Examples of symmetry-preserving truncations in tensor field theory

Abstract

We consider the tensor formulation of the non-linear O(2) sigma model and its gauged version (the compact Abelian Higgs model), on a $D$-dimensional cubic lattice, and show that tensorial truncations are compatible with the general identities derived from the symmetries of these models. This means that the universal properties of these models can be reproduced with highly simplified formulations desirable for implementations with quantum computers or for quantum simulations experiments. We briefly discuss the extensions to non-Abelian symmetries and models with fermions.

arXiv commentComments and new section on non-Abelian symmetries and pure gauge models added, 8 pages, uses Revtex

References in corpus (29)

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Tensor renormalization group approach to 2D classical lattice models
• Corner Transfer Matrix Renormalization Group Method
• Coarse-graining renormalization by higher-order singular value decomposition
• Tensor Network Renormalization
• Worm algorithms for classical statistical models
• Quantum Link Models: A Discrete Approach to Gauge Theories
• Second Renormalization of Tensor-Network States
• QCD as a Quantum Link Model
• Faster Methods for Contracting Infinite 2D Tensor Networks
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Exact blocking formulas for spin and gauge models
• Tensor renormalization group study of classical XY model on the square lattice
• Quantum simulation of the universal features of the Polyakov loop
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Grassmann tensor renormalization group for one-flavor lattice Gross-Neveu model with finite chemical potential
• Renormalization group flows of Hamiltonians using tensor networks
• Controlling sign problems in spin models using tensor renormalization
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• Finite size effects in the presence of a chemical potential: A study in the classical non-linear O(2) sigma-model
• A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory
• Universal features of the Abelian Polyakov loop in 1+1 dimension
• Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group
• Progress towards quantum simulating the classical O(2) model
• Accurate exponents from approximate tensor renormalizations
• The fine structure of the entanglement entropy in the classical XY model
• Tensor Renormalization Group Algorithms with a Projective Truncation Method

Cited by in corpus (8)

• Quantum Simulation for High Energy Physics
• General Methods for Digital Quantum Simulation of Gauge Theories
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model
• Discrete aspects of continuous symmetries in the tensorial formulation of Abelian gauge theories
• Clock model interpolation and symmetry breaking in O(2) models
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions