Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

Marino, Jamir; Eckstein, Martin; Foster, Matthew S.; Rey, Ana Maria

doi:10.1088/1361-6633/ac906c

Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments

Journal Article · 19 October 2022 · Reports on Progress in Physics

DOI:https://doi.org/10.1088/1361-6633/ac906c· OSTI ID:2423166

Marino, Jamir; Eckstein, Martin; Foster, Matthew S.; Rey, Ana Maria

Abstract

We overview the concept of dynamical phase transitions (DPTs) in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behavior on the two sides of a certain dynamical critical point. DPTs are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions,ϕ⁴quantum field theories, and Fermi–Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models.

Research Organization:: National Quantum Information Science (QIS) Research Centers (United States). Quantum Systems Accelerator (QSA)

Sponsoring Organization:: USDOE

DOE Contract Number:: AC02-05CH11231;

OSTI ID:: 2423166

Journal Information:: Reports on Progress in Physics, Journal Name: Reports on Progress in Physics Journal Issue: 11 Vol. 85; ISSN 0034-4885

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

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Quantum quench in interacting field theory: A self-consistent approximation Sotiriadis, Spyros; Cardy, John Physical Review B, Vol. 81, Issue 13 https://doi.org/10.1103/physrevb.81.134305	journal	April 2010
Nonequilibrium dynamical mean-field calculations based on the noncrossing approximation and its generalizations Eckstein, Martin; Werner, Philipp Physical Review B, Vol. 82, Issue 11 https://doi.org/10.1103/physrevb.82.115115	journal	September 2010
Lifetime of double occupancies in the Fermi-Hubbard model Sensarma, Rajdeep; Pekker, David; Altman, Ehud Physical Review B, Vol. 82, Issue 22 https://doi.org/10.1103/physrevb.82.224302	journal	December 2010
Quantum phase diagram of the integrable p x + i p y fermionic superfluid Rombouts, Stefan M. A.; Dukelsky, Jorge; Ortiz, Gerardo Physical Review B, Vol. 82, Issue 22 https://doi.org/10.1103/physrevb.82.224510	journal	December 2010
Quantum quenches in the Hubbard model: Time-dependent mean-field theory and the role of quantum fluctuations Schiró, Marco; Fabrizio, Michele Physical Review B, Vol. 83, Issue 16 https://doi.org/10.1103/physrevb.83.165105	journal	April 2011
Superfluid turbulence: Nonthermal fixed point in an ultracold Bose gas Nowak, Boris; Sexty, Dénes; Gasenzer, Thomas Physical Review B, Vol. 84, Issue 2 https://doi.org/10.1103/physrevb.84.020506	journal	July 2011
Thermalization of a pump-excited Mott insulator Eckstein, Martin; Werner, Philipp Physical Review B, Vol. 84, Issue 3 https://doi.org/10.1103/physrevb.84.035122	journal	July 2011
Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems Kollar, Marcus; Wolf, F. Alexander; Eckstein, Martin Physical Review B, Vol. 84, Issue 5 https://doi.org/10.1103/physrevb.84.054304	journal	August 2011
Linear ramps of interaction in the fermionic Hubbard model Sandri, Matteo; Schiró, Marco; Fabrizio, Michele Physical Review B, Vol. 86, Issue 7 https://doi.org/10.1103/physrevb.86.075122	journal	August 2012
Nonthermal symmetry-broken states in the strongly interacting Hubbard model Werner, Philipp; Tsuji, Naoto; Eckstein, Martin Physical Review B, Vol. 86, Issue 20 https://doi.org/10.1103/physrevb.86.205101	journal	November 2012
Dynamical transition in interaction quenches of the one-dimensional Hubbard model Hamerla, Simone A.; Uhrig, Götz S. Physical Review B, Vol. 87, Issue 6 https://doi.org/10.1103/physrevb.87.064304	journal	February 2013
Equilibration and coarsening in the quantum O ( N ) model at infinite N Chandran, Anushya; Nanduri, Arun; Gubser, S. S. Physical Review B, Vol. 88, Issue 2 https://doi.org/10.1103/physrevb.88.024306	journal	July 2013
Extended dynamic Mott transition in the two-band Hubbard model out of equilibrium Behrmann, Malte; Fabrizio, Michele; Lechermann, Frank Physical Review B, Vol. 88, Issue 3 https://doi.org/10.1103/physrevb.88.035116	journal	July 2013
Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium Foster, Matthew S.; Dzero, Maxim; Gurarie, Victor Physical Review B, Vol. 88, Issue 10 https://doi.org/10.1103/physrevb.88.104511	journal	September 2013
Nonequilibrium dynamics in the antiferromagnetic Hubbard model Sandri, Matteo; Fabrizio, Michele Physical Review B, Vol. 88, Issue 16 https://doi.org/10.1103/physrevb.88.165113	journal	October 2013
Nonequilibrium dynamical mean-field theory based on weak-coupling perturbation expansions: Application to dynamical symmetry breaking in the Hubbard model Tsuji, Naoto; Werner, Philipp Physical Review B, Vol. 88, Issue 16 https://doi.org/10.1103/physrevb.88.165115	journal	October 2013
Quantum quenches, dynamical transitions, and off-equilibrium quantum criticality Sciolla, Bruno; Biroli, Giulio Physical Review B, Vol. 88, Issue 20 https://doi.org/10.1103/physrevb.88.201110	journal	November 2013
Quench dynamics in a model with tuneable integrability breaking Essler, F. H. L.; Kehrein, S.; Manmana, S. R. Physical Review B, Vol. 89, Issue 16 https://doi.org/10.1103/physrevb.89.165104	journal	April 2014
Topological blocking in quantum quench dynamics Kells, G.; Sen, D.; Slingerland, J. K. Physical Review B, Vol. 89, Issue 23 https://doi.org/10.1103/physrevb.89.235130	journal	June 2014
Signatures of nonadiabatic BCS state dynamics in pump-probe conductivity Krull, H.; Manske, D.; Uhrig, G. S. Physical Review B, Vol. 90, Issue 1 https://doi.org/10.1103/physrevb.90.014515	journal	July 2014
Nonequilibrium dynamical cluster theory Tsuji, Naoto; Barmettler, Peter; Aoki, Hideo Physical Review B, Vol. 90, Issue 7 https://doi.org/10.1103/physrevb.90.075117	journal	August 2014
Solving nonequilibrium dynamical mean-field theory using matrix product states Wolf, F. Alexander; McCulloch, Ian P.; Schollwöck, Ulrich Physical Review B, Vol. 90, Issue 23 https://doi.org/10.1103/physrevb.90.235131	journal	December 2014
Exploring dynamical phase transitions and prethermalization with quantum noise of excitations Smacchia, Pietro; Knap, Michael; Demler, Eugene Physical Review B, Vol. 91, Issue 20 https://doi.org/10.1103/physrevb.91.205136	journal	May 2015
Amplitude modes and dynamic coexistence of competing orders in multicomponent superconductors Dzero, Maxim; Khodas, Maxim; Levchenko, Alex Physical Review B, Vol. 91, Issue 21 https://doi.org/10.1103/physrevb.91.214505	journal	June 2015
Short-time universal scaling in an isolated quantum system after a quench Chiocchetta, Alessio; Tavora, Marco; Gambassi, Andrea Physical Review B, Vol. 91, Issue 22 https://doi.org/10.1103/physrevb.91.220302	journal	June 2015
Theory of Anderson pseudospin resonance with Higgs mode in superconductors Tsuji, Naoto; Aoki, Hideo Physical Review B, Vol. 92, Issue 6 https://doi.org/10.1103/physrevb.92.064508	journal	August 2015
Dynamics of many-body localization in a translation-invariant quantum glass model van Horssen, Merlijn; Levi, Emanuele; Garrahan, Juan P. Physical Review B, Vol. 92, Issue 10 https://doi.org/10.1103/physrevb.92.100305	journal	September 2015
Causality and quantum criticality in long-range lattice models Maghrebi, Mohammad F.; Gong, Zhe-Xuan; Foss-Feig, Michael Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/physrevb.93.125128	journal	March 2016
Nonlinear optical effects and third-harmonic generation in superconductors: Cooper pairs versus Higgs mode contribution Cea, T.; Castellani, C.; Benfatto, L. Physical Review B, Vol. 93, Issue 18 https://doi.org/10.1103/physrevb.93.180507	journal	May 2016
Nonequilibrium self-energy functional approach to the dynamical Mott transition Hofmann, Felix; Eckstein, Martin; Potthoff, Michael Physical Review B, Vol. 93, Issue 23 https://doi.org/10.1103/physrevb.93.235104	journal	June 2016
Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in d spatial dimensions Chiocchetta, Alessio; Tavora, Marco; Gambassi, Andrea Physical Review B, Vol. 94, Issue 13 https://doi.org/10.1103/physrevb.94.134311	journal	October 2016
Unifying time evolution and optimization with matrix product states Haegeman, Jutho; Lubich, Christian; Oseledets, Ivan Physical Review B, Vol. 94, Issue 16 https://doi.org/10.1103/physrevb.94.165116	journal	October 2016
