Classification of Dipolar Symmetry-Protected Topological Phases: Matrix Product States, Stabilizer Hamiltonians and Finite Tensor Gauge Theories

• URL: http://arxiv.org/abs/2311.04962v1
• Date: Wed, 8 Nov 2023 19:00:00 GMT
• Title: Classification of Dipolar Symmetry-Protected Topological Phases: Matrix Product States, Stabilizer Hamiltonians and Finite Tensor Gauge Theories
• Authors: Ho Tat Lam
• Abstract summary: We classify one-dimensional symmetry-protected topological phases protected by dipole symmetries. For each phase in the classification, we explicitly construct a stabilizer Hamiltonian to realize the SPT phase. These field theories generalize the Dijkgraaf-Witten theories to twisted finite tensor gauge theories.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We classify one-dimensional symmetry-protected topological (SPT) phases protected by dipole symmetries. A dipole symmetry comprises two sets of symmetry generators: charge and dipole operators, which together form a non-trivial algebra with translations. Using matrix product states (MPS), we show that for a $G$ dipole symmetry with $G$ a finite abelian group, the one-dimensional dipolar SPTs are classified by the group $H^2[G\times G,U(1)]/H^2[G,U(1)]^2$. Because of the symmetry algebra, the MPS tensors exhibit an unusual property, prohibiting the fractionalization of charge operators at the edges. For each phase in the classification, we explicitly construct a stabilizer Hamiltonian to realize the SPT phase and derive the response field theories by coupling the dipole symmetry to background tensor gauge fields. These field theories generalize the Dijkgraaf-Witten theories to twisted finite tensor gauge theories.

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