Topological Phase Transitions for Interacting Finite Systems

Abstract

In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the topological transition, even in finite-size systems. Spatial symmetries are argued to play a fundamental role in the selection of the boundary conditions to be used to locate topological transitions in finite systems. We discuss the theoretical implications of this result, and utilize exact diagonalization to demonstrate its manifestations in the Haldane-Fermi-Hubbard model. Our findings provide an efficient way to detect topological transitions in experiments and in numerical calculations that cannot access the ground-state wave function.

5 pages, 3 figures. Updated text and references to match published version

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• Characterization of a topological Mott insulator in one dimension
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• Interaction driven phases in the honeycomb lattice from exact diagonalization
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• Interaction-induced anomalous quantum Hall state on the honeycomb lattice
• First order topological phase transition of the Haldane--Hubbard model
• Topological transitions of interacting bosons in one-dimensional bi-chromatic optical lattices
• Topological order in a correlated Chern insulator
• Diagnosis of interaction-driven topological phase via exact diagonalization
• Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
• Dropping an impurity into a Chern insulator: a polaron view on topological matter
• Competing Chiral Orders in the Topological Haldane-Hubbard Model of Spin-1/2 Fermions and Bosons
• 1/4 is the new 1/2 when topology is intertwined with Mottness
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Interaction effect in two-dimensional Dirac fermions
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Edge excitations of bosonic fractional quantum Hall phases in optical lattices
• Interaction-Induced Topological and Magnetic Phases in the Hofstadter-Hubbard Model
• Topological Mott insulators of ultracold atomic mixtures induced by interactions in one-dimensional optical superlattices
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Nonlinear Dirac Cones
• Change of an insulator's topological properties by a Hubbard interaction
• Interacting Stochastic Topology and Mott Transition from Light Response
• Weyl-type topological phase transitions in fractional quantum Hall like systems
• Mean field study of the topological Haldane-Hubbard model of spin-$1/2$ fermions
• Quantum phases of disordered flatband lattice fractional quantum Hall systems
• Topological Phase Transition in the Hofstadter-Hubbard Model
• Interplay of interactions, disorder and topology in the Haldane-Hubbard model
• Topological Invariants and Ground-State Wave Functions of Topological Insulators on a Torus
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• Theory of competing Chern-Simons orders and emergent phase transitions
• Topological phase transitions and universality in the Haldane-Hubbard model
• Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions
• Topological Phases of Fermionic Ladders with Periodic Magnetic Fields
• Phase transitions in the Haldane-Hubbard model
• Correlation-driven phase transition in a Chern insulator
• Adiabatic continuity, wavefunction overlap and topological phase transitions
• Topological phase transitions with and without energy gap closing
• Quantum phases of strongly-interacting bosons on a two-leg Haldane ladder
• Polaron in a $p+ip$ Fermi topological superfluid
• Fibonacci anyon excitations of one-dimensional dipolar lattice bosons
• Nature of continuous phase transitions in interacting topological insulators
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Photoinduced anomalous Hall effect in the interacting Haldane model: targeting topological states with pump pulses
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Hubbard model on the kagome lattice with time-reversal invariant flux and spin-orbit coupling
• From Fractional Quantum Anomalous Hall Smectics to Polar Smectic Metals: Nontrivial Interplay Between Electronic Liquid Crystal Order and Topological Order in Correlated Topological Flat Bands
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Phase transitions in the Haldane-Hubbard model with ionic potentials
• Quantum Monte Carlo simulation of topological phase transitions
• Topological insulator on honeycomb lattices and ribbons without inversion symmetry
• Winding number order in the Haldane model with interactions
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• Thermodynamic and topological phase diagrams of correlated topological insulators
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• Enhanced superconductivity and various edge modes in modulated $t$-$J$ chains
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