Gauging quantum states with non-anomalous matrix product operator symmetries

Abstract

Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When this happens the symmetry is dubbed anomalous. Such obstructions are related to the fact that the global symmetry cannot be written as a tensor product of local operators. In this manuscript we study non-local symmetries that have an additional structure: they take the form of a matrix product operator (MPO). We exploit the tensor network structure of the MPOs to construct local operators from them satisfying the same group relations, that is, we are able to localize even anomalous MPOs. For non-anomalous MPOs, we use these local operators to explicitly gauge the MPO symmetry of a one-dimensional quantum state obtaining non-trivial gauged states. We show that our gauging procedure satisfies all the desired properties as the standard on-site case does. We also show how this procedure is naturally represented in matrix product states protected by MPO symmetries. In the case of anomalous MPOs, we shed light on the obstructions to gauging these symmetries.

arXiv comment13 pages, 1 figure v2: minor typos corrected, projection to ungauge added and section with examples added

References in corpus (23)

• Symmetry protected topological orders and the group cohomology of their symmetry group
• An Area Law for One Dimensional Quantum Systems
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Classifying quantum phases using Matrix Product States and PEPS
• 2D symmetry protected topological orders and their protected gapless edge excitations
• On finite symmetries and their gauging in two dimensions
• PEPS as ground states: degeneracy and topology
• Solving Gapped Hamiltonians Locally
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Entropy and Entanglement in Quantum Ground States
• Anyons and matrix product operator algebras
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Lattice Gauge Tensor Networks
• Building Projected Entangled Pair States with a Local Gauge Symmetry
• Characterizing Topological Order with Matrix Product Operators
• A generalization of the injectivity condition for Projected Entangled Pair States
• Normal projected entangled pair states generating the same state
• Classification of Matrix Product States with a Local (Gauge) Symmetry

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