Yang-Lee Criticality as a Dissipative Dynamical Phase Transition: Quantum Simulation of non-Hermitian Physics without Post-selection

Abstract:We show that the $d+0$-dimensional Yang-Lee theory describing classical Ising spins in an imaginary magnetic field can be realized, without post-selection, within a $(d-1)+1$ open quantum system whose dynamics consist of local unitaries and engineered dissipation. Competition between the coherent unitary and dissipative dynamics drives a transition wherein the time-dependence of a particular class of linear observables changes from damped oscillatory "underdamped" to purely exponential "overdamped" decay. Our construction relies on an extensive number of weak-symmetries of the Lindbladian fixed by the choice of observable but is otherwise exact. Consequently, we show that the dynamics are described by the non-Hermitian generator of the Yang-Lee transfer matrix, leading to an effective Yang-Lee theory defined on the spacetime history of the open system. By locally modifying the dynamics, we directly measure spin correlation functions of the Yang-Lee theory as well as a related "Loschmidt Echo" correlator which we detail. We explicitly show that the required dissipation channels can be obtained through local $2$-qubit gates and discuss potential realization on near-term quantum simulator devices. Finally, we generalize our construction to embed arbitrary non-Hermitian Hamiltonians within an open quantum system under Lindbladian time-evolution without post-selection, drawing connections between unconditional open quantum dynamics, exceptional point physics, and non-unitary statistical mechanics.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2608.26082 [quant-ph]

(or arXiv:2608.26082v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.26082 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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