Gauging the Kitaev chain

TL;DR

This paper explores the effects of gauging fermion parity symmetry in the Kitaev chain, revealing new topological phases, boundary phenomena, and criticality, with implications for understanding gauge-invariant topological matter.

Contribution

It introduces a gauged version of the Kitaev chain, uncovering boundary Majorana operators, a distinct Higgs phase with fermionic SPT order, and a comprehensive analysis of the interpolating model.

Findings

Gauging transforms the bulk into an Ising chain of gauge-invariant spins.

The Higgs phase exhibits fermionic SPT order different from the original Kitaev chain.

Deconfined phase remains stable with vortices, and gauging induces gapless SPT phases due to anomalies.

Abstract

We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.