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Bulletin of the American Physical Society

Identification of Topological Phase Transitions in Kitaev Quantum Spin Liquids

Ara Go, Kyusung Hwang, Beom Hyun Kim, Ji Heon Seong, Eun-Gook Moon

Published Mar 5, 2020• 0 citations
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Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments.
We investigate signatures of topological quantum phase transitions (TQPTs) between the Z_{2} quantum spin liquids (QSLs). In two spatial dimensions, Z_{2} QSLs and their TQPTs are only well defined at zero temperature (T=0), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between Z_{2} QSLs with Majorana fermions in terms of thermal Hall conductivity κ_{xy} at nonzero temperatures. The κ_{xy}/T shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near T=0 and the peak of κ_{xy}/T around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions finding TQPTs between the phases with different Chern numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in α-RuCl_{3}.
How to characterize the topological order of quantum spin liquids remains a long-standing theoretical challenge. In this work, we employ the pattern decomposition method to analyze the fine structure of the Kitaev spin liquid on a finite honeycomb lattice. The Kitaev Hamiltonian decomposes into six sub-Hamiltonians whose weight factors form periodic patterns under unit cell translations. Correspondingly, the eigenstates of the Kitaev spin liquid are partitioned into six degenerate subspaces, unveiling the ordered structure of the spin liquid state. The critical point of the topological phase transition from a gapped to a gapless phase is identified through the sub-Hamiltonians. This Hamiltonian dissection approach reveals the fine structure of the Kitaev spin liquid and offers a promising platform for the quantum simulation of spin liquids.