Subdiffusion and many-body quantum chaos with kinetic constraints

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 $z\simeq 8/3$.

4 pages, 2 figures plus 26 pages supplemental material, v2: additional results, new XNOR constraint

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Cited by in corpus (19)

• Random Quantum Circuits
• Anomalous hydrodynamics in a class of scarred frustration-free Hamiltonians
• Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models
• Superdiffusive Energy Transport in Kinetically Constrained Models
• Anomalous transport from hot quasiparticles in interacting spin chains
• Distinct universality classes of diffusive transport from full counting statistics
• Measurement-induced phases of matter require feedback
• Universal anomalous fluctuations in charged single-file systems
• Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains
• Emergent tracer dynamics in constrained quantum systems
• Slow dynamics and large deviations in classical stochastic Fredkin chains
• Fracton magnetohydrodynamics
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• The Fredkin staircase: An integrable system with a finite-frequency Drude peak
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• Slow thermalization and subdiffusion in $U(1)$ conserving Floquet random circuits
• Open-system spin transport and operator weight dissipation in spin chains
• Real-time broadening of bath-induced density profiles from closed-system correlation functions
• Dissipative quantum North-East-Center model: steady-state phase diagram, universality and nonergodic dynamics