Dissipative Dynamical Phase Transition as a Complex Ising Model

• URL: http://arxiv.org/abs/2412.09591v1
• Date: Thu, 12 Dec 2024 18:56:36 GMT
• Title: Dissipative Dynamical Phase Transition as a Complex Ising Model
• Authors: Stephen W. Yan, Diego Barberena, Matthew P. A. Fisher, Sagar Vijay,
• Abstract summary: We investigate a quantum dynamical phase transition induced by the competition between local unitary evolution and dissipation in a qubit chain. We show that the dynamical behavior of certain non-local observables is dictated by a quantum Ising model with a $textitcomplex$ transverse-field (cTFIM) We show that the weak-dissipation limit corresponds to a cTFIM with a large magnitude of the imaginary transverse-field.
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• Abstract: We investigate a quantum dynamical phase transition induced by the competition between local unitary evolution and dissipation in a qubit chain with a strong, on-site $\mathbb{Z}_2$ symmetry. While the steady-state of this evolution is always maximally-mixed, we show that the dynamical behavior of certain non-local observables on the approach to this steady-state is dictated by a quantum Ising model with a $\textit{complex}$ transverse-field (cTFIM). We investigate these observables analytically, uncovering a dynamical phase transition as the relative rate of unitary evolution and dissipation is tuned. We show that the weak-dissipation limit corresponds to a cTFIM with a large magnitude of the imaginary transverse-field, for which the many-body "ground-state" (with smallest real eigenvalue) is gapless, exhibiting quasi-long-range correlations of the local magnetization with a continuously-varying exponent. Correspondingly, the dynamics of the non-local observables show oscillatory behavior with an amplitude decaying exponentially in time. The strong-dissipation limit corresponds to a gapped ferromagnetic phase of the cTFIM, and non-local observables show exponential decay on the approach to equilibrium. This transition in (1+1)-dimensions has a peculiar, "two-sided" nature appearing as either first- or second-order depending on the phase from which the transition is approached, an analytic result which is corroborated by numerical studies. In higher dimensions, we present a field-theoretic understanding of the first-order nature of this transition, when approaching from the ferromagnetic phase of the cTFIM, though the nature of the phase with large imaginary transverse-field remains to be understood.

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