Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain

Trapin, Daniele; Heyl, Markus

doi:10.1103/physrevb.97.174303

Cited by 24 publications

(26 citation statements)

References 47 publications

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“…Despite the recent progresses in understanding the dynamics of this paradigmatic model and of quantum many-body systems in general, it remains an outstanding challenge to extract universal quantum out-of-equilibrium behavior [71][72][73][74][75][76][77][78]. For slow near-adiabatic sweeps across a critical region, the Kibble-Zurek mechanism [79,80] has provided deep insights, including universal scaling laws [80,81].…”

Section: Introductionmentioning

confidence: 99%

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Bandyopadhyay¹,

Uhrich²,

Paviglianiti³

et al. 2021

Preprint

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Equilibrium quantum many-body systems in the vicinity of phase transitions generically manifest universality. In contrast, limited knowledge has been gained on possible universal characteristics in the non-equilibrium evolution of systems in quantum critical phases. Here, we present such a universal feature in the equilibration dynamics of the Sachdev-Ye-Kitaev (SYK) Hamiltonian-a paradigmatic system of disordered, all-to-all interacting fermions that has been designed as a phenomenological description of quantum critical regions. We drive the system far away from equilibrium by performing a global quench, and track how its ensemble average relaxes to a steady state. Employing state-ofthe-art numerical simulations for the exact evolution, we reveal that the disorder-averaged evolution of few-body observables, including the quantum Fisher information (QFI) and low-order moments of local operators, exhibit within numerical resolution a universal equilibration process. Under a straightforward rescaling, data that correspond to different initial states collapse onto a universal curve, which can be well approximated by a Gaussian throughout large parts of the evolution. To reveal the physics behind this process, we formulate a general theoretical framework based on the Novikov-Furutsu theorem. This framework extracts the disorder-averaged dynamics of a many-body system as an effective dissipative evolution, and can have applications beyond this work. The exact non-Markovian evolution of the SYK ensemble is very well captured by Bourret-Markov approximations, which contrary to common lore become justified thanks to the extreme chaoticity of the system, and universality is revealed in a spectral analysis of the corresponding Liouvillian. We expect our findings to shed light on challenging questions for quantum systems far from equilibrium, such as thermalization and equilibration of closed and disordered quantum many-body systems, and to stimulate further studies on out-of-equilibrium universality.

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Section: Introductionmentioning

confidence: 99%

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Bandyopadhyay¹,

Uhrich²,

Paviglianiti³

et al. 2021

Preprint

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“…These are sufficient to construct Landau or effective field theories, which describe the universal properties in the vicinity of the transition. Although for one particular model system a Landau theory for DQPTs has been derived from microscopics [63], for a general understanding of DQPTs it will be of central importance to explore ways that can approach DQPTs from a macroscopic perspective. As emphasized also before, the theory of DQPTs is facing a major challenge in this context, since it is the central property of the considered nonequilibrium quantum states, that they defy a thermodynamic description and therefore a description in terms a free energy in an equilibrium sense.…”

Section: Scaling and Universalitymentioning

confidence: 99%

Dynamical quantum phase transitions: A brief survey

Heyl

2019

EPL

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Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to quantum states with novel properties of genuine nonequilibrium nature. In turn, for the theoretical description it is in general not sufficient to understand nonequilibrium dynamics on the basis of the properties of the involved Hamiltonians. Instead it becomes important to characterize time-evolution operators which adds time as an additional scale to the problem. In these Perspectives we summarize recent progress in the field of dynamical quantum phase transitions, which are phase transitions in time with temporal nonanalyticities in matrix elements of the time-evolution operator. These transitions are not driven by an external control parameter, but rather occur due to sharp internal changes generated solely by unitary real-time dynamics. We discuss the obtained insights on general properties of dynamical quantum phase transitions, their physical interpretation, potential future research directions, as well as recent experimental observations.

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“…The discontinuity in the first derivative is akin to a first order EPT, further marking this behaviour as distinct from the DQPTs in the Ising model. Recently there have been attempts to construct Ginzburg-Landau type theories describing the system in the region of DQPTs and analyse their scaling behaviour [25,26,29]. This has been achieved in certain quenches of the Ising model using a mapping to the equilibrium scaling RG flow of the model.…”

Section: A a Single Revivalmentioning

confidence: 99%

Dynamical Quantum Phase transitions and Recurrences in the Non-Equilibrium BCS model

Rylands,

Galitski

2020

Preprint

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Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics of fermions with pairing interactions. The recently introduced notion of a dynamical quantum phase transition is an attempt to classify the myriad of possible phenomena which can result in such far from equilibrium systems. These are defined as non-analytic points of the logarithm of the Loschmidt echo and are linked to oscillations in the dynamics a systems order parameter. In this work we analytically investigate the relation between DQPTs and oscillation of the superconducting order parameter in quenches of the BCS model. We find that each oscillation of the order parameter is accompanied by a DQPT which is first order in nature. We show this for a variety of initial states and furthermore find that when the order parameter attains a constant steady state then no DQPTS occur.

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Constructing effective free energies for dynamical quantum phase transitions in the transverse-field Ising chain

Cited by 24 publications

References 47 publications

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

Dynamical quantum phase transitions: A brief survey

Dynamical Quantum Phase transitions and Recurrences in the Non-Equilibrium BCS model

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