Subdiffusion and many-body quantum chaos with kinetic constraints

TL;DR

This paper explores how kinetic constraints affect spectral properties and transport dynamics in many-body quantum systems, revealing various universality classes including anomalous transport with a specific dynamical exponent.

Contribution

It introduces a novel approach connecting spectral form factors to transport via an effective Hamiltonian and classifies universality classes based on constraints.

Findings

Identifies universality classes: diffusive, subdiffusive, localized.

Shows Fredkin-constrained systems exhibit anomalous transport with z ≈ 8/3.

Connects spectral form factors to transport properties through transfer matrices.

Abstract

We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic time scales are given by the inverse gap of an effective Hamiltonian$-$or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, $t_{\text{Th}}$, determined by the spectral form factor, to transport properties and linear response correlators. Using tensor network methods, we determine the dynamical exponent, $z$, for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with 'Fredkin constraints' exhibit anomalous transport with dynamical exponent $z \simeq 8/3$.