Lattice Gauge Tensor Networks

Abstract

We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant subspace. Compared to a standard tensor network description, the gauge invariant one allows to speed-up real and imaginary time evolution of a factor that is up to the square of the dimension of the link variable. The gauge invariant tensor network description is based on the quantum link formulation, a compact and intuitive formulation for gauge theories on the lattice, and it is alternative to and can be combined with the global symmetric tensor network description. We present some paradigmatic examples that show how this architecture might be used to describe the physics of condensed matter and high-energy physics systems. Finally, we present a cellular automata analysis which estimates the gauge invariant Hilbert space dimension as a function of the number of lattice sites and that might guide the search for effective simplified models of complex theories.

28 pages, 9 figures

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• DMRG and periodic boundary conditions: a quantum information perspective
• Criticality, the area law, and the computational power of PEPS
• Topological Order and Conformal Quantum Critical Points
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Continuous Matrix Product States for Quantum Fields
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Optical Abelian Lattice Gauge Theories
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Entanglement renormalization and gauge symmetry
• Simulation of time evolution with the MERA
• Density Matrix Renormalization Group for Dummies

Cited by in corpus (8)

• A Formulation of Lattice Gauge Theories for Quantum Simulations
• 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
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states