Boundary dissipative spin chains with partial solvability inherited from system Hamiltonians

TL;DR

This paper demonstrates that partial solvability in quantum many-body systems can persist even with boundary dissipation, revealing exact eigenmodes and phenomena like quantum synchronization in open spin chains.

Contribution

It introduces two mechanisms for maintaining partial solvability in boundary dissipative systems and derives exact eigenmodes for open quantum spin chains.

Findings

Exact eigenmodes of Lindblad equation derived for boundary dissipative spin chains

Identification of persistent oscillations and quantum synchronization phenomena

Numerical simulations confirm impact on long-time observable behavior

Abstract

Partial solvability plays an important role in the context of statistical mechanics, since it has turned out to be closely related to the emergence of quantum many-body scar states, i.e., exceptional energy eigenstates which do not obey the strong version of the eigenstate themalization hypothesis. We show that partial solvability of a quantum many-body system can be maintained even when the system is coupled to boundary dissipators under certain conditions. We propose two mechanisms that support partially solvable structures in boundary dissipative systems: The first one is based on the restricted spectrum generating algebra, while the second one is based on the Hilbert space fragmentation. From these structures, we derive exact eigenmodes of the Gorini-Kossakowski-Sudarshan-Lindblad equation for a family of quantum spin chain models with boundary dissipators, where we find various intriguing phenomena arising from the partial solvability of the open quantum systems, including persistent oscillations (quantum synchronization) and the existence of the matrix product operator symmetry. We discuss how the presence of solvable eigenmodes affects long-time behaviors of observables in boundary dissipative spin chains based on numerical simulations using the quantum trajectory method.