We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new “sequestered” basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.
Grabowska, Dorota M., Kane, Christopher F., & Bauer, Christian W. (2025). Fully gauge-fixed SU(2) Hamiltonian for quantum simulations. Physical Review D, 111(11). https://doi.org/10.1103/physrevd.111.114516
Grabowska, Dorota M., Kane, Christopher F., and Bauer, Christian W., "Fully gauge-fixed SU(2) Hamiltonian for quantum simulations," Physical Review D 111, no. 11 (2025), https://doi.org/10.1103/physrevd.111.114516
@article{osti_2998372,
author = {Grabowska, Dorota M. and Kane, Christopher F. and Bauer, Christian W.},
title = {Fully gauge-fixed SU(2) Hamiltonian for quantum simulations},
annote = {We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new “sequestered” basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.},
doi = {10.1103/physrevd.111.114516},
url = {https://www.osti.gov/biblio/2998372},
journal = {Physical Review D},
issn = {ISSN 2470-0029},
number = {11},
volume = {111},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2025},
month = {06}}
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
Quantum Information Science Enabled Discovery (QuantISED) for High Energy Physics; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Nuclear Physics (NP)