. [PMID: 25872613 DOI: 10.1088/0034-4885/78/5/052501] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This article reviews the 40+ year old spin-glass field and one of its earliest model interpretations as a spin density wave. Our description is from an experimental phenomenological point of view with emphasis on new spin glass materials and their relation to topical problems and strongly correlated materials in condensed matter physics. We first simply define a spin glass (SG), give its basic ingredients and explain how the spin glasses enter into the statistical mechanics of classical phase transitions. We then consider the four basic experimental properties to solidly characterize canonical spin glass behavior and introduce the early theories and models. Here the spin density wave (SDW) concept is used to explain the difference between a short-range SDW, i.e. a SG and, in contrast, a long-range SDW, i.e. a conventional magnetic phase transition. We continue with the present state of SG, its massive computer simulations and recent proposals of chiral glasses and quantum SG. We then collect and mention the various SG 'spin-off's'. A major section uncovers the fashionable unconventional materials that display SG-like freezing and glassy ground states, such as (high temperature) superconductors, heavy fermions, intermetallics and Heuslers, pyrochlor and spinels, oxides and chalogenides and exotics, e.g. quasicrystals. Some conclusions and future directions complete the review.
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Affiliation(s)
- J A Mydosh
- Kamerlingh Onnes Laboratory and Institute Lorentz, Leiden University, PO Box 9504, 2300RA Leiden, The Netherlands
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14
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Gingras MJP, Henelius P. Collective Phenomena in the LiHoxY1−xF4Quantum Ising Magnet: Recent Progress and Open Questions. ACTA ACUST UNITED AC 2011. [DOI: 10.1088/1742-6596/320/1/012001] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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15
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Carleo G, Tarzia M, Zamponi F. Bose-Einstein condensation in quantum glasses. PHYSICAL REVIEW LETTERS 2009; 103:215302. [PMID: 20366050 DOI: 10.1103/physrevlett.103.215302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2009] [Revised: 10/10/2009] [Indexed: 05/29/2023]
Abstract
The role of geometrical frustration in strongly interacting bosonic systems is studied with a combined numerical and analytical approach. We demonstrate the existence of a novel quantum phase featuring both Bose-Einstein condensation and spin-glass behavior. The differences between such a phase and the otherwise insulating "Bose glasses" are elucidated.
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Affiliation(s)
- Giuseppe Carleo
- SISSA-Scuola Internazionale Superiore di Studi Avanzati and CNR-INFM DEMOCRITOS-National Simulation Center, via Beirut 2-4, I-34014 Trieste, Italy
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16
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Ancona-Torres C, Silevitch DM, Aeppli G, Rosenbaum TF. Quantum and classical glass transitions in LiHoxY1-xF4. PHYSICAL REVIEW LETTERS 2008; 101:057201. [PMID: 18764428 DOI: 10.1103/physrevlett.101.057201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2008] [Revised: 04/02/2008] [Indexed: 05/26/2023]
Abstract
When performed in the proper low-field, low-frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in a transverse field LiHo(x)Y(1-x)F(4) prove the existence of a spin-glass transition for x=0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields.
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Affiliation(s)
- C Ancona-Torres
- The James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637, USA
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17
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Schechter M, Stamp PCE. Significance of the hyperfine interactions in the phase diagram of LiHoxY1-xF4. PHYSICAL REVIEW LETTERS 2005; 95:267208. [PMID: 16486398 DOI: 10.1103/physrevlett.95.267208] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2005] [Indexed: 05/06/2023]
Abstract
We consider the quantum magnet at LiHo(x)Y(1-x)F(4) at x = 0.167. Experimentally the spin glass to paramagnet transition in this system was studied as a function of the transverse magnetic field and temperature, showing peculiar features: for example, (i) the spin glass order is destroyed much faster by thermal fluctuations than by the transverse field; and (ii) the cusp in the nonlinear susceptibility signaling the glass state decreases in size at lower temperature. Here we show that the hyperfine interactions of the Ho atom must dominate in this system, and that along with the transverse inter-Ho dipolar interactions they dictate the structure of the phase diagram. The experimental observations are shown to be natural consequences of this.
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Affiliation(s)
- M Schechter
- Department of Physics & Astronomy and Pacific Institute for Theoretical Physics, University of British Columbia, Vancouver, Canada
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18
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Werner P, Völker K, Troyer M, Chakravarty S. Phase diagram and critical exponents of a dissipative Ising spin chain in a transverse magnetic field. PHYSICAL REVIEW LETTERS 2005; 94:047201. [PMID: 15783589 DOI: 10.1103/physrevlett.94.047201] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2004] [Indexed: 05/24/2023]
Abstract
We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character of the quantum phase transition is radically altered from the corresponding nondissipative model and the double well coupled to a dissipative heat bath with linear friction. Spatial couplings and the dissipative dynamics combine to form a new quantum criticality which is independent of dissipation strength.
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Affiliation(s)
- Philipp Werner
- Institut für theoretische Physik, ETH Hönggerberg, CH-8093 Zürich, Switzerland
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19
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Sandvik AW. Stochastic series expansion method for quantum Ising models with arbitrary interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:056701. [PMID: 14682905 DOI: 10.1103/physreve.68.056701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2003] [Indexed: 05/24/2023]
Abstract
A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power-series expansion of the density matrix (stochastic series expansion), and avoids the interaction summations necessary in conventional methods. In the case of long-range interactions, the scaling of the computation time with the system size N is therefore reduced from N2 to N ln(N). The method is tested on a one-dimensional ferromagnet in a transverse field, with interactions decaying as 1/r(2).
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Affiliation(s)
- Anders W Sandvik
- Department of Physics, Abo Akademi University, Porthansgatan 3, FIN-20500 Turku, Finland
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20
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Alet F, Sørensen ES. Cluster Monte Carlo algorithm for the quantum rotor model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:015701. [PMID: 12636557 DOI: 10.1103/physreve.67.015701] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2002] [Indexed: 05/24/2023]
Abstract
We propose a highly efficient "worm"-like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the algorithm even in the presence of disorder. For the pure quantum rotor model with mu=0, the algorithm yields high- precision estimates for the critical point K(c)=0.333 05(5) and the correlation length exponent nu=0.670(3). For the disordered case, mu=1 / 2+/-1 / 2, we find nu=1.15(10).
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Affiliation(s)
- Fabien Alet
- Laboratoire de Physique Quantique and UMR 5626, Université Paul Sabatier, 31062 Toulouse, France
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21
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Carlon E, Lajkó P, Iglói F. Disorder induced cross-over effects at quantum critical points. PHYSICAL REVIEW LETTERS 2001; 87:277201. [PMID: 11800910 DOI: 10.1103/physrevlett.87.277201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2001] [Revised: 10/16/2001] [Indexed: 05/23/2023]
Abstract
Critical properties of quantum spin chains with varying degrees of disorder are studied at zero temperature by analytical and extensive density matrix renormalization methods. Generally the phase diagram is found to contain three phases. The weak disorder regime, where the critical behavior is controlled by the fixed points of the pure system, and the strong disorder regime, which is attracted by an infinite randomness fixed point, are separated by an intermediate disorder regime, where dynamical scaling is anisotropic and the static and dynamical exponents are disorder dependent.
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Affiliation(s)
- E Carlon
- INFM, Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy
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22
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Marqués MI, Gonzalo JA. Dynamic scaling in diluted systems: deactivation through thermal dilution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:056114. [PMID: 11414968 DOI: 10.1103/physreve.63.056114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2000] [Indexed: 05/23/2023]
Abstract
Activated scaling is confirmed to hold in transverse field-induced phase transitions of randomly diluted Ising systems. Quantum Monte Carlo calculations have been made not just at the percolation threshold (pc) but also well below and above it. We follow the evolution of the activated scaling at zero temperature in the phase transition from ferromagnetic to quantum Griffiths phase (p>pc) at the phase boundary (p=pc) and for transitions inside the nonferromagnetic quantum Griffiths phase (p<pc). A novel deactivation phenomenon inside the nonferromagnetic Griffiths-McCoy phase (p<pc) is observed using a thermal (in contrast to random) dilution of the system.
