Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Abstract

We introduce the notion of combinatorial gauge symmetry -- a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states) -- that preserve the commutation and anti-commutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated to the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.

arXiv commentUpdated to published version

References in corpus (10)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Topological order in an exactly solvable 3D spin model
• Quantum mechanical and information theoretic view on classical glass transitions
• Majorana Quantum Lego, a Route Towards Fracton Matter

Cited by in corpus (15)

• Simulating Lattice Gauge Theories within Quantum Technologies
• Prediction of Toric Code Topological Order from Rydberg Blockade
• Qubit spin ice
• Kagome qubit ice
• Experimental Realization of Classical ${\mathbb{Z}}_2$ Spin Liquids in a Programmable Quantum Device
• Quantum Simulation of Lattice Gauge Theories on Superconducting Circuits: Quantum Phase Transition and Quench Dynamics
• A superconducting circuit realization of combinatorial gauge symmetry
• $U(1)$ symmetry-enriched toric code
• Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry
• Probing fractional statistics in quantum simulators of spin liquid Hamiltonians
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions
• ${\mathbb{Z}}_3$ quantum double in a superconducting wire array
• Fracton and topological order in the XY checkerboard toric code
• Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Absence of topological order in the $U(1)$ checkerboard toric code