Perturbative post-quench overlaps in quantum field theory

Hódsági, Kristóf; Kormos, Márton; Takács, Gábor

doi:10.1007/jhep08(2019)047

Cited by 24 publications

(26 citation statements)

References 102 publications

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“…quasi-particle gaps) m 1 and m 2 , and the binding energy m 2 − 2m 1 goes to zero when h approaches h crit from above. As a result, the quench dynamics contains slow oscillations with the frequency m 2 − 2m 1 , similar to those recently observed in the time evolution of entropies and one-point functions in mass quenches in the E 8 field theory [42,43]. It turns out that in the E 8 case entanglement growth is suppressed and iTEBD numerics can be performed for very long times, which allows to extract the frequency with a very high precision.…”

Section: Large Quenches Above the Threshold: Slow Oscillationssupporting

confidence: 78%

Relaxation and entropy generation after quenching quantum spin chains

2020

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This work considers entropy generation and relaxation in quantum quenches in the Ising and 3-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving Rényi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the “dynamical Gibbs effect” which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum.

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Section: Large Quenches Above the Threshold: Slow Oscillationssupporting

confidence: 78%

Relaxation and entropy generation after quenching quantum spin chains

2020

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“…For a low-density state this probability is indeed tiny, hence the pair factorisation is a good approximation. This assumption is also verified by previous works modeling the non-equilibrium dynamics of the Ising Field Theory that show that time evolution after sudden quenches is dominated by few-particle overlaps in the regime of low post-quench density [81,84,92].…”

Section: Application To the Ising Field Theorysupporting

confidence: 80%

“…The resulting Hamiltonian matrix is then made finite dimensional by truncating the basis, hence the name of the method. Recently, it has been applied with success to model the non-equilibrium dynamics of different theories, in particular the Ising Field Theory [81,84,86,92]. We dedicate this section to briefly introduce the method and set up some notation along the course.…”

Section: Truncated Conformal Space Approachmentioning

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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“…For a low-density state this probability is indeed tiny, hence the pair factorization is a good approximation. This assumption is also verified by previous works modeling the non-equilibrium dynamics of the Ising Field Theory that show that time evolution after sudden quenches is dominated by few-particle overlaps in the regime of low post-quench density [79,82,88].…”

Section: Application To the Ising Field Theorysupporting

confidence: 80%

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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Perturbative post-quench overlaps in quantum field theory

Cited by 24 publications

References 102 publications

Relaxation and entropy generation after quenching quantum spin chains

Relaxation and entropy generation after quenching quantum spin chains

Kibble–Zurek mechanism in the Ising Field Theory

Report on scipost_202007_00061v1

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