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arXiv:2304.03155 · Physical review. B./Physical review. B

Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars

Alexander Evgen’evich Teretenkov, Oleg Valentinovich Lychkovskiy

Published Dec 13, 2024• 10 citations
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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.

DOI
10.1103/physrevb.110.l241105

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Hydrodynamic relaxation in open quantum many-body systems can be understood in terms of diffusive Nambu--Goldstone (NG) modes associated with strong-to-weak spontaneous symmetry breaking (SWSSB). Here, we find a common structure underlying weak ergodicity breaking in closed quantum systems and diffusive hydrodynamics in open quantum systems. We establish a spectral correspondence between the parent Hamiltonian of rainbow quantum many-body scar (RQMBS) states in closed systems and the effective Lindbladian of strongly dissipative open systems with strong U(1)U(1)U(1) symmetry and local charge-dephasing Lindblad operators. For broad classes of spin, fermionic, and bosonic systems, we construct asymptotic RQMBS (ARQMBS) states. Within the enlarged scar subspace, the parent Hamiltonian admits a local Rokhsar--Kivelson-type frustration-free decomposition. A single-mode variational construction gives an O(k2)O(k^2)O(k2) upper bound on its lowest excitation energy and yields states satisfying the defining ARQMBS criteria: orthogonality, vanishing energy variance, and characteristic entanglement scaling. Under vectorization, RQMBS states are mapped to maximally mixed infinite-temperature states in fixed-charge sectors, which exhibit long-range SWSSB order under finite-density conditions. Assuming uniformly bounded positive transition rates, the effective Lindbladian has the same local projectors as the parent Hamiltonian but with positive transition-dependent weights, yielding two-sided spectral bounds and the same system-size scaling of their gaps. For uniform rates, the two operators are proportional to each other and their eigenmodes coincide. Therefore, an exact quadratic parent-Hamiltonian branch maps directly to a diffusive NG mode. Our results connect different mechanisms of slow relaxation in closed and open quantum many-body systems.
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Isolated quantum many-body systems are often well described by the eigenstate thermalization hypothesis. There are, however, mechanisms that cause different behavior: many-body localization and quantum many-body scars. Here, we show how one can find disordered Hamiltonians hosting a tower of scars by adapting a known method for finding parent Hamiltonians. Using this method, we construct a spin-12\frac{1}{2}21​ model which is both partially localized and contains scars. We demonstrate that the model is partially localized by studying numerically the level spacing statistics and bipartite entanglement entropy. As disorder is introduced, the adjacent gap ratio transitions from the Gaussian orthogonal ensemble to the Poisson distribution and the entropy shifts from volume-law to area-law scaling. We investigate the properties of scars in a partially localized background and compare with a thermal background. At strong disorder, states initialized inside or outside the scar subspace display different dynamical behavior but have similar entanglement entropy and Schmidt gap. We demonstrate that localization stabilizes scar revivals of initial states with support both inside and outside the scar subspace. Finally, we show how strong disorder introduces additional approximate towers of eigenstates.
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