Quantum many-body spin ratchets

TL;DR

This paper introduces SU(2) invariant quantum circuits to study spin transport, revealing how symmetry breaking causes a universal drift velocity and violations of equilibrium fluctuation relations, with implications for quantum many-body dynamics.

Contribution

It develops a new class of quantum circuits to analyze spin transport, linking symmetry breaking to universal drift velocities and fluctuation relation violations in quantum many-body systems.

Findings

Breaking space-reflection symmetry induces a universal drift velocity.

In integrable models, the drift velocity is confirmed analytically.

Stationary states violate Gallavotti-Cohen symmetry but obey a generalized fluctuation relation.

Abstract

Introducing a class of SU(2) invariant quantum unitary circuits generating chiral transport, we examine the role of broken space-reflection and time-reversal symmetries on spin transport properties. Upon adjusting parameters of local unitary gates, the dynamics can be either chaotic or integrable. The latter corresponds to a generalization of the space-time discretized (Trotterized) higher-spin quantum Heisenberg chain. We demonstrate that breaking of space-reflection symmetry results in a drift in the dynamical spin susceptibility. Remarkably, we find a universal drift velocity given by a simple formula which, at zero average magnetization, depends only on the values of SU(2) Casimir invariants associated with local spins. In the integrable case, the drift velocity formula is confirmed analytically based on the exact solution of thermodynamic Bethe ansatz equations. Finally, by inspecting the large fluctuations of the time-integrated current between two halves of the system in stationary maximum-entropy states, we demonstrate violation of the Gallavotti-Cohen symmetry, implying that such states cannot be regarded as equilibrium ones. We show that the scaled cumulant generating function of the time-integrated current instead obeys a generalized fluctuation relation.