Projected state ensemble of a generic model of many-body quantum chaos
- URL: http://arxiv.org/abs/2402.16939v1
- Date: Mon, 26 Feb 2024 19:00:00 GMT
- Title: Projected state ensemble of a generic model of many-body quantum chaos
- Authors: Amos Chan and Andrea De Luca
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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 $k$-th 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 $t_k = O(\log
k)$. Our results are supported with numerical simulations performed at $q=2$.
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