Full Counting Statistics of Topological Defects after Crossing a Phase Transition

Gómez-Ruiz, Fernando Javier; Mayo, Jack J.; Campo, Adolfo del

doi:10.1103/physrevlett.124.240602

Cited by 51 publications

(79 citation statements)

References 59 publications

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“…Extensive numerical computations using iTEBD with QUAPI support this conclusion. In the classical KZM, it is indeed the case that the constancy of cumulant ratios is a robust feature [79], but a generalization of this classical theory to the quantum case is nontrivial.…”

Section: Discussionmentioning

confidence: 99%

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Bando

Susa

Oshiyama

et al. 2020

Phys. Rev. Research

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119

112

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The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors, with certain quantitative deviations from the theory likely caused by factors such as random control errors and transient effects. In addition, we probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks and their decay, and again find agreement with the quantum simulator results. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system. We support this result by extensive numerical computations. To check whether an alternative, classical interpretation of these results is possible, we used the spin-vector Monte Carlo model, a candidate classical description of the D-Wave device. We find that the degree of agreement with the experimental data from the D-Wave annealing devices is better for the KZM, a quantum theory, than for the classical spin-vector Monte Carlo model, thus favoring a quantum description of the device. Our work provides an experimental test of quantum critical dynamics in an open quantum system, and paves the way to new directions in quantum simulation experiments.

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Section: Discussionmentioning

confidence: 99%

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Bando

Susa

Oshiyama

et al. 2020

Phys. Rev. Research

Self Cite

119

112

View full text Add to dashboard Cite

show abstract

“…As Ref. [37] demonstrates, the universal scaling of cumulants can be observed in models apart from the transverse field Ising spin chain, hence it is natural to explore their behaviour in the Ising Field Theory.…”

Section: Cumulants Of Workmentioning

confidence: 99%

“…The Kibble-Zurek mechanism was also extended beyond the mean values to the full statistics of observables. The number distribution of defects was computed in the Ising chain [13,36] and was argued to exhibit universality [37]. Similarly, the work statistics and its cumulants were also studied and found to satisfy scaling relations [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Kibble–Zurek mechanism in the Ising Field Theory

Hódsági

Kormos

2020

SciPost Phys.

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The Kibble--Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble--Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.

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“…As Ref. [35] demonstrates, the universal scaling of cumulants can be observed in models apart from the transverse field Ising spin chain, hence it is natural to explore their behaviour in the Ising Field Theory.…”

Section: Cumulants Of Workmentioning

confidence: 99%

“…The Kibble-Zurek mechanism was also extended beyond the mean values to the full statistics of observables. The number distribution of defects was computed in the Ising chain [13,34] and was argued to exhibit universality [35]. Similarly, the work statistics and its cumulants were also studied and found to satisfy scaling relations [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Report on scipost_202007_00061v1

2020

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The Kibble-Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble-Zurek mechanism in a genuinely interacting field theory. We demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities, including higher cumulants of the excess heat. Contents 1 Introduction 2 2 Model and methods 4 2.1 The Kibble-Zurek mechanism 4 2.2 KZM in the Ising Field Theory 6 2.3 Adiabatic Perturbation Theory 9 2.3.1 Application to the Ising Field Theory 11 2.4 Truncated Conformal Space Approach 13 3 Work statistics and overlaps 14 3.1 Ramps along the free fermion line 15 3.1.1 The paramagnetic-ferromagnetic (PF) direction 15 3.1.2 The ferromagnetic-paramagnetic (FP) direction 17 3.2 Ramps along the E 8 line 19 3.3 Probability of adiabaticity 20 3.4 Ramps ending at the critical point 21 4 Dynamical scaling in the non-adiabatic regime 22 4.1 Free fermion line 23 4.2 Ramps along the E 8 axis 24 5 Cumulants of work 25 5.1 ECP protocol: ramps ending at the critical point 26 5.2 TCP protocol: ramps crossing the critical point 28 6 Conclusions 29 A Application of the adiabatic perturbation theory to the E 8 model 31 A.1 One-particle states 31 A.2 Two-particle states 32 B Ramp dynamics in the free fermion field theory 35 C TCSA: detailed description, extrapolation 36 C.1 Conventions and applying truncation 36 C.2 Extrapolation details 37 References 41

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Full Counting Statistics of Topological Defects after Crossing a Phase Transition

Cited by 51 publications

References 59 publications

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond

Kibble–Zurek mechanism in the Ising Field Theory

Report on scipost_202007_00061v1

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