Subdiffusion and Many-Body Quantum Chaos with Kinetic Constraints

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Statistical mechanics

Background:

• Many-body quantum systems exhibit complex behaviors governed by conserved charges and kinetic constraints.
• Understanding the interplay between spectral properties and transport is crucial for characterizing quantum dynamics.

Purpose of the Study:

• To investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints.
• To establish a direct connection between spectral characteristics, such as the Thouless time, and transport phenomena.
• To classify the dynamical behavior of constrained quantum systems.

Main Methods:

• Utilized random unitary circuits to compute ensemble-averaged spectral form factors and linear-response correlation functions.
• Employed tensor network methods to determine the dynamical exponent (z) for various constrained, conserving models.
• Connected characteristic timescales to the gap of an effective Hamiltonian or transfer matrix.

Main Results:

• Identified characteristic timescales governed by the inverse gap of an effective Hamiltonian or transfer matrix.
• Established a direct link between the Thouless time (tTh) and transport properties.
• Discovered universality classes exhibiting diffusive, subdiffusive, quasilocalized, and localized dynamics.
• Demonstrated anomalous transport with a dynamical exponent z≃8/3 in quantum systems with Fredkin constraints.

Conclusions:

• The spectral properties of constrained quantum systems directly inform their transport characteristics.
• The severity of kinetic constraints dictates the universality class of the system's dynamics.
• Fredkin constraints lead to unique anomalous transport behavior.