Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars
Year: 2024
Type: article
Abstract: We establish a duality between open many-body systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation and satisfying the detailed balance condition on the one side, and closed bilayer systems with a self-adjoint Hamiltonian on the other side. Under this duality, the identity operator on the open-system side maps to a quantum many-body scar of the dual Hamiltonian $\mathcal{H}$. This scar eigenstate has a form of a thermofield double state for a single-body conserved quantity entering the detailed balance conditions. A remarkable feature of this thermofield scar is a tunable single-layer entanglement entropy controlled by the reservoir temperature on the open-system side. Further, we identify broad classes of many-body open systems with nontrivial explicit eigenoperators $Q$ of the Lindbladian superoperator. The expectation values of the corresponding observables exhibit a simple exponential decay, ${\ensuremath{\langle}Q\ensuremath{\rangle}}_{t}={e}^{\ensuremath{-}\mathrm{\ensuremath{\Gamma}}t}{\ensuremath{\langle}Q\ensuremath{\rangle}}_{0}$, irrespectively of the initial state. Under the above duality, these eigenoperators give rise to additional (towers of) scars. Finally, we point out that more general superoperators (not necessarily of the GKSL form) can be mapped to self-adjoint Hamiltonians of bilayer systems harboring scars and provide an example thereof.
Authors: Alexander Teretenkov, Oleg Lychkovskiy
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G3519964750, G6509858906
OpenAlex ID: W4405369201