Criticality revealed through quench dynamics in the Lipkin-Meshkov-Glick model Campbell, Steve Physical Review B, Vol. 94, Issue 18 https://doi.org/10.1103/physrevb.94.184403	journal	November 2016
Prethermalization from a low-density Holstein-Primakoff expansion Marcuzzi, M.; Marino, J.; Gambassi, A. Physical Review B, Vol. 94, Issue 21 https://doi.org/10.1103/physrevb.94.214304	journal	December 2016
Dynamical Cooper pairing in nonequilibrium electron-phonon systems Knap, Michael; Babadi, Mehrtash; Refael, Gil Physical Review B, Vol. 94, Issue 21 https://doi.org/10.1103/physrevb.94.214504	journal	December 2016
Thermalization and light cones in a model with weak integrability breaking Bertini, Bruno; Essler, Fabian H. L.; Groha, Stefan Physical Review B, Vol. 94, Issue 24 https://doi.org/10.1103/physrevb.94.245117	journal	December 2016
Linear ramps of the mass in the O ( N ) model: Dynamical transition and quantum noise of excitations Maraga, Anna; Smacchia, Pietro; Silva, Alessandro Physical Review B, Vol. 94, Issue 24 https://doi.org/10.1103/physrevb.94.245122	journal	December 2016
Prethermalization and persistent order in the absence of a thermal phase transition Halimeh, Jad C.; Zauner-Stauber, Valentin; McCulloch, Ian P. Physical Review B, Vol. 95, Issue 2 https://doi.org/10.1103/physrevb.95.024302	journal	January 2017
Twisting Anderson pseudospins with light: Quench dynamics in terahertz-pumped BCS superconductors Chou, Yang-Zhi; Liao, Yunxiang; Foster, Matthew S. Physical Review B, Vol. 95, Issue 10 https://doi.org/10.1103/physrevb.95.104507	journal	March 2017
Nonequilibrium optical conductivity: General theory and application to transient phases Kennes, D. M.; Wilner, E. Y.; Reichman, D. R. Physical Review B, Vol. 96, Issue 5 https://doi.org/10.1103/physrevb.96.054506	journal	August 2017
Time-resolved spectral density of interacting fermions following a quench to a superconducting critical point Lemonik, Yonah; Mitra, Aditi Physical Review B, Vol. 96, Issue 10 https://doi.org/10.1103/physrevb.96.104506	journal	September 2017
Slow dynamics in translation-invariant quantum lattice models Michailidis, Alexios A.; Žnidarič, Marko; Medvedyeva, Mariya Physical Review B, Vol. 97, Issue 10 https://doi.org/10.1103/physrevb.97.104307	journal	March 2018
Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model Lang, Johannes; Frank, Bernhard; Halimeh, Jad C. Physical Review B, Vol. 97, Issue 17 https://doi.org/10.1103/physrevb.97.174401	journal	May 2018
Quench dynamics of superconducting fluctuations and optical conductivity in a disordered system Lemonik, Yonah; Mitra, Aditi Physical Review B, Vol. 98, Issue 21 https://doi.org/10.1103/physrevb.98.214514	journal	December 2018
Transient superconductivity without superconductivity Chiriacò, Giuliano; Millis, Andrew J.; Aleiner, Igor L. Physical Review B, Vol. 98, Issue 22 https://doi.org/10.1103/physrevb.98.220510	journal	December 2018
Nonequilibrium dynamics of superconductivity in the attractive Hubbard model Chern, Gia-Wei; Barros, Kipton Physical Review B, Vol. 99, Issue 3 https://doi.org/10.1103/physrevb.99.035162	journal	January 2019
Impact of nonequilibrium fluctuations on prethermal dynamical phase transitions in long-range interacting spin chains Lerose, Alessio; Žunkovič, Bojan; Marino, Jamir Physical Review B, Vol. 99, Issue 4 https://doi.org/10.1103/physrevb.99.045128	journal	January 2019
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Noise correlations in time- and angle-resolved photoemission spectroscopy Stahl, Christopher; Eckstein, Martin Physical Review B, Vol. 99, Issue 24 https://doi.org/10.1103/physrevb.99.241111	journal	June 2019
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Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections Ribeiro, Pedro; Vidal, Julien; Mosseri, Rémy Physical Review E, Vol. 78, Issue 2 https://doi.org/10.1103/physreve.78.021106	journal	August 2008
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Dephasing and the Steady State in Quantum Many-Particle Systems Barthel, T.; Schollwöck, U. Physical Review Letters, Vol. 100, Issue 10 https://doi.org/10.1103/physrevlett.100.100601	journal	March 2008
