Signature of Phase Transitions in the Disordered Quantum Spin Hall State From the Entanglement Spectrum

Abstract

Of the available classes of insulators which have been shown to contain topologically non-trivial properties one of the most important is class AII, which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$ This class has been the subject of significant attention as it encompasses non-trivial Z${}_2$ topological insulators such as the quantum spin Hall (QSH) state and the 3D strong topological insulator. One of the defining properties of this system is the robustness of the state under the addition of disorder that preserves $T.$ In this letter, we explore the phase diagram of the disordered QSH state as a function of disorder strength and chemical potential by examining the entanglement spectrum for disordered class AII symplectic systems. As for the case of the $T$ breaking Chern insulator we show that there is a correspondence between the level-spacing statistics of the Hamiltonian and that of the level spacing statistics of the entanglement spectrum. We observe a feature in the statistics of the entanglement spectrum that aids the identification of delocalized states and consequently critical energies across which phase transitions occur.

5 pages, 4 figures

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• The Quantum Spin Hall Effect: Theory and Experiment
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells

Cited by in corpus (11)

• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• AIII and BDI Topological Systems at Strong Disorder
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Characterizing disordered fermion systems using the momentum-space entanglement spectrum
• Maximally Entangled Mode, Metal-Insulator Transition and Violation of Entanglement Area Law in Non-interacting Fermion Ground States
• Entanglement entropy of (3+1)D topological orders with excitations
• Anderson Topological Superconductor
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Entanglement analysis of isotropic spin-1 chains
• Correspondence between many-particle excitations and the entanglement spectrum of disordered ballistic one-dimensional systems
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor