`Gauging' time reversal symmetry in tensor network states

Abstract

It is well known that unitary symmetries can be `gauged', i.e. defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an anti-unitary symmetry. Here we discuss a route to gauging time reversal symmetry which applies to gapped quantum ground states that admit a tensor network representation. The tensor network representation of quantum states provides a notion of locality for the wave function coefficient and hence a notion of locality for the action of complex conjugation in anti-unitary symmetries. Based on that, we show how time reversal can be applied locally and also describe time reversal symmetry twists which act as gauge fluxes through nontrivial loops in the system. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain time reversal symmetric topological phases in $D=1,2$ are readily extracted using these ideas.

13 papges, 16 figures. v2, conclusion changed regarding time reversal symmetric double semion state

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• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
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• Irreducible Projective Representations and Their Physical Applications
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• Entanglement properties of the Haldane phases: A finite system-size approach
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• From gauging to duality in one-dimensional quantum lattice models