Subdiffusion and many-body quantum chaos with kinetic constraints

• URL: http://arxiv.org/abs/2108.02205v3
• Date: Thu, 2 Dec 2021 21:22:17 GMT
• Title: Subdiffusion and many-body quantum chaos with kinetic constraints
• Authors: Hansveer Singh, Brayden Ware, Romain Vasseur, and Aaron J. Friedman
• Abstract summary: We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics. In particular, we show that quantum systems with 'Fredkin constraints' exhibit anomalous transport with dynamical exponent $z simeq 8/3$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $z \simeq 8/3$.

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