Abstract
Material realizations of the bond-dependent Kitaev interactions with $S$=1/2 local moments have vitalized the research in quantum spin liquids. Recently, it has been proposed that higher-spin analogues of the Kitaev interactions may also occur in a number of materials with strong spin-orbit coupling. In contrast to the celebrated $S$=1/2 Kitaev model on the honeycomb lattice, the higher-spin Kitaev models are not exactly solvable. Hence, the existence of quantum spin liquids in these systems remains an outstanding question. In this work, we use the density matrix renormalization group (DMRG) methods to numerically investigate the $S$=1 Kitaev model with both ferromagnetic (FM) and antiferromagnetic (AFM) interactions. Using results on a cylindrical geometry with various circumferences, we conclude that the ground state of the $S$=1 Kitaev model is a quantum spin liquid with a $\mathbb{Z}_2$ gauge structure. We also put a bound on the excitation gap, which turns out to be quite small. The magnetic field responses for the FM and AFM models are similar to those of the $S$=1/2 counterparts. In particular, in the AFM $S$=1 model, a gapless quantum liquid state emerges in an intermediate window of magnetic field strength, before the system enters a trivial polarized state.
Highlights
A quantum spin liquid is a phase of matter characterized by long-range entanglement and fractionalized excitations in magnetic systems described by spin models [1,2,3,4,5]
We retain 7200 states in the reduced density matrix, with no symmetries kept, and we found that 45 sweeps were sufficient for good convergence
In the current work we used density matrix renormalization group (DMRG) and Exact diagonalization (ED) to investigate the nature of the ground states for the S = 1 Kitaev model with both FM and AFM exchange interactions
Summary
A quantum spin liquid is a phase of matter characterized by long-range entanglement and fractionalized excitations in magnetic systems described by spin models [1,2,3,4,5]. We investigate the excitation energy gap as a function of an external magnetic field and find that it vanishes as one approaches the aforementioned transition This is consistent with the picture of a gapless intermediate phase, illustrated in the phase diagram appearing, just as for the S = 1/2 AFM model subject to a magnetic field [27,28,33]. The general overall picture emerging from these studies is that the ground state of the S = 1 Kitaev model is a quantum spin liquid with a Z2 gauge structure, and that the response to external magnetic fields is very similar to the S = 1/2 case.
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