- Letter
- Open Access
Disorder-induced dynamical Griffiths singularities after certain quantum quenches
Phys. Rev. B 106, L140201 – Published 10 October, 2022
DOI: https://doi.org/10.1103/PhysRevB.106.L140201
Abstract
We demonstrate that in a class of disordered quantum systems the dynamical partition function is not an analytical function in a time window after certain quantum quenches. We related this behavior to rare and large regions with atypical inhomogeneity configurations. We also quantify the strength of the associated singularities and their signatures in experiments and numerical studies.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (50)
- M. E. Fisher, The nature of critical points, in Lectures in Theoretical Physics, edited by W. E. Brittin (University of Colorado Press, Boulder, 1965), Vol. VII C.
- C. N. Yang and T. D. Lee, Statistical theory of equations of state and phase transitions. I. Theory of condensation, Phys. Rev. 87, 404 (1952).
- X. Peng, H. Zhou, B.-B. Wei, J. Cui, J. Du, and R.-B. Liu, Experimental Observation of Lee-Yang Zeros, Phys. Rev. Lett. 114, 010601 (2015).
- K. Brandner, V. F. Maisi, J. P. Pekola, J. P. Garrahan, and C. Flindt, Experimental Determination of Dynamical Lee-Yang Zeros, Phys. Rev. Lett. 118, 180601 (2017).
- A. B. Harris, Effect of random defects on the critical behaviour of Ising models, J. Phys. C: Solid State Phys. 7, 1671 (1974).
- T. Vojta, Disorder-Induced Rounding of Certain Quantum Phase Transitions, Phys. Rev. Lett. 90, 107202 (2003).
- J. A. Hoyos and T. Vojta, Theory of Smeared Quantum Phase Transitions, Phys. Rev. Lett. 100, 240601 (2008).
- Y. Imry and S.-k. Ma, Random-Field Instability of the Ordered State of Continuous Symmetry, Phys. Rev. Lett. 35, 1399 (1975).
- R. B. Griffiths, Nonanalytic Behavior Above the Critical Point in a Random Ising Ferromagnet, Phys. Rev. Lett. 23, 17 (1969).
- B. M. McCoy, Incompleteness of the Critical Exponent Description for Ferromagnetic Systems Containing Random Impurities, Phys. Rev. Lett. 23, 383 (1969).
- M. Wortis, Griffiths singularities in the randomly dilute one-dimensional Ising model, Phys. Rev. B 10, 4665 (1974).
- A. B. Harris, Nature of the “Griffiths” singularity in dilute magnets, Phys. Rev. B 12, 203 (1975).
- F. Iglói and C. Monthus, Strong disorder RG approach of random systems, Phys. Rep. 412, 277 (2005).
- T. Vojta, Rare region effects at classical, quantum and nonequilibrium phase transitions, J. Phys. A: Math. Gen. 39, R143 (2006).
- F. Iglói and C. Monthus, Strong disorder RG approach – a short review of recent developments, Eur. Phys. J. B 91, 290 (2018).
- M. Randeria, J. P. Sethna, and R. G. Palmer, Low-Frequency Relaxation in Ising Spin-Glasses, Phys. Rev. Lett. 54, 1321 (1985).
- A. J. Bray, Nature of the Griffiths phase, Phys. Rev. Lett. 59, 586 (1987).
- A. J. Bray, Dynamics of Dilute Magnets above , Phys. Rev. Lett. 60, 720 (1988).
- M. J. Thill and D. A. Huse, Equilibrium behaviour of quantum Ising spin glass, Physica A 214, 321 (1995).
- T. Vojta and J. A. Hoyos, Criticality and Quenched Disorder: Harris Criterion Versus Rare Regions, Phys. Rev. Lett. 112, 075702 (2014).
- I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
- I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
- P. Calabrese and J. Cardy, Time Dependence of Correlation Functions Following a Quantum Quench, Phys. Rev. Lett. 96, 136801 (2006).
- A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011).
- A. Mitra, Quantum quench dynamics, Annu. Rev. Condens. Matter Phys. 9, 245 (2018).
