Tensor Networks for Lattice Gauge Theories with continuous groups

Abstract

We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge invariant states that can be used in actual numerical computation. Our construction is also applied to the simplest realization of the quantum link models/gauge magnets and provides a clear way to understand their microscopic relation with Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge invariant operators that modify continuously Rokshar-Kivelson wave functions and can be used to extend the phase diagram of known models. As an example we characterize the transition between the deconfined phase of the $Z_2$ lattice gauge theory and the Rokshar-Kivelson point of the U(1) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.

27 pages, 25 figures, 2nd version the same as the published version

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Cited by in corpus (13)

• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Quantum phases of Rydberg atoms on a kagome lattice
• Many-body localization dynamics from gauge invariance
• Digital lattice gauge theories
• Gauging quantum states: from global to local symmetries in many-body systems
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Tensor renormalization group study of the non-Abelian Higgs model in two dimensions
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Gauge Theories with Ultracold Atoms
• Selected topics of quantum computing for nuclear physics
• Simulating both parity sectors of the Hubbard Model with Tensor Networks
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states