Abstract
Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of)O(2)×O(2)symmetries, which is broken toO(2)by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystemAwith lengthLAcorresponds to the energy of the half-vortex pairS∼ρslogLA, whereρsis the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.
Highlights
Under unitary evolution, local quantum information of a generic closed many-body system goes through the process of scrambling and disperses into the entire system
It has long been known that such a process is closely related to thermalization, in which the entanglement entropy of a small subsystem approaches thermal entropy with volume law scaling
The underlying mechanism applies to other non-unitary dynamics that host exotic non-thermal phases [26,27,28,29,30,31,32]
Summary
Local quantum information of a generic closed many-body system goes through the process of scrambling and disperses into the entire system. In free fermion non-unitary systems, it is shown that a stable critical phase exists, in which the entanglement entropy is logarithmic in the subsystem size and the correlation functions in the spatial direction exhibit power-law decay [25, 33,34,35]. While these results have been corroborated in numerous numerical simulations, concrete solvable models, in which the entanglement entropy and correlation function can be determined analytically, are still lacking and will prove valuable in the understanding of the intimate relation between quantum thermalization and non-Hermiticity. We comment that when the interaction is added, the Goldstone mode acquires a mass, leading to volumelaw scaling in the entanglement entropy, which can again be understood from a domain wall picture
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