Non-Bloch Dynamical Quantum Phase Transitions with Memory

Abstract

Dynamical quantum phase transitions (DQPTs) of periodic chains are determined by real Bloch momenta. We identify non-Bloch DQPTs, which occur only in open chains and are determined by complex momenta instead. They arise in a Hermitian chain coupled to a simple substrate, whose memory is treated exactly, and originate from the point-gap winding number $W$ of the projected propagator: for $W\neq0$, open boundaries change both the dynamical free energy and the critical times, even in the thermodynamic limit. We find that both follow from an analytic continuation to complex momenta, and show that $W$ can be measured by particle counting. This reveals a dynamical bulk-boundary correspondence, in which non-Hermitian topology emerges from Hermitian dynamics with memory.

Can boundaries change a dynamical quantum phase transition (DQPT) in the thermodynamic limit, and can bulk topology determine when they do? This paper studies a Hermitian, time-reversal-breaking SSH chain coupled to a semi-infinite substrate, retaining the substrate’s memory exactly. The relevant amplitude is $\mathcal D(t)=\det U_S(t)$, with $U_S$ the propagator projected onto the chain; for initially filled, noninteracting fermions on the chain, it is also the many-body Loschmidt amplitude. For the parameter set studied, the open- and periodic-boundary dynamical free energies coincide when the point-gap winding $W$ of $\det U_S(k,t)$ vanishes, despite a skin effect, but differ when $W\ne0$. Periodic-boundary DQPTs at $gt\simeq1.67,3.80,7.05$ disappear under open boundaries. A new open-boundary transition occurs at $gt_p\simeq2.83$, determined by complex momentum with imaginary shift $\mu_p\simeq-0.581$. Analytically continuing the periodic propagator to a zero-winding contour reproduces the open-boundary rate; closure of the zero-winding plateau produces its kink. Fisher-zero calculations and finite-chain extrapolations support this construction. A proposed particle-counting protocol measures $W$ through conditional charge transfer after postselecting a locally restored occupation pattern. Numerically, the correct charge occurs with probability $0.991$ for a four-cell window at $gt=2.5$, but postselection becomes exponentially costly with window size. The study treats one noninteracting model and parameter set; the open-boundary prescription is numerically supported rather than generally proved. Finite-size rounding and exponentially small singular values limit extrapolation near the transition. Experimental tests and interacting extensions remain proposals.