Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces

Abstract

How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. From a dimension reduction approach, we propose the concept of high-order band inversion surfaces (BISs) which enable the optimal schemes to characterize equilibrium topological phases by far-from-equilibrium quantum dynamics, and further report the experimental simulation. We show that characterization of a d-dimensional (dD) topological phase can be reduced to lower-dimensional topological invariants in the high-order BISs, of which the nth-order BIS is a (d-n)D interface in momentum space. In quenching the system from trivial phase to topological regime, we unveil a high-order dynamical bulk-surface correspondence that the quantum dynamics exhibits nontrivial topological pattern in arbitrary nth-order BISs, which universally corresponds to and so characterizes the equilibrium topological phase of the post-quench Hamiltonian. This high-order dynamical bulk-surface correspondence provides new and optimal dynamical schemes with fundamental advantages to simulate and detect topological states, in which through the highest-order BISs that are of zero dimension, the detection of topological phase relies on only minimal measurements. We experimentally build up a quantum simulator with spin qubits to investigate a 3D chiral topological insulator through emulating each momentum one by one and measure the high-order dynamical bulk-surface correspondence, with the advantages of topological characterization via highest-order BISs being demonstrated.

References in corpus (56)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• The nitrogen-vacancy colour centre in diamond
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Quantized Electric Multipole Insulators
• Topological Materials: Weyl Semimetals
• Experimental discovery of Weyl semimetal TaAs
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Topological superconductors: a review
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• A Four Dimensional Generalization of the Quantum Hall Effect
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topology of crystalline insulators and superconductors
• Dynamic polarization of single nuclear spins by optical pumping of NV color centers in diamond at room temperature
• Observation of a dynamical topological phase transition
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Topological classification with additional symmetries from Clifford algebras
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Dynamical preparation of Floquet Chern insulators
• Measuring topology by dynamics: Chern number from linking number
• Realization of ideal Weyl semimetal band in ultracold quantum gas with 3D Spin-Orbit coupling
• Uncover Topology by Quantum Quench Dynamics
• Quantum Quenches in Chern Insulators
• Observation of symmetry-protected topological band with ultracold fermions
• Dynamical classification of topological quantum phases
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Observation of nodal-line semimetal with ultracold fermions in an optical lattice
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• Dynamical Buildup of a Quantized Hall Response from Non-Topological States
• Boundary-bulk relation in topological orders
• Dynamical detection of topological charges
• Observing topological charges and dynamical bulk-surface correspondence with ultracold atoms
• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Classification of topological insulators and superconductors out of equilibrium
• Quantum simulation for three-dimensional chiral topological insulator
• Unified theory to characterize Floquet topological phases by quench dynamics
• Experimental Detection of the Quantum Phases of a Three-Dimensional Topological Insulator on a Spin Quantum Simulator
• Characterizing topological phases by quantum quenches: A general theory
• Experimental observation of dynamical bulk-surface correspondence for topological phases
• T-duality simplifies bulk-boundary correspondence
• T-duality and the bulk-boundary correspondence

Cited by in corpus (23)

• Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Topological holographic quench dynamics in a synthetic dimension
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Unified characterization for higher-order topological phase transitions
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
• Unconventional Floquet topological phases from quantum engineering of band inversion surfaces
• Emergent topology and symmetry-breaking order in correlated quench dynamics
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Generic theory of characterizing topological phases under quantum slow dynamics
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Topological spin-orbit-coupled fermions beyond rotating wave approximation
• Unconventional hybrid-order topological insulators
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Dynamical characterization of topological phases beyond the minimal models
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Generic reduction theory for Fermi sea topology in metallic systems
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• Loop unitary and phase band topological invariant in generic multi-band Chern insulators
• Observation of symmetry-protected selection rules in periodically driven quantum systems