Nonthermal Steady States after an Interaction Quench in the Falicov-Kimball Model Eckstein, Martin; Kollar, Marcus Physical Review Letters, Vol. 100, Issue 12 https://doi.org/10.1103/physrevlett.100.120404	journal	March 2008
Interaction Quench in the Hubbard Model Moeckel, Michael; Kehrein, Stefan Physical Review Letters, Vol. 100, Issue 17 https://doi.org/10.1103/physrevlett.100.175702	journal	May 2008
Equivalence of Critical Scaling Laws for Many-Body Entanglement in the Lipkin-Meshkov-Glick Model Orús, Román; Dusuel, Sébastien; Vidal, Julien Physical Review Letters, Vol. 101, Issue 2 https://doi.org/10.1103/physrevlett.101.025701	journal	July 2008
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Steady-State Nonequilibrium Density of States of Driven Strongly Correlated Lattice Models in Infinite Dimensions Joura, A. V.; Freericks, J. K.; Pruschke, Th. Physical Review Letters, Vol. 101, Issue 19 https://doi.org/10.1103/physrevlett.101.196401	journal	November 2008
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Thermalization after an Interaction Quench in the Hubbard Model Eckstein, Martin; Kollar, Marcus; Werner, Philipp Physical Review Letters, Vol. 103, Issue 5 https://doi.org/10.1103/physrevlett.103.056403	journal	July 2009
Nonequilibrium Dynamics of Weakly and Strongly Paired Superconductors Gurarie, V. Physical Review Letters, Vol. 103, Issue 7 https://doi.org/10.1103/physrevlett.103.075301	journal	August 2009
Observation of Elastic Doublon Decay in the Fermi-Hubbard Model Strohmaier, Niels; Greif, Daniel; Jördens, Robert Physical Review Letters, Vol. 104, Issue 8 https://doi.org/10.1103/physrevlett.104.080401	journal	February 2010
Spin Self-Rephasing and Very Long Coherence Times in a Trapped Atomic Ensemble Deutsch, C.; Ramirez-Martinez, F.; Lacroûte, C. Physical Review Letters, Vol. 105, Issue 2 https://doi.org/10.1103/physrevlett.105.020401	journal	July 2010
Time-Dependent Mean Field Theory for Quench Dynamics in Correlated Electron Systems Schiró, Marco; Fabrizio, Michele Physical Review Letters, Vol. 105, Issue 7 https://doi.org/10.1103/physrevlett.105.076401	journal	August 2010
Quantum Quenches and Off-Equilibrium Dynamical Transition in the Infinite-Dimensional Bose-Hubbard Model Sciolla, Bruno; Biroli, Giulio Physical Review Letters, Vol. 105, Issue 22 https://doi.org/10.1103/physrevlett.105.220401	journal	November 2010
Damping of Bloch Oscillations in the Hubbard Model Eckstein, Martin; Werner, Philipp Physical Review Letters, Vol. 107, Issue 18 https://doi.org/10.1103/physrevlett.107.186406	journal	October 2011
Self-Trapping in an Array of Coupled 1D Bose Gases Reinhard, Aaron; Riou, Jean-Félix; Zundel, Laura A. Physical Review Letters, Vol. 110, Issue 3 https://doi.org/10.1103/physrevlett.110.033001	journal	January 2013
Nonequilibrium Dynamical Mean-Field Theory: An Auxiliary Quantum Master Equation Approach Arrigoni, Enrico; Knap, Michael; von der Linden, Wolfgang Physical Review Letters, Vol. 110, Issue 8 https://doi.org/10.1103/physrevlett.110.086403	journal	February 2013
Dynamical Formation and Manipulation of Majorana Fermions in Driven Quantum Wires in Contact with a Superconductor Perfetto, E. Physical Review Letters, Vol. 110, Issue 8 https://doi.org/10.1103/physrevlett.110.087001	journal	February 2013
Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model Heyl, M.; Polkovnikov, A.; Kehrein, S. Physical Review Letters, Vol. 110, Issue 13 https://doi.org/10.1103/physrevlett.110.135704	journal	March 2013
Nonthermal Antiferromagnetic Order and Nonequilibrium Criticality in the Hubbard Model Tsuji, Naoto; Eckstein, Martin; Werner, Philipp Physical Review Letters, Vol. 110, Issue 13 https://doi.org/10.1103/physrevlett.110.136404	journal	March 2013
Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level Schäfer, T.; Rohringer, G.; Gunnarsson, O. Physical Review Letters, Vol. 110, Issue 24 https://doi.org/10.1103/physrevlett.110.246405	journal	June 2013
