Field-induced QCD3 -Chern-Simons quantum criticalities in Kitaev materials

Abstract

Kitaev materials are promising to realize exotic quantum spin liquid phases, such as a non-Abelian chiral spin liquid. Motivated by recent experiments in these materials, we theoretically study the novel field-induced quantum phase transitions from the non-Abelian chiral spin liquid to the symmetry-broken zigzag phase and to the trivial polarized state. Utilizing the recently developed dualities of gauge theories, we find these transitions can be described by critical bosons or gapless fermions coupled to emergent non-Abelian gauge fields, and the critical theories are of the type of a QCD3-Chern-Simons theory. We propose that all these exotic quantum phase transitions can potentially be direct and continuous in Kitaev materials, and we present sound evidence for this proposal. Therefore, besides being systems with intriguing quantum magnetism, Kitaev materials may also serve as table-top experimental platforms to study the interesting dynamics of emergent strongly interacting quarks and gluons in 2 + 1 dimensions. Contents

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].…”