Abstract
Classical arguments for thermalization of isolated systems do not apply in a straightforward way to the quantum case. Recently, there has been interest in diagnostics of quantum chaos in many-body systems. In the classical case, chaos is a popular explanation for the legitimacy of the methods of statistical physics. In this work, we relate a previously proposed criteria of quantum chaos in the unitary time evolution operator to the entanglement entropy growth for a far-from-equilibrium initial pure state. By mapping the unitary time evolution operator to a doubled state, chaos can be characterized by suppression of mutual information between subsystems of the past and that of the future. We show that when this mutual information is small, a typical unentangled initial state will evolve to a highly entangled final state. Our result provides a more concrete connection between quantum chaos and thermalization in many-body systems.
Highlights
JHEP06(2019)025 experimental probes of few-body quantum systems that do thermalize [2], generic thermalization in quantum systems appears to be inherently a many-body effect [3]
We show that when this mutual information is small, a typical unentangled initial state will evolve to a highly entangled final state
The Canonical Typicality (CT) approach can be extended to the dynamical result [7] that, under weak assumptions about the distribution of eigenvalues of the Hamiltonian, a subsystem interacting with a sufficiently large bath will spend most of its time close to its time average, independent of the initial state of the subsystem and for almost all initial states of the bath
Summary
We start by reviewing some recent results in understanding quantum chaos. In classical systems, one diagnostic of chaos is exponential sensitivity to initial conditions, quantified by the exponential growth of the Poisson bracket of some pair of phase space coordi-. We can expect that the OTOC will decay as some polynomial of the logarithm of the total Hilbert space dimension This sum I[ρU(t); AF , BP ] + I[ρU(t); AF , BP ] minus I[ρU(t); AF , BP BP ] ≡ 2 ln DA is called tripartite information and its negativity is proposed as a measure of “scrambling” due to unitary time evolution; quantum chaos as measured by the decay of C4 implies scrambling. We treat I(2) and I for ρU(t) as operator-independent diagnostics of chaos It is clear from the discussion above that if the OTOC and two-point functions decay generically, I(2) will be small, which implies I is small as well. In the remainder of the work, we will focus on I(2), but (2.6) should be kept in mind as a way to bound I(2) in terms of the true mutual information
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