Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

Abstract

The Kitaev model with an applied magnetic field in the H||[111] direction shows two transitions: from a non-abelian gapped quantum spin liquid (QSL) to a gapless QSL at Hc1 0.2K and a second transition at a higher field Hc2 0.35K to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL, and determine the spin structure function S(k) and the Fermi surface S F (k) of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature specific heat and entropy, corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.The inspired exact solution of the Kitaev model on a twodimensional honeycomb lattice with bond dependent spin exchange interaction [1] (Eq. 1) has emerged as a paradigmatic model for quantum spin liquids (QSL). For equal bond interactions (K), the ground state of the Kitaev model is known to be a topologically non-trivial gapless QSL with fractionalized excitations. The multiple ground state degeneracy reflects the topology of the lattice manifold (2-fold degeneracy on a cylinder and 4-fold degeneracy on a torus). The promise of utilizing fractionalized excitations for applications in robust quantum computing [1][2][3][4][5] has led to considerable excitement and activity in the field from diverse directions, all the way from fundamental developments to applications. Upon breaking time-reversal symmetry (TRS), for example by applying a magnetic field, the exact solvability of the Kitaev model is lost but perturbatively it can be shown that the Kitaev gapless QSL becomes a gapped QSL phase with non-abelian anyonic excitations [1].In order to realize the exotic properties of the Kitaev model, there has been keen interest to discover Kitaev physics in materials. To this end, Mott insulators with magnetic frustration and large spin-orbit coupling have been proposed [6], leading to the discovery of α-RuCl 3 and A 2 IrO 3 (A = Na, Li). These are candidate QSL materials with the desired honeycomb geometry. Although given additional interactions beyond the Kitaev interaction in materials, there is still controversy about the regimes where Kitaev physics can be accessed [7][8][9][10][11][12]. Additionally, triangular and Kagome lattice with spin frustration has also been proposed as a candidate for a QSL [13][14][15][16][17][18][19]. In this context, organics such as κ-(BEDT-TTF) 2 Cu 2 (CN) 3 [20] and EtMe 3 Sb[Pd(dmit) 2 ] 2 [21], the transition metal dichalcogenides 1T-TaS 2 [19] and a large family of rare-earth dichalcogenides AReX 2 (A = alkali or monovalent ions, Re = rare earth, X = O, S, Se) [22] have been explored. Remarkably, recent NMR and thermal Hall conductivity experiments on α-RuCl 3 demonstrate th...

Field-induced quantum spin liquid in the Kitaev-Heisenberg model and its relation to α−RuCl3

“…The system enters into a gapless spin liquid phase for higher magnetic fields, as shown in the left inset of Fig. 2, which is consistent with the spin liquid with spinon Fermi surfaces proposed recently [9][10][11][12]. Finally, the system becomes fully polarized for sufficiently high magnetic fields h c * > 0.…”

“…Our study indicates that for most sets of parameters extracted from previous studies, a field-induced spin liquid or an intermediate phase between a zigzag ordered phase at low magnetic field and a fully polarized phase at high magnetic field, is absent. However, for the set of parameters with AFM Kitaev coupling and out-of-plane magnetic fields, we find strong evidence of an intermediate field-induced paramagnetic phase consistent with a gapless spin liquid with a spinon Fermi surface as proposed recently [9][10][11][12].…”

“…2 as the right inset. With the increase of system size, it is clear that the intermediate phase at large J 1 is smoothly connected to the gapless spin liquid phase of the Kitaev model under external magnetic field, indicating that the intermediate state is consistent with the gapless spin liquid with spinon Fermi surface proposed recently [9][10][11][12]. More details are provided in the SM.…”

“…We choose two representative strengths of magnetic field h c * = 0.143 and 0.214 deep inside the intermediate and polarized phases, respectively. The h c * = 0.143 data has c ∼ 1.94 suggesting that there are c = 2 gapless modes, which is consistent with the gapless spin liquid with spinon Fermi surfaces [9][10][11][12]. On the contrary, c ∼ 0 at h c * = 0.214 in the fully polarized phase, indicating a gapped ground state.…”

“…The search for quantum spin liquids (QSLs) in frustrated quantum magnets has enjoyed a surge of interest in modern condensed matter physics [1,2]. The Kitaev model on the honeycomb lattice is exact solvable and known to exhibit a gapless spin liquid ground state (for equal coupling along the links) that can be gapped out into a topological phase with non-Abelian quasiparticle excitations by certain time-reversal symmetry breaking perturbations such as magnetic fields [3][4][5][6][7][8][9][10][11][12], which is an important ingredient for fault-tolerant quantum computation [13]. Consequently, there has been enormous interest in exploring the possible realization of Kitaev physics in a large family of layered Mott insulators with strong spin-orbit couplings such as α-RuCl 3 [14][15][16][17][18].…”