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Higher structures in matrix product states
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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.
Forward citations
Cited by 2 Pith papers
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Higher Structures on Boundary Conformal Manifolds: Higher Berry Phase and Boundary Conformal Field Theory
A 2-form higher Berry connection on boundary conformal manifolds is defined from boundary-condition-changing operator OPE phases; it reproduces the B-field and WZ term in string theory examples.
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Space of conformal boundary conditions from the view of higher Berry phase: Flow of Berry curvature in parametrized BCFTs
In a Dirac fermion BCFT with SU(2) conformal boundary conditions parametrized by a three-sphere, the filled Fermi sea carries a higher Berry curvature whose integral is quantized, realizing Berry curvature flow and Ch...
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