- M. Heyl, A. Polkovnikov, and S. Kehrein, Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model, Phys. Rev. Lett. 110, 135704 (2013).
- F. Andraschko and J. Sirker, Dynamical quantum phase transitions and the loschmidt echo: A transfer matrix approach, Phys. Rev. B 89, 125120 (2014).
- S. Vajna and B. Dóra, Disentangling dynamical phase transitions from equilibrium phase transitions, Phys. Rev. B 89, 161105(R) (2014).
- M. Schmitt and S. Kehrein, Dynamical quantum phase transitions in the Kitaev honeycomb model, Phys. Rev. B 92, 075114 (2015).
- J. C. Halimeh and V. Zauner-Stauber, Dynamical phase diagram of quantum spin chains with long-range interactions, Phys. Rev. B 96, 134427 (2017).
- B. Žunkovič, M. Heyl, M. Knap, and A. Silva, Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging Different Concepts of Nonequilibrium Criticality, Phys. Rev. Lett. 120, 130601 (2018).
- R. Jafari, Dynamical quantum phase transition and quasi particle excitation, Sci. Rep. 9, 2871 (2019).
- P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System, Phys. Rev. Lett. 119, 080501 (2017).
- J. Zhang, G. Pagano, P. W. Hess, A. Kyprianidis, P. Becker, H. Kaplan, A. V. Gorshkov, Z.-X. Gong, and C. Monroe, Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator, Nature (London) 551, 601 (2017).
- H. Bernie, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Probing many-body dynamics on a 51-atom quantum simulator, Nature (London) 551, 579 (2017).
- N. Fläschner, D. Vogel, M. Tarnowski, B. S. Rem, D.-S. Lühmann, M. Heyl, J. C. Budich, L. Mathey, K. Sengstock, and C. Weitenberg, Observation of dynamical vortices after quenches in a system with topology, Nat. Phys. 14, 265 (2018).
- X.-Y. Guo, C. Yang, Y. Zeng, Y. Peng, H.-K. Li, H. Deng, Y.-R. Jin, S. Chen, D. Zheng, and H. Fan, Observation of a Dynamical Quantum Phase Transition by a Superconducting Qubit Simulation, Phys. Rev. Appl. 11, 044080 (2019).
- Markus Heyl, Dynamical quantum phase transitions: a review, Rep. Prog. Phys. 81, 054001 (2018).
- T. Obuchi and K. Takahashi, Dynamical singularities of glassy systems in a quantum quench, Phys. Rev. E 86, 051125 (2012).
- C. Yang, Y. Wang, P. Wang, X. Gao, and S. Chen, Dynamical signature of localization-delocalization transition in a one-dimensional incommensurate lattice, Phys. Rev. B 95, 184201 (2017).
- H. Yin, S. Chen, X. Gao, and P. Wang, Zeros of Loschmidt echo in the presence of Anderson localization, Phys. Rev. A 97, 033624 (2018).
- V. Gurarie, Dynamical quantum phase transitions in the random field Ising model, Phys. Rev. A 100, 031601(R) (2019).
- K. Cao, W. Li, M. Zhong, and P. Tong, Influence of weak disorder on the dynamical quantum phase transitions in the anisotropic XY chain, Phys. Rev. B 102, 014207 (2020).
- U. Mishra, R. Jafari, and A. Akbari, Disordered Kitaev chain with long-range pairing: Loschmidt echo revivals and dynamical phase transitions, J. Phys. A: Math. Theor. 53, 375301 (2020).
- P. Pfeuty, An exact result for the 1D random Ising model in a transverse field, Phys. Lett. A 72, 245 (1979).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.106.L140201 for technical details and a description of our numerical approach, which includes Refs. [48, 49, 50].
- B. Gardas, J. Dziarmaga, W. H. Zurek, and M. Zwolak, Defects in quantum computers, Sci. Rep. 8, 4539 (2018).
- D. S. Fisher, Critical behavior of random transverse-field Ising spin chains, Phys. Rev. B 51, 6411 (1995).
- E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. 16, 407 (1961).
- A. P. Young and H. Rieger, Numerical study of the random transverse-field Ising spin chain, Phys. Rev. B 53, 8486 (1996).