Exact NESS of XXZ circuits boundary driven with arbitrary resets or fields

TL;DR

This paper introduces an exact, inhomogeneous matrix product ansatz for the steady state of boundary-driven XXZ quantum circuits with arbitrary resets or fields, enabling analysis of complex nonequilibrium states.

Contribution

It presents a novel infinite-bond-dimension ansatz for the density operator of boundary-driven XXZ circuits, accommodating hybrid coherent and incoherent driving mechanisms.

Findings

Derivation of a family of robust, separable NESS.

Extension of spin-helix states to circuit models.

Potential for experimental realization and investigation.

Abstract

We propose spatially inhomogeneous matrix product ansatz for an exact many-body density operator of a boundary driven XXZ quantum circuit. The ansatz has formally infinite bond-dimension and is fundamentally different from previous constructions. The circuit is driven by a pair of reset quantum channels applied on the boundary qubits, which polarize the qubits to arbitrary pure target states. Moreover, one of the reset channels can be replaced by an arbitrary local unitary gate, thus representing a hybrid case with coherent/incoherent driving. Analyzing the ansatz we obtain a family of relatively robust separable nonequilibrium steady states (NESS), which can be viewed as a circuit extension of spin-helix states, and are particularly suited for experimental investigations.