Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators

Abstract

Dynamical quantum phase transitions occur in dynamically evolving quantum systems when non-analyticities occur at critical times in the return rate, a dynamical analogue of the free energy. This extension of the concept of phase transitions can be brought into contact with another, namely that of topological phase transitions in which the phase transition is marked by a change in a topological invariant. Following a quantum quench dynamical quantum phase transitions can happen in topological matter, a fact which has already been explored in one dimensional topological insulators and in two dimensional Chern insulators. Additionally in one dimensional systems a dynamical bulk boundary correspondence has been seen, related to the periodic appearance of zero modes of the Loschmidt echo itself. Here we extend both of these concepts to two dimensional higher order topological matter, in which the topologically protected boundary modes are corner modes. We consider a minimal model which encompasses all possible forms of higher order topology in two dimensional topological band structures. We find that DQPTs can still occur, and can occur for quenches which cross both bulk and boundary gap closings. Furthermore a dynamical bulk boundary correspondence is also found, which takes a different form to that in one dimension.

References in corpus (25)

• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Fluctuation theorems: Work is not an observable
• Topology of crystalline insulators and superconductors
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Topological classification of dynamical phase transitions
• Decoherence induced by interacting quantum spin baths
• Mixed state dynamical quantum phase transition and emergent topology
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Loschmidt Echo Revivals: Critical and Noncritical
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• Dynamical Topological Quantum Phase Transitions at Criticality
• Dynamical quantum phase transitions in the quantum Potts chain
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Dynamical quantum phase transition in a system of non-interacting bosons
• Dynamical topological quantum phase transitions in nonintegrable models
• Dynamical phase transitions in dissipative quantum dynamics with quantum optical realization
• Decoherence from spin environments: Loschmidt echo and quasiparticle excitations
• Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Dynamical quantum phase transitions in a spin chain with deconfined quantum critical points
• Dynamical Phase Transitions in Topological Insulators

Cited by in corpus (11)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Emerging topological characterization in non-equilibrium states of quenched Kitaev chains
• Relaxation dynamics in the alternating XY chain following a quantum quench
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter