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Gauge Loop-String-Hadron Formulation on General Graphs and Applications to Fully Gauge Fixed Hamiltonian Lattice Gauge Theory

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arxiv 2409.13812 v2 pith:3NTVMMK7 submitted 2024-09-20 hep-lat hep-phhep-thquant-ph

I. M. Burbano , Christian W. Bauer This is my paper · ORCID
classification hep-lathep-phhep-thquant-ph
keywords gaugegeneralformulationgraphstheorydefineddevelopfixed
verification ladder T0 review T1 audit T2 compute T3 formal

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We develop a gauge invariant, Loop-String-Hadron (LSH) based representation of SU(2) Yang-Mills theory defined on a general graph consisting of vertices and half-links. Inspired by weak coupling studies, we apply this technique to maximal tree gauge fixing. This allows us to develop a fully gauge fixed representation of the theory in terms of LSH quantum numbers. We explicitly show how the quantum numbers in this formulation directly relate to the variables in the magnetic description. In doing so, we will also explain in detail the way that the Kogut-Susskind formulation, prepotentials, and point splitting, work for general graphs. In the appendix of this work we provide a self-contained exposition of the mathematical details of Hamiltonian pure gauge theories defined on general graphs.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Local Thermalization of SU(2) Lattice Gauge Fields on Quantum Computers

    hep-lat 2026-03 unverdicted novelty 7.0 of 10

    Quantum hardware simulation of SU(2) lattice gauge thermalization matches classical extrapolations up to 101 plaquettes after error mitigation, establishing feasibility for chaotic quantum field systems.

  2. Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories

    quant-ph 2025-11 conditional novelty 6.0 of 10

    Gauss's law constraints in jmax=1/2 SU(2) lattice gauge theory are converted into stabilizer codes that correct single-qubit errors using about 9N or 12N physical qubits per N plaquettes.

  3. Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory

    hep-lat 2025-09 conditional novelty 6.0 of 10

    A site-singlet energy truncation plus strong-coupling-perturbation-inspired circuits prepares SU(3) lattice gauge theory ground states with percent-level fidelity at g≈1 on small lattices, with reduced resource costs.

  4. Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions

    hep-th 2025-09 conditional novelty 6.0 of 10

    Exact diagonalization shows 1+1D SU(2) lattice gauge theory with dynamical fermions satisfies ETH, including for non-local string operators that display a memory peak.

  5. Obtaining continuum physics from dynamical simulations of Hamiltonian lattice gauge theories

    hep-lat 2025-06 conditional novelty 6.0 of 10

    The paper introduces the SBTE protocol, which treats approximate time evolution error as negligible once it is below statistical uncertainty, and shows this makes continuum-limit renormalization in lattice gauge theor...

  6. Quantum computation of hadron scattering in a lattice gauge theory

    quant-ph 2025-05 conditional novelty 6.0 of 10

    On a trapped-ion quantum computer, the authors prepared multiple meson wave packets and simulated their early-time collisions in a 1+1D Z2 lattice gauge theory.

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