Dissipative dynamical phase transition as a complex Ising model
Phys. Rev. B 114, 204312 – Published 23 October, 2026
DOI: https://doi.org/10.1103/n5rq-rf2b
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 symmetry. While the steady state of this evolution is always maximally mixed, we show that the dynamical behavior of certain nonlocal observables on the approach to this steady state is dictated by a quantum Ising model with a complex transverse field (cTFIM). A crucial feature of our mapping to the cTFIM is an extensive number of local, weak symmetries possessed by the dynamics, allowing us to investigate these observables analytically and uncover 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 nonlocal 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 nonlocal observables show exponential decay on the approach to equilibrium. This transition in () 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.
