Thermal and dissipative effects on the heating transition in a driven  critical system

Choo, Kenny; Lapierre, Bastien; Kuhlenkamp, Clemens; Tiwari, Apoorv; Neupert, Titus; Читра, Р.

doi:10.21468/scipostphys.13.5.104

Cited by 4 publications

(4 citation statements)

References 68 publications

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“…Periodic driving 16 with such Hamiltonians was considered in the context of Floquet CFT [62,90,92,98]. For such periodic processes, the dynamics is controlled by the iteration of a Möbius transformation on the disk and the asymptotic behavior of the trajectory under iteration gives the distinction between heating and non-heating phases.…”

Section: Möbius Processes and Hyperbolic Geometrymentioning

confidence: 99%

“…At late times, there are different possible behaviors depending on the type of Möbius transformation that we iterate, elliptic, parabolic or hyperbolic [150]. We then have two possible phases [62,90,98]:…”

Section: Phases Of Periodic Möbius Processesmentioning

confidence: 99%

“…The relation between Virasoro process and spacetime metrics explains some of the observations in [63,96] related to the "emergent Rindler space". Effects related to dissipation and chaos were considered in [97][98][99]. Floquet CFTs are particularly interesting because they are relevant experimentally, see for example [100,101].…”

Section: Introductionmentioning

confidence: 99%

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Quantum hypothesis testing in many-body systems

2021

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One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as ``is the system in state A or state B?''. In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number n of identical copies of the system, and estimate the expected error as n becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.

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Section: Möbius Processes and Hyperbolic Geometrymentioning

confidence: 99%

Section: Phases Of Periodic Möbius Processesmentioning

confidence: 99%

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Quantum hypothesis testing in many-body systems

2021

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“…Finally, we focus on a periodic sequence of metric quenches applied to a relativistic fermions (Fig 1(d)). This procedure induces a Floquet state recently described within Floquet conformal field theory [33][34][35][36][37][38][39]. While the total energy of this state increases exponentially, it concentrates on a few points [35,36] which effectively behave as black holes [36]: the rate of increase of their energy is strongly corrected by quantum anomaly corrections, and the energy density is negative in their vicinity as in a black hole atmosphere.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches

Bermond,

Chernodub,

Grushin

et al. 2024

SciPost Phys.

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Building on the idea of Tolman and Ehrenfest that heat has weight, Luttinger established a deep connection between gravitational fields and thermal transport. However, this relation does not include anomalous quantum fluctuations that become paramount in strongly curved spacetime. In this work, we revisit the celebrated Tolman-Ehrenfest and Luttinger relations and show how to incorporate the quantum energy scales associated with these fluctuations, captured by gravitational anomalies of quantum field theories. We point out that such anomalous fluctuations naturally occur in the quantum atmosphere of a black hole. Our results reveal that analogous fluctuations are also observable in thermal conductors in flat-space time provided local temperature varies strongly. As a consequence, we establish that the gravitational anomalies manifest themselves naturally in non-linear thermal response of a quantum wire. In addition, we propose a systematic way to identify thermal analogues of black hole’s anomalous quantum fluctuations associated to gravitational anomalies. We identify their signatures in propagating energy waves following a thermal quench, as well as in the energy density of heating Floquet states induced by repeated thermal quenches.

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Quantum information geometry of driven CFTs

de Boer,

Godet,

Kastikainen

et al. 2023

J. High Energ. Phys.

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Driven quantum systems exhibit a large variety of interesting and sometimes exotic phenomena. Of particular interest are driven conformal field theories (CFTs) which describe quantum many-body systems at criticality. In this paper, we develop both a spacetime and a quantum information geometry perspective on driven 2d CFTs. We show that for a large class of driving protocols the theories admit an alternative but equivalent formulation in terms of a CFT defined on a spacetime with a time-dependent metric. We prove this equivalence both in the operator formulation as well as in the path integral description of the theory. A complementary quantum information geometric perspective for driven 2d CFTs employs the so-called Bogoliubov-Kubo-Mori (BKM) metric, which is the counterpart of the Fisher metric of classical information theory, and which is obtained from a perturbative expansion of relative entropy. We compute the BKM metric for the universal sector of Virasoro excitations of a thermal state, which captures a large class of driving protocols, and find it to be a useful tool to classify and characterize different types of driving. For Möbius driving by the SL(2, ℝ) subgroup, the BKM metric becomes the hyperbolic metric on the disk. We show how the non-trivial dynamics of Floquet driven CFTs is encoded in the BKM geometry via Möbius transformations. This allows us to identify ergodic and non-ergodic regimes in the driving. We also explain how holographic driven CFTs are dual to driven BTZ black holes with evolving horizons. The deformation of the black hole horizon towards and away from the asymptotic boundary provides a holographic understanding of heating and cooling in Floquet CFTs.

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Thermal and dissipative effects on the heating transition in a driven critical system

Cited by 4 publications

References 68 publications

Quantum hypothesis testing in many-body systems

Quantum hypothesis testing in many-body systems

Anomalous Luttinger equivalence between temperature and curved spacetime: From black holes to thermal quenches

Quantum information geometry of driven CFTs

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