Entanglement Spectrum of a Disordered Topological Chern Insulator

Abstract

How much information is stored in the ground-state of a system without \emph{any symmetry} and how can we extract it? This question is investigated by analyzing the behavior of a topological Chern Insulator (CI) in the presence of disorder, with a focus on its entanglement spectrum (EtS) constructed from the ground state. For systems with symmetries, the EtS was shown to contain explicit information revealed by sorting the EtS against the conserved quantum numbers. In the absence of any symmetry, we demonstrate that statistical methods such as the level statistics of the EtS can be equally insightful, allowing us to distinguish when an insulator is in a topological or trivial phase and to map the boundary between the two phases, where EtS becomes entirely delocalized. The phase diagram of a CI is explicitly computed as function of Fermi level ($E_F$) and disorder strength using the level statistics of the EtS and energy spectrum (EnS), together with a computation of the Chern number via an efficient real-space formula.

4.2 pages, 3 figures

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Topological delocalization of two-dimensional massless Dirac fermions
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions
• The edge spectrum of Chern insulators with rough boundaries

Cited by in corpus (29)

• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Virtual Topological Insulators with Real Quantized Physics
• Quantized charge transport in chiral Majorana edge modes
• Bound states and entanglement in the excited states of quantum spin chains
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Determining topological order from a local ground state correlation function
• Quantum criticality at the Chern-to-normal insulator transition
• Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States
• Disordered Chern insulator with a two step Floquet drive
• Entanglement Spectra of the quantum hard-square model: Holographic minimal models
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Disorder effects in correlated topological insulators
• Entanglement Chern number for an extensive partition of a topological ground state
• The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• On integrable matrix product operators with bond dimension $D=4$