Bridging Fermionic and Bosonic Short Range Entangled States

Abstract

In this paper we construct bosonic short range entangled (SRE) states in all spatial dimensions by coupling a $Z_2$ gauge field to fermionic SRE states with the same symmetries, and driving the $Z_2$ gauge field to its confined phase. We demonstrate that this approach allows us to construct many examples of bosonic SRE states, and we demonstrate that the previous descriptions of bosonic SRE states such as the semiclassical nonlinear sigma model field theory and the Chern-Simons field theory can all be derived using the fermionic SRE states.

7 pages

References in corpus (38)

• Quantum Spin Hall Effect in Graphene
• Anyons in an exactly solved model and beyond
• Topological Insulators in Three Dimensions
• Topological invariants of time-reversal-invariant band structures
• Periodic table for topological insulators and superconductors
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Topological phases of fermions in one dimension
• Topological Superconductivity and Superfluidity
• Braiding statistics approach to symmetry-protected topological phases
• The effects of interactions on the topological classification of free fermion systems
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Classification of Topological Insulators and Superconductors
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Interacting fermionic topological insulators/superconductors in three dimensions
• Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid
• Interacting topological phases and modular invariance
• Theta-terms in nonlinear sigma-models
• Interaction effect on topological classification of superconductors in two dimensions
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• Topological field theory and thermal responses of interacting topological superconductors
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• Spin-charge Separated Solitons in a Topological Band Insulator
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Wave Functions of Bosonic Symmetry Protected Topological Phases
• Mutual Chern-Simons theory for Z_2 topological order
• Universal Signatures of Fractionalized Quantum Critical Points
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
• Quantum phase transitions between bosonic symmetry protected topological phases in two dimensions: emergent $QE{D}_3$ and anyon superfluid
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation
• Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries
• Short-Range Entangled Bosonic States with Chiral Edge Modes and $T$-duality of Heterotic Strings
• Two dimensional Symmetry Protected Topological Phases with PSU(N) and time reversal symmetry

Cited by in corpus (30)

• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Topological phases protected by point group symmetry
• Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene
• Higher order symmetry-protected topological states for interacting bosons and fermions
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
• Symmetry protected topological phases under decoherence
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
• Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term
• Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1D
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Stripe melting, a transition between weak and strong symmetry protected topological phases
• Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
• Bilayer Graphene as a platform for Bosonic Symmetry Protected Topological States
• Visualizing a Bosonic Symmetry Protected Topological Phase in an Interacting Fermion Model
• Surface field theories of point group symmetry protected topological phases
• Geometry defects in Bosonic symmetry protected topological phases
• Worldsheet matter for electric flux strings
• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
• Interacting Topological Insulators with Synthetic Dimensions
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases
• Realization of the topological Hopf term in two-dimensional lattice models