Dynamic transition of the density-matrix topology under parity-time symmetry
arXiv:2404.14776 · doi:10.1103/PhysRevB.110.155141
Abstract
Density-matrix topology, defined through the geometric property of the relevant modular Hamiltonian, can undergo transitions in the corresponding open-system dynamics. While symmetry considerations are crucial to ensure such a dynamic topological transition, we show that a hidden parity-time symmetry can further facilitate it. Considering the Lindbladian dynamics of a fermionic Gaussian state, we extract the time-evolved density-matrix topology from the single-particle correlation, whose dynamics is governed by a non-Hermitian damping matrix. We show that, for a parity-time symmetric damping matrix and a chiral symmetric correlation matrix, a dynamic transition in the density-matrix topology necessarily occurs in the parity-time unbroken regime where eigenvalues of the damping matrix are real. We illustrate our results using a concrete model, and map out the dynamic phase diagram.Remarkably, we find that the dynamic transition can also happen periodically in the parity-time symmetry broken regime.
arXiv comment9 pages, 2 figures
References in corpus (46)
- Topological Insulators
- Topological insulators and superconductors
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Gaussian Quantum Information
- Making Sense of Non-Hermitian Hamiltonians
- Edge states and topological invariants of non-Hermitian systems
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Topological phases of non-Hermitian systems
- Symmetry and Topology in Non-Hermitian Physics
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Nonlinear waves in -symmetric systems
- Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
- Non-Hermitian skin effect and chiral damping in open quantum systems
- Non-Hermitian Topology and Exceptional-Point Geometries
- Topology by Dissipation in Atomic Quantum Wires
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
- Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
- Observation of a dynamical topological phase transition
- Topological Non-Hermitian skin effect
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
- Uncover Topology by Quantum Quench Dynamics
- Measuring Topological Number of a Chern-Insulator from Quench Dynamics
- Quantum Quenches in Chern Insulators
- Quantum jumps in the non-Hermitian dynamics of a superconducting qubit
- Dynamical classification of topological quantum phases
- Topology of density matrices
- Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
- Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
- Dynamical Control of Quantum Heat Engines Using Exceptional Points
- Density Matrix Topological Insulators
- Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
- Probing the topology of density matrices
- Dynamical topological invariant after a quantum quench
- Topology of one dimensional quantum systems out of equilibrium
- Topological Entanglement-Spectrum Crossing in Quench Dynamics
- Persistent Hall response in a quantum quench
- Fixed points and emergent topological phenomena in a parity-time-symmetric quantum quench
- Homotopy, Symmetry, and Non-Hermitian Band Topology
- Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
- Many-body non-Hermitian skin effect under dynamic gauge coupling
- Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
- Finite-temperature topological invariant for interacting systems
- Chiral state transfer under dephasing
- Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
- Topological characterization of one-dimensional open fermionic systems