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Exact Nonequilibrium Steady State of XXZ Circuits Boundary Driven with Arbitrary Resets or Fields

Vladislav Popkov1,2 and Tomaž Prosen1,3

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Phys. Rev. Lett. 135, 070401 – Published 11 August, 2025

DOI: https://doi.org/10.1103/31p7-lcgh

Abstract

We propose a 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 and incoherent driving. Analyzing the Ansatz, we obtain a family of relatively robust separable nonequilibrium steady states, which can be viewed as a circuit extension of spin-helix states and are particularly suited for experimental investigations.

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Phys. Rev. Lett. 135, 070401– Published 11 August, 2025
  • Received 20 February 2025
  • Accepted 11 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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