Higher structures in matrix product states

• URL: http://arxiv.org/abs/2304.05356v2
• Date: Sat, 15 Apr 2023 13:30:22 GMT
• Title: Higher structures in matrix product states
• Authors: Shuhei Ohyama, Shinsei Ryu
• Abstract summary: We introduce a gerbe structure, a higher generalization of complex line bundles, as an underlying mathematical structure describing topological properties of a parameterized family of matrix product states. We also introduce a "triple inner product" for three matrix product states, which allows us to extract a topological invariant, the Dixmier-Douady class over the parameter space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For a parameterized family of invertible states (short-range-entangled states) in $(1+1)$ dimensions, we discuss a generalization of the Berry phase. Using translationally-invariant, infinite matrix product states (MPSs), we introduce a gerbe structure, a higher generalization of complex line bundles, as an underlying mathematical structure describing topological properties of a parameterized family of matrix product states. We also introduce a "triple inner product" for three matrix product states, which allows us to extract a topological invariant, the Dixmier-Douady class over the parameter space.

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