It has recently been established that open quantum systems may exhibit a strong spectral sensitivity to boundary conditions, known as the non-Hermitian/Liouvillian skin effect (NHSE/LSE), making the topological properties of the system boundary-condition sensitive. In this Letter, we ask the query: Can topological phase transitions of open quantum systems, captured by open boundary conditioned invariants, be observed in the dynamics of a system under periodic boundary conditions, even in the presence of NHSE/LSE? We affirmatively respond to this question, by considering the quench dynamics of entanglement spectrum in a periodic open quantum fermionic system. We demonstrate that the entanglement spectrum exhibits zero-crossings only when this periodic system is quenched from a topologically trivial to nontrivial phase, defined from the spectrum under open boundary conditions, even in systems featuring LSE. Our results reveal that non-Hermitian topological phases leave a distinctive imprint on the unconditional dynamics within a subsystem of fermionic systems.
Dynamical phase transitions (DPT) are receiving a rising interest. They are known to behave analogously to equilibrium phase transitions (EPT) to a large extend. However, it is easy to see that DPT can occur in finite systems, while EPT are only possible in the thermodynamic limit. So far it is not clear how far the analogy of DPT and EPT goes. It was suggested, that there is a relation between topological phase transitions (TPT) and DPT, but many open questions remain. Typically, to study DPT, the Loschmidt echo (LE) after a quench is investigated, where DPT are visible as singularities. For one-dimensional systems, each singularity is connected to a certain critical time scale, which is given by the dispersion in the chain. In topological free-fermion models with winding numbers 0 or 1, only the LE in periodic boundary conditions (PBC) has been investigated. In open boundary conditions (OBC), these models are characterized by symmetry protected edge modes in the topologically non-trivial phase. It is completely unclear how these modes affect DPT. We investigate systems with PBC governed by multiple time scales with a Z topological invariant. In OBC, we provide numerical evidence for the presence of bulk-boundary correspondence in DPT in quenches across a TPT.
Entanglement entropy has proven to be a powerful probe of phenomena such as quantum chaos and phase transitions. Pseudo entropy is a recently proposed time-like generalization of an entanglement measure, motivated by de Sitter holography. In this work, we find that pseudo entropy can also serve as a novel probe for distinguishing topological phases of matter. For this, we consider the Su--Schrieffer--Heeger model as a representative example and investigate the averaged excess entropy
ΔS12, defined as the difference between pseudo entropy and the average entanglement entropy, across the topological-to-trivial and trivial-to-topological phase transitions. When the two states are in the same phase, we find that $ ΔS_{12}$ is non-positive under periodic boundary conditions, while for open boundary conditions, it is non-positive only when the system is sufficiently large. Moreover, we analyze ground-state quench protocols for topology-crossing quenches and find that the imaginary pseudo entropy tracks the critical times predicted by the Fisher zeros.
We investigate dissipation-driven topological phase transitions in one-dimensional quantum open systems governed by the Lindblad equation with linear dissipation operators, which ensure the density matrix retains its Gaussian form throughout the dynamics. By employing the modular Hamiltonian framework, we rigorously demonstrate that the
Z2 topological invariant characterizing steady states in one-dimensional class D systems is exclusively dependent on the dissipation operators, rather than the system Hamiltonian. Through a sudden quench protocol where the system evolves from the steady state of one Lindbladian to another, we reveal that topological transitions can occur at analytically predictable critical times, even when the initial and final steady states share identical topological indices. These transitions are shown, both analytically and numerically, to depend solely on dissipation parameters. Entanglement spectrum analysis demonstrates bulk-edge correspondence in non-equilibrium density matrices via coexisting single-particle gap closures (periodic boundaries) and topologically protected zero modes (open boundaries), directly underpinning the detection of dissipation-induced topology in quantum simulators.