Projected state ensemble of a generic model of many-body quantum chaos

Chan, Amos and De Luca, Andrea (2024) Projected state ensemble of a generic model of many-body quantum chaos. Journal of Physics A: Mathematical and Theoretical, 57 (40): 405001. ISSN 1751-8113

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Abstract

The projected ensemble is based on the study of the quantum state of a subsystem A conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the kth moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension q, we find that all moments converge simultaneously with a time scaling linearly in the size of region A, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite q on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times tk=O(log⁡k). Our results are supported with numerical simulations performed at q = 2.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Physics A: Mathematical and Theoretical
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/3100
Subjects:
?? many-body quantum chaosquantum circuitsquantum many-body dynamicsprojected state ensemblethermalizationphysics and astronomy(all)modelling and simulationmathematical physicsstatistical and nonlinear physicsstatistics and probability ??
ID Code:
224264
Deposited By:
Deposited On:
24 Sep 2024 08:40
Refereed?:
Yes
Published?:
Published
Last Modified:
10 Oct 2024 00:32