Hongji Yu, Dmitry Green, Andrei E. Ruckenstein, Claudio Chamon
SciPost Phys. Core 7, 014 (2024) ·
published 26 March 2024
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Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This paper is a generalization of the construction to any finite Abelian group. In addition to the general mathematical construction, we present a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians.
SciPost Phys. 15, 067 (2023) ·
published 22 August 2023
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We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic $ZZ$ interactions, plus longitudinal and transverse fields, and therefore is an explicit example of a spin Hamiltonian with no sign problem that realizes a non-Abelian topological phase. In addition to the spin model, we propose a superconducting quantum circuit version with the same symmetry.
Prof. Green: "We thank referee 2 for the use..."
in Submissions | report on Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry