A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States

Abstract

In an earlier work we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension $d$, the critical states of fermionic SPT phase transitions has an emergent $Z_2^T$ symmetry and can be realized on the boundary of a $d+1$-dimensional bulk SPT with an extra $Z_2^T$ symmetry.

arXiv comment35 pages, 10 figures

References in corpus (14)

• Classification of topological insulators and superconductors in three spatial dimensions
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum of topological insulators and superconductors
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Symmetry protected topological phases from decorated domain walls
• A geometric proof of the equality between entanglement and edge spectra
• Symmetry protected topological phases in non-interacting fermion systems
• Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases
• The effects of interaction on quantum spin Hall insulators
• Edge quantum criticality and emergent supersymmetry in topological phases
• Quantum Phase Transitions Between a Class of Symmetry Protected Topological States
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Exactly Solvable Model for Two Dimensional Topological Superconductor
• The "non-regularizability" of gapless free fermion Hamiltonian protected by on-site symmetries

Cited by in corpus (8)

• Holographic theory for continuous phase transitions -- the emergence and symmetry protection of gaplessness
• Pivot Hamiltonians as generators of symmetry and entanglement
• Building models of topological quantum criticality from pivot Hamiltonians
• Non-abelian bosonization in two and three spatial dimensions and applications
• Bootstrapping Lieb-Schultz-Mattis anomalies
• Dynamic critical exponents as an emergent property at interacting topological quantum critical points
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions