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arXiv:2205.04727 · Physical review. B./Physical review. B

Spectra of a gapped quantum spin liquid with a strong chiral excitation on the triangular lattice

Ta Tang, Brian Moritz, Thomas Devereaux

Published Aug 23, 2022• 11 citations
arXivHTMLPDF

Abstract

Whereas a quantum spin liquid (QSL) phase has been identified in the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on a triangular lattice via numerical calculations, debate persists about whether or not such a QSL is gapped or gapless with contradictory conclusions from different techniques. Moreover, information about excitations and dynamics is crucial for the experimental detection of such a phase. In this paper, we use exact diagonalization to characterize signatures of a QSL phase on the triangular lattice through the dynamical spin structure factor $\mathcal{S}(q,\ensuremath{\omega})$ and Raman susceptibility $\ensuremath{\chi}(\ensuremath{\omega})$. We find that spectra for the QSL phase show distinct features compared to those of neighboring phases; and both the Raman spectra and spin structure factor show gapped behavior in the QSL phase. Interestingly, there is a prominent excitation mode in the Raman ${A}_{2}$ channel, indicating a strong subleading tendency toward a chiral spin liquid phