Abstract
The question of how to efficiently formulate Hamiltonian gauge theories is experiencing renewed interest due to advances in building quantum simulation platforms. We introduce a reformulation of an SU(2) Hamiltonian lattice gauge theory---a loop-string-hadron (LSH) formulation---that describes dynamics directly in terms of its loop, string, and hadron degrees of freedom, while alleviating several disadvantages of quantumly simulating the Kogut-Susskind formulation. This LSH formulation transcends the local loop formulation of $d+1$-dimensional lattice gauge theories by incorporating staggered quarks, furnishing the algebra of gauge-singlet operators, and being used to reconstruct dynamics between states that have Gauss's law built in to them. LSH operators are then factored into products of "normalized" ladder operators and diagonal matrices, priming them for classical or quantum information processing. Self-contained expressions of the Hamiltonian are given up to $d=3$. The LSH formalism makes little use of structures specific to SU(2) and its conceptual clarity makes it an attractive approach to apply to other non-Abelian groups like SU(3).
Highlights
Non-Abelian gauge symmetries play a fundamental role in modeling the interactions observed in Nature
Gauge symmetry plays an important role in understanding the theory of high-temperature superconductors
Nonrelativistic and dynamical SU(2) gauge fields emerge in the low-energy effective theory of doped and undoped Mott insulators in their spin-liquid phase, which models the physics of high-temperature superconductivity [4,5]
Summary
Non-Abelian gauge symmetries play a fundamental role in modeling the interactions observed in Nature. The idea is that degrees of freedom of the system under study be mapped onto those of the quantum computer, and unitary operations are done on it to mimic time evolution In this scenario, it seems far more natural to express theories with Hamiltonians and Hilbert spaces rather than functional integrals and classical field configurations. Most of the attempts far have been for simpler models like Z2 gauge theories [17,23,24] or U(1) gauge theories in 1 þ 1 dimensions [25,26,27,28], including the first digital quantum simulation of the Schwinger model on a small lattice [29] Such simulations are instructive, but generalizing to nonAbelian gauge groups and multidimensional space is necessary to address the important problems where classical computers fall short.
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