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Register a new userHidden Fermi Liquidity and Topological Criticality in the Finite Temperature Kitaev Model
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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 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 Laughlins gossamer (here, p-wave) superconductor (g-SC), and $(c)$ the Kitaev Toric Code phase (TC) is a {it fully} Gutzwiller-projected p-wave SC. These findings establish the finite-$T$ QSL phases in the $d = 2$ to be {it hidden} Fermi liquid(s) of neutral fermions.
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We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle point solutions at large number $N$ of fermions are obtained and show a characteristic scale-invariant $sim |omega|^{-1/2}$ behavior of the spectral function below the transition which is replaced by a $sim |omega|^{-1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle point equations and discussed in the broader context of the field.
We investigate the quantum spin liquid (QSL) ground state of anisotropic Kitaev model with antiferromagnetic (AFM) coupling under the $[001]$ magnetic field with the finite-temperature Lanczos method (FTLM). In this anisotropic AFM Kitaev model with $K_{X}=K_{Y}$, $K_{X}+K_{Y}+K_{Z}=-3K$, and $K_{Z}<-K$, with magnetic field increasing, the gapped QSL experiences a transition to a gapless QSL at $h_{c1}=gmu_{B}H_{z1}/K$, to another gapless QSL with $C_{6}$ rotational symmetry at $h_{c2}$, and to a new $U(1)$ gapless QSL between $h_{c3}$ and $h_{c4}$, respectively. These indicate that magnetic field could first turn the anisotropic gapped or gapless QSL back into the isotropic $C_{6}$ gapless one and then make it to undergo the similar evolution as the isotropic case. Moreover, the critical magnetic fields $h_{c1}$, $h_{c2}$, $h_{c3}$, and $h_{c4}$ come up monotonically with the increasing Kitaev coupling; this suggests that the magnetic field can be applied to the modulation of the anisotropic Kitaev materials.
With the advancement in synthesizing and analyzing Kitaev materials, the Kitaev-Heisenberg model on the honeycomb lattice has attracted a lot of attention in the last few years. Several variations, which include additional anisotropic interactions as well as response to external magnetic field, have been investigated and many exotic ordered phases have been discussed. On the other hand, quantum spin systems are proving to be a fertile ground to realize and study bosonic analogues of fermionic topological states of matter. Using the spin-wave theory we show that the ferromagnetic phase of the extended Kitaev-Heisenberg model hosts topological excitations. Along the zig-zag edge of the honeycomb lattice we find chiral edge states, which are protected by a non-zero Chern number topological invariant. We discuss two different scenarios for the direction of the spin polarization namely $[001]$ and $[111]$, which are motivated by possible directions of applied field. Dynamic structure factor, accessible in scattering experiments, is shown to exhibit signatures of these topological edge excitations. Furthermore, we show that in case of spin polarization in $[001]$ direction, a topological phase transition occurs once the Kitaev couplings are made anisotropic.
We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^circ$ magnetic order, a nonmagnetic insulator (NMI), and an interacting Chern insulator (CI) with a nonzero Chern number. The transition from CI to NMI is characterized by the change of the charge gap from an indirect band gap to a direct Mott gap. Based on the slave-rotor mean-field theory, the NMI phase is further suggested to be a gapless Mott insulator with a spinon Fermi surface or a fractionalized CI with nontrivial spinon topology, depending on the strength of Kitaev-like hopping. Our work highlights the rising field that interesting phases emerge from the interplay of band topology and Mott physics.
We study finite temperature topological phase transitions of the Kitaevs spin honeycomb model in the vortex-free sector with the use of the recently introduced mean Uhlmann curvature. We employ an appropriate Fermionisation procedure to study the system as a two-band p-wave superconductor described by a BdG Hamiltonian. This allows to study relevant quantities such as Berry and mean Uhlmann curvatures in a simple setting. More specifically, we consider the spin honeycomb in the presence of an external magnetic field breaking time reversal symmetry. The introduction of such an external perturbation opens a gap in the phase of the system characterised by non-Abelian statistics, and makes the model to belong to a symmetry protected class, so that the Uhmann number can be analysed. We first consider the Berry curvature on a particular evolution line over the phase diagram. The mean Uhlmann curvature and the Uhlmann number are then analysed considering the system to be in a Gibbs state at finite temperature. Then, we show that the mean Uhlmann curvature describes a cross-over effect of the phases at high temperature. We also find an interesting nonmonotonic behaviour of the Uhlmann number as a function of the temperature in the trivial phase, which is due to the partial filling of the conduction band around Dirac points.
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