Unitary preparation of many body Chern insulators: Adiabatic bulk boundary correspondence

Abstract

We approach the long-standing problem of preparing an out-of-equilibrium many-body Chern insulator (CI) and associated bulk-boundary correspondence unitarily. Herein, this is addressed by constructing a dynamical many-body Chern invariant exploiting the property of the bulk macroscopic electric polarisation (Resta polarisation) of the CI. This Chern invariant defined from observable correlations is also established to topologically classify many body Chern states in equilibrium. The non-equilibrium behavior of the invariant is probed by ramping the paradigmatic Haldane model of graphene from its trivial to the topological phase. We show that a non-linear ramp may work more efficiently in approaching the topological state, thereby establishing the existence of an optimal topological state preparation. Furthermore, to ensure the near adiabatic dynamics across the quantum critical point, we propose a novel counter-diabatic scheme. The topological nature of the prepared state is firmly established by observing an emerging $U(1)$ topological charge. We also compute the edge current in the time evolved state of the system under a semi-periodic boundary condition and clearly establish an adiabatic bulk-boundary correspondence which firmly ensconces the validity of the many-body invariant.

arXiv comment17 Pages, 9 figures, title modified, changed figures and text, Appendices added

References in corpus (77)

• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Anyons in an exactly solved model and beyond
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Nonequilibrium dynamics of closed interacting quantum systems
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Detecting topological order in a ground state wave function
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Search for Majorana fermions in superconductors
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Photovoltaic Hall effect in graphene
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• All-graphene integrated circuits via strain engineering
• Topological orders and Edge excitations in FQH states
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Introduction to topological superconductivity and Majorana fermions
• Dynamics of a Quantum Phase Transition
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• The Quantum-Mechanical Position Operator in Extended Systems
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamical quantum phase transitions: a review
• Universal adiabatic dynamics across a quantum critical point
• Floquet topological insulators
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• Floquet generation of Majorana end modes and topological invariants
• Multiterminal Conductance of a Floquet Topological Insulator
• Dynamical Topological Order Parameters far from Equilibrium
• Out of equilibrium electrons and the Hall conductance of a Floquet topological insulator
• The Kibble-Zurek Problem: Universality and the Scaling Limit
• A Short Introduction to Topological Quantum Computation
• Topological classification of dynamical phase transitions
• Transport signatures of Floquet Majorana fermions in driven topological superconductors
• Defect production in non-linear quench across a quantum critical point
• Floquet-engineering counterdiabatic protocols in quantum many-body systems
• Dynamical preparation of Floquet Chern insulators
• Topology induced anomalous defect production by crossing a quantum critical point
• Quantum Quenches in Chern Insulators
• Optimal non-linear passage through a quantum critical point
• Slow quenches in a quantum Ising chain; dynamical phase transitions and topology
• Understanding electron behavior in strained graphene as a reciprocal space distortion
• Pseudo magnetic field in strained graphene: revisited
• Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
• Electric polarization in a Chern insulator
• Quench-induced Floquet topological p-wave superfluids
• Critical dynamics of decoherence
• Topology of one dimensional quantum systems out of equilibrium
• Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
• Persistent Hall response in a quantum quench
• Strain controlled valley filtering in multi-terminal graphene structures
• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Phase transitions and adiabatic preparation of a fractional Chern insulator in a boson cold atom model
• Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model
• Survival probability of an edge Majorana in a 1-D p-wave superconducting chain under sudden quenching of parameters
• Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons
• The scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points
• Effective Dirac Hamiltonian for anisotropic honeycomb lattices: optical properties
• Stroboscopic versus non-stroboscopic dynamics in the Floquet realization of the Harper-Hofstadter Hamiltonian
• Dynamical band gap tuning in Weyl semi-metals by intense elliptically polarized normal illumination and its application to $8-Pmmn$ borophene
• Signatures of topology in quantum quench dynamics and their interrelation
• Quenching in Chern insulators with satellite Dirac points: The fate of edge states
• Topology and edge states survive quantum criticality between topological insulators
• Dynamics of edge current in a linearly quenched Haldane model
• Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven SSH chain
• Dynamical preparation of a topological state and out of equilibrium bulk boundary correspondence in a SSH chain under periodic driving

Cited by in corpus (6)

• Driven quantum many-body systems and out-of-equilibrium topology
• Dissipative preparation of many-body Floquet Chern insulators
• Counterdiabatic route for preparation of state with long-range topological order
• Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
• Bilayer Haldane system: Topological characterization and adiabatic passages connecting Chern phases
• Universal Landau-Zener regimes in dynamical topological phase transitions