Abstract
Quantum many-body scar states are exceptional finite energy density eigenstates in an otherwise thermalizing system that do not satisfy the eigenstate thermalization hypothesis. We investigate the fate of exact many-body scar states under perturbations. At small system sizes, deformed scar states described by perturbation theory survive. However, we argue for their eventual thermalization in the thermodynamic limit from the finite-size scaling of the off-diagonal matrix elements. Nevertheless, we show numerically and analytically that the nonthermal properties of the scars survive for a parametrically long time in quench experiments. We present a rigorous argument that lower-bounds the thermalization time for any scar state as $t^{*} \sim O(\lambda^{-1/(1+d)})$, where $d$ is the spatial dimension of the system and $\lambda$ is the perturbation strength.
Highlights
Wigner pioneered the application of random matrix theory to describe quantum chaos [1]
The eigenstate thermalization hypothesis (ETH) implies that the reduced density matrix of a single eigenstate is equal to that of the microcanonical/canonical ensemble, and it is how statistical mechanics emerges in closed quantum systems
In this paper we examine the fate of exact quantum manybody scar states under perturbations
Summary
Wigner pioneered the application of random matrix theory to describe quantum chaos [1]. A consequence of our results is that the exact scar states discovered or constructed in different special models can be used to understand the persisting dynamical signatures under perturbations up to some parametrically large timescale and in the thermodynamic limit. The nonthermal properties of the exact scar states can survive in quench experiments under perturbations to some parametrically long time even in the thermodynamic limit, which we expect to diverge as power law in λ in generic cases. We note that by the latter term we mean that only some special eigenstates are known analytically, while the other eigenstates are not known analytically and are in overwhelming numbers thermal It is only these special eigenstates or the corresponding special initial states that produce observable scar signatures either in small system sizes or quench dynamics.
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