Hidden Fermi liquidity and topological criticality in the finite temperature Kitaev model

Abstract

The fate of exotic spin liquid states with fractionalized excitations at finite temperature (T) is of great interest, since signatures of fractionalization manifest in finite-temperature (T) dynamics in real systems, above the tiny magnetic ordering scales. Here, we study a Jordan–Wigner (JW) fermionized Kitaev spin liquid at finite T employing combined exact diagonalization and Monte Carlo simulation methods. We uncover (i) checkerboard or stripy-ordered flux crystals depending on density of flux, and (ii) establish, surprisingly, that: (a) the finite-T version of the T=0 transition from a gapless to gapped phases in the Kitaev model is a Mott transition of the fermions, belonging to the two-dimensional Ising universality class. These transitions correspond to a topological transition between a string condensate and a dilute closed string state (b) the Mott “insulator” phase is a precise realization of Laughlin’s gossamer (here, p-wave) superconductor (g-SC), and (c) the Kitaev Toric Code phase (TC) is adiabatically connected to the g-SC, and is a fully Gutzwiller-projected fermi sea of JW fermions. These findings establish the finite-T quantum spin liquid phases in the d=2 to be hidden Fermi liquid(s) of neutral fermions.