A superconducting circuit realization of combinatorial gauge symmetry
Abstract
We propose a superconducting wire array that realizes a family of quantum Hamiltonians that possess combinatorial gauge symmetry  a local symmetry where monomial transformations play a central role. This physical system exhibits a rich structure. In the classical limit its ground state consists of two superimposed spin liquids; one is a crystal of small loops containing disordered $U(1)$ degrees of freedom, and the other is a soup of loops of all sizes associated to $\mathbb{Z}_2$ topological order. We show that the classical results carry over to the quantum case when fluctuations are gradually tuned via the wire capacitances, yielding ${\mathbb Z}_2$ quantum topological order. In an extreme quantum limit where the capacitances are all small, we arrive at an effective quantum spin Hamiltonian that we conjecture would sustain ${\mathbb Z}_2$ quantum topological order with a gap of the order of the Josephson coupling in the array. The principles behind the construction for superconducting arrays extends to other bosonic and fermionic systems, and offers a promising path towards topological qubits and the study of other manybody systems.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.10060
 Bibcode:
 2020arXiv200610060C
 Keywords:

 Quantum Physics;
 Condensed Matter  Superconductivity
 EPrint:
 5 figures