Conformal symmetry in quasi-free Markovian open quantum systems

Abstract

Conformal symmetry governs the behavior of closed systems near second-order phase transitions, and is expected to emerge in open systems going through dissipative phase transitions. We propose a framework allowing for a manifest description of conformal symmetry in open Markovian systems. The key difference from the closed case is that both conformal algebra and the algebra of local fields are realized on the space of superoperators. We illustrate the framework by a series of examples featuring systems with quadratic Hamiltonians and linear jump operators, where the Liouvillian dynamics can be efficiently analyzed using the formalism of third quantization. We expect that our framework can be extended to interacting systems using an appropriate generalization of the conformal bootstrap.

15 pages, supplementary Wolfram Mathematica notebook available at https://github.com/idnm/third_quantization v2: minor revision (references added, typos corrected) v2: Minor revisions done and typos corrected

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Cited by in corpus (3)

• The Open Effective Field Theory of Inflation
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• Chiral Instabilities in Driven-Dissipative Quantum Liquids