Counting gauge-invariant states with matter fields and finite gauge groups

Abstract

Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we generalize this counting to include the case of scalar and fermionic matter, as well as various kinds of boundary conditions. As a byproduct, we consider several related questions, such as the implementation of charge conjugation for a generic finite group. These results are relevant for resource estimation and also as a crosscheck when working in a gauge-invariant basis.

arXiv comment42 pages, 2 figures. Matches journal version

References in corpus (39)

• Spin Network States in Gauge Theory
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Digitization of Scalar Fields for Quantum Computing
• CP Violation from Finite Groups
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Loop, String, and Hadron Dynamics in SU(2) Hamiltonian Lattice Gauge Theories
• Gluon Field Digitization for Quantum Computers
• Solving Gauss's Law on Digital Quantum Computers with Loop-String-Hadron Digitization
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Charged hadrons in local finite-volume QED+QCD with C* boundary conditions
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Phase Transitions in $Z_n$ Gauge Models: Towards Quantum Simulations of the Schwinger-Weyl QED
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Eliminating fermionic matter fields in lattice gauge theories
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• Primitive Quantum Gates for an SU(2) Discrete Subgroup: BT
• Scars from protected zero modes and beyond in $U(1)$ quantum link and quantum dimer models
• Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
• Lattice Abelian-Higgs model with noncompact gauge fields
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• The basis of the physical Hilbert space of lattice gauge theories
• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
• Comments on the classification of the finite subgroups of SU(3)
• Generalized liquid crystals: giant fluctuations and the vestigial chiral order of $I$, $O$ and $T$ matter
• Primitive Quantum Gates for an SU(3) Discrete Subgroup: $\Sigma (36\times 3)$
• Unexpected results in asymptotically free quantum field theories
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group
• Quantum Yang-Mills theory: an overview of a programme
• Sublattice scars and beyond in two-dimensional $U(1)$ quantum link lattice gauge theories
• Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematics
• Nonlinear Realization of Chiral Symmetry on the Lattice
• Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
• CP as a Symmetry of Symmetries
• Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups
• Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories
• Higgs Phases and Boundary Criticality
• Spontaneous symmetry breaking in a $SO(3)$ non-Abelian lattice gauge theory in $2+1$D with quantum algorithms
• Quantum Simulation with Gauge Fixing: from Ising Lattice Gauge Theory to Dynamical Flux Model
• Toolkit for Scalar Fields in Universes with finite-dimensional Hilbert Space