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Prethermalization in a Nonintegrable Quantum Spin Chain after a Quench Marcuzzi, Matteo; Marino, Jamir; Gambassi, Andrea Physical Review Letters, Vol. 111, Issue 19 https://doi.org/10.1103/physrevlett.111.197203	journal	November 2013
Realization of the Dicke Model Using Cavity-Assisted Raman Transitions Baden, Markus P.; Arnold, Kyle J.; Grimsmo, Arne L. Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/physrevlett.113.020408	journal	July 2014
Quench-Induced Floquet Topological p -Wave Superfluids Foster, Matthew S.; Gurarie, Victor; Dzero, Maxim Physical Review Letters, Vol. 113, Issue 7 https://doi.org/10.1103/physrevlett.113.076403	journal	August 2014
Quantum Quench and Prethermalization Dynamics in a Two-Dimensional Fermi Gas with Long-Range Interactions Nessi, N.; Iucci, A.; Cazalilla, M. A. Physical Review Letters, Vol. 113, Issue 21 https://doi.org/10.1103/physrevlett.113.210402	journal	November 2014
Universal Postquench Prethermalization at a Quantum Critical Point Gagel, Pia; Orth, Peter P.; Schmalian, Jörg Physical Review Letters, Vol. 113, Issue 22 https://doi.org/10.1103/physrevlett.113.220401	journal	November 2014
Prethermalization and Thermalization in Models with Weak Integrability Breaking Bertini, Bruno; Essler, Fabian H. L.; Groha, Stefan Physical Review Letters, Vol. 115, Issue 18 https://doi.org/10.1103/physrevlett.115.180601	journal	October 2015
Quantum Quenches in Chern Insulators Caio, M. D.; Cooper, N. R.; Bhaseen, M. J. Physical Review Letters, Vol. 115, Issue 23 https://doi.org/10.1103/physrevlett.115.236403	journal	December 2015
Transient Dynamics of d -Wave Superconductors after a Sudden Excitation Peronaci, Francesco; Schiró, Marco; Capone, Massimo Physical Review Letters, Vol. 115, Issue 25 https://doi.org/10.1103/physrevlett.115.257001	journal	December 2015
Dynamical Buildup of a Quantized Hall Response from Nontopological States Hu, Ying; Zoller, Peter; Budich, Jan Carl Physical Review Letters, Vol. 117, Issue 12 https://doi.org/10.1103/physrevlett.117.126803	journal	September 2016
Competition between Spin Echo and Spin Self-Rephasing in a Trapped Atom Interferometer Solaro, C.; Bonnin, A.; Combes, F. Physical Review Letters, Vol. 117, Issue 16 https://doi.org/10.1103/physrevlett.117.163003	journal	October 2016
Remnant Geometric Hall Response in a Quantum Quench Wilson, Justin H.; Song, Justin C. W.; Refael, Gil Physical Review Letters, Vol. 117, Issue 23 https://doi.org/10.1103/physrevlett.117.235302	journal	November 2016
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Dynamical Crossovers in Prethermal Critical States Chiocchetta, Alessio; Gambassi, Andrea; Diehl, Sebastian Physical Review Letters, Vol. 118, Issue 13 https://doi.org/10.1103/physrevlett.118.135701	journal	March 2017
Disorder-Free Localization Smith, A.; Knolle, J.; Kovrizhin, D. L. Physical Review Letters, Vol. 118, Issue 26 https://doi.org/10.1103/physrevlett.118.266601	journal	June 2017
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Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System Jurcevic, P.; Shen, H.; Hauke, P. Physical Review Letters, Vol. 119, Issue 8 https://doi.org/10.1103/physrevlett.119.080501	journal	August 2017
Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization Smith, A.; Knolle, J.; Moessner, R. Physical Review Letters, Vol. 119, Issue 17 https://doi.org/10.1103/physrevlett.119.176601	journal	October 2017
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Formation of a Spin Texture in a Quantum Gas Coupled to a Cavity Landini, M.; Dogra, N.; Kroeger, K. Physical Review Letters, Vol. 120, Issue 22 https://doi.org/10.1103/physrevlett.120.223602	journal	May 2018
Quantum Slow Relaxation and Metastability due to Dynamical Constraints Lan, Zhihao; van Horssen, Merlijn; Powell, Stephen Physical Review Letters, Vol. 121, Issue 4 https://doi.org/10.1103/physrevlett.121.040603	journal	July 2018
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Uncover Topology by Quantum Quench Dynamics Sun, Wei; Yi, Chang-Rui; Wang, Bao-Zong Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/physrevlett.121.250403	journal	December 2018
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