Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries

Abstract

We present a fully many-body formulation of topological invariants for various topological phases of fermions protected by antiunitary symmetry, which does not refer to single particle wave functions. For example, we construct the many-body ${\mathbb{Z}}_2$ topological invariant for time-reversal symmetric topological insulators in two spatial dimensions, which is a many-body counterpart of the Kane-Mele ${\mathbb{Z}}_2$ invariant written in terms of single-particle Bloch wave functions. We show that an important ingredient for the construction of the many-body topological invariants is a fermionic partial transpose which is basically the standard partial transpose equipped with a sign structure to account for anti-commuting property of fermion operators. We also report some basic results on various kinds of pin structures -- a key concept behind our strategy for constructing many-body topological invariants -- such as the obstructions, isomorphism classes, and Dirac quantization conditions.

83 pages, 23 figures. references added

References in corpus (18)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Entanglement negativity in quantum field theory
• On the $Z_2$ classification of Quantum Spin Hall Models
• Topology of density matrices
• On the partial transpose of fermionic Gaussian states
• Two-Dimensional Density-Matrix Topological Fermionic Phases: Topological Uhlmann Numbers
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Topological indices for open and thermal systems via Uhlmann's phase
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Topological Phases Protected By Reflection Symmetry and Cross-cap States
• CPT theorem and classification of topological insulators and superconductors
• Topological order of mixed states in quantum many-body systems
• Universal entropy of conformal critical theories on a Klein bottle
• Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions

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