Classification of Matrix Product States with a Local (Gauge) Symmetry

Abstract

Matrix Product States (MPS) are a particular type of one dimensional tensor network states, that have been applied to the study of numerous quantum many body problems. One of their key features is the possibility to describe and encode symmetries on the level of a single building block (tensor), and hence they provide a natural playground for the study of symmetric systems. In particular, recent works have proposed to use MPS (and higher dimensional tensor networks) for the study of systems with local symmetry that appear in the context of gauge theories. In this work we classify MPS which exhibit local invariance under arbitrary gauge groups. We study the respective tensors and their structure, revealing known constructions that follow known gauging procedures, as well as different, other types of possible gauge invariant states.

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• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks
• Phase diagram of 1+1D Abelian-Higgs model and its critical point
• Field Tensor Network States
• Gauging quantum states with non-anomalous matrix product operator symmetries
• Internal structure of gauge-invariant Projected Entangled Pair States
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Entanglement renormalization and symmetry fractionalization
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions