Matrix Product Operator Constructions for Gauge Theories in the Thermodynamic Limit

Fuente: arXiv
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Main Authors: Godfrey, Nicholas, McCulloch, Ian P.
Format: Preprint
Published: 2025
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author Godfrey, Nicholas
McCulloch, Ian P.
author_facet Godfrey, Nicholas
McCulloch, Ian P.
contents We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space associated with gauge degrees of freedom. In one spatial dimension, Gauss's law permits these gauge fields to be integrated out, yielding an effective Hamiltonian with long-range interactions among matter fields. We construct efficient matrix product operator (MPO) representations of these Hamiltonians directly in the thermodynamic limit. Our formulation naturally includes background fields and $θ$-terms, requiring no modifications to the standard iDMRG algorithm. This provides a broadly applicable framework for 1+1D gauge theories and can be extended to quasi-two-dimensional geometries such as infinite cylinders, where tensor-network methods remain tractable. As a benchmark, we apply our construction to the Schwinger model, reproducing expected features including confinement, string breaking, and the critical behavior at finite mass. Because the method alters only the MPO structure, it can be incorporated with little effort into a wide range of iMPS and infinite-boundary-condition algorithms, opening the way to efficient studies of both equilibrium and non-equilibrium gauge dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2508_14145
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Matrix Product Operator Constructions for Gauge Theories in the Thermodynamic Limit
Godfrey, Nicholas
McCulloch, Ian P.
Strongly Correlated Electrons
High Energy Physics - Lattice
Quantum Physics
We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space associated with gauge degrees of freedom. In one spatial dimension, Gauss's law permits these gauge fields to be integrated out, yielding an effective Hamiltonian with long-range interactions among matter fields. We construct efficient matrix product operator (MPO) representations of these Hamiltonians directly in the thermodynamic limit. Our formulation naturally includes background fields and $θ$-terms, requiring no modifications to the standard iDMRG algorithm. This provides a broadly applicable framework for 1+1D gauge theories and can be extended to quasi-two-dimensional geometries such as infinite cylinders, where tensor-network methods remain tractable. As a benchmark, we apply our construction to the Schwinger model, reproducing expected features including confinement, string breaking, and the critical behavior at finite mass. Because the method alters only the MPO structure, it can be incorporated with little effort into a wide range of iMPS and infinite-boundary-condition algorithms, opening the way to efficient studies of both equilibrium and non-equilibrium gauge dynamics.
title Matrix Product Operator Constructions for Gauge Theories in the Thermodynamic Limit
topic Strongly Correlated Electrons
High Energy Physics - Lattice
Quantum Physics
url https://arxiv.org/abs/2508.14145