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Affiliation(s)
- M I Marqués
- Departamento de Física de Materiales C-IV, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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23
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Cugliandolo LF, Grempel DR. From second to first order transitions in a disordered quantum magnet. PHYSICAL REVIEW LETTERS 2000; 85:2589-2592. [PMID: 10978114 DOI: 10.1103/physrevlett.85.2589] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2000] [Indexed: 05/23/2023]
Abstract
We study the spin-glass transition in a disordered quantum model. In a region of the phase diagram quantum effects are small and the phase transition is second order, as in the classical case. In another region, quantum fluctuations drive the transition to first order. Across the first order line the susceptibility is discontinuous and shows hysteresis. Our findings qualitatively reproduce observations on LiHoxY1-xF4. We also discuss a marginally stable spin-glass state and derive some results previously obtained from the real-time dynamics of the model coupled to a bath.
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Affiliation(s)
- LF Cugliandolo
- Laboratoire de Physique Theorique de l'Ecole Normale Superieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
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24
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Rieger H, Young AP. Griffiths singularities in the disordered phase of a quantum Ising spin glass. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:3328-3335. [PMID: 9986232 DOI: 10.1103/physrevb.54.3328] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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25
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Guo M, Bhatt RN, Huse DA. Quantum Griffiths singularities in the transverse-field Ising spin glass. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:3336-3342. [PMID: 9986233 DOI: 10.1103/physrevb.54.3336] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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26
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Sachdev S, Read N, Oppermann R. Quantum field theory of metallic spin glasses. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:10286-10294. [PMID: 9980079 DOI: 10.1103/physrevb.52.10286] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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27
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Kopec TK. Discontinuous spin-glass transition in a random quantum Heisenberg magnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:9590-9594. [PMID: 9980007 DOI: 10.1103/physrevb.52.9590] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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28
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Read N, Sachdev S, Ye J. Landau theory of quantum spin glasses of rotors and Ising spins. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:384-410. [PMID: 9979617 DOI: 10.1103/physrevb.52.384] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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29
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Hartman JW, Weichman PB. Spherical model for a quantum spin glass. PHYSICAL REVIEW LETTERS 1995; 74:4584-4587. [PMID: 10058547 DOI: 10.1103/physrevlett.74.4584] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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30
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Pázmándi F, Domanski Z. Quantum phase transitions in XY spin models. PHYSICAL REVIEW LETTERS 1995; 74:2363-2366. [PMID: 10057909 DOI: 10.1103/physrevlett.74.2363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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31
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Fisher DS. Critical behavior of random transverse-field Ising spin chains. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:6411-6461. [PMID: 9977181 DOI: 10.1103/physrevb.51.6411] [Citation(s) in RCA: 171] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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32
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Sandvik AW, Vekic M. Disorder induced phase transition in a two-dimensional random quantum antiferromagnet. PHYSICAL REVIEW LETTERS 1995; 74:1226-1229. [PMID: 10058966 DOI: 10.1103/physrevlett.74.1226] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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33
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Sandvik AW. Numerical study of a two-dimensional quantum antiferromagnet with random ferromagnetic bonds. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:15803-15807. [PMID: 9975947 DOI: 10.1103/physrevb.50.15803] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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34
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Continentino MA, Boechat B. Scaling theory for the quantum spin-glass transition. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:13528-13532. [PMID: 9975547 DOI: 10.1103/physrevb.50.13528] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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35
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Rieger H, Young AP. Zero-temperature quantum phase transition of a two-dimensional Ising spin glass. PHYSICAL REVIEW LETTERS 1994; 72:4141-4144. [PMID: 10056392 DOI: 10.1103/physrevlett.72.4141] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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