Gauging the Kitaev chain

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.

Long-range entanglement from measuring symmetry-protected topological phases

“…Furthermore, we define the hopping operator S 2n = iγ 2n−2 γ 2n , which hops a fermion from site 2n − 2 to 2n. We create a Z 2 × Z F 2 SPT [107][108][109][110] with the following circuit…”

Spinless fermions in a $\mathbb{Z}_{2}$ gauge theory on the triangular ladder

“…A, technical details of a mapping of the SFIGT on the triangular ladder to a pure spin model with only two sets of spin operators, (X, Y, Z) r,i per triangle are described. Variants of this have already been used for 1D 54,55,62,63 and 2D 1 systems. The new spins are gaugeinvariant, and the pure spin model acts only in the sector of zero gauge charge by construction.…”

“…The new spin degrees of freedom are gauge-invariant and the gauge constraint is satisfied by construction, i.e., the pure spin model acts only in the physical subspace of zero gauge charge. Variants of this approach have been described for 1D 54,55,62,63 and 2D 1 systems in the literature. The details are specific to the particular lattice considered.…”

“…In line with these general developments, lattice IGTs, constrained or unconstrained, and minimally coupled to either free fermions 1,[48][49][50][51][52][53][54][55] , the Hubbard model 56,57 , or composite fermions 58 , are currently experiencing an upsurge of attention. The phases of these models are very diverse.…”

“…While spinful fermions allow for magnetic order, spinless fermions or Majorana combinations thereof, are also among the parton matter which has been coupled to lattice IGTs in one 54,55 , and two 1 dimensions (1D,2D). In 2D, many similarities arise with theories comprising spinful fermions.…”