2019/08/31 by Claudio Chamon, Dmitry Green, Zhi-Cheng Yang · 33 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Algebraic structures and combinatorial models #Combinatorics #Condensed matter physics #Gauge theory #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Qubit #Spins #Symmetry (geometry) #Theoretical physics #Topology (electrical circuits) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevlett.125.067203
published in Physical Review Letters 125(6), 067203 (American Physical Society) · Updated to published version
openalex publication_date 2020/08/07 · arxiv created 2020/08/08 · arxiv updated 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 anticommutation 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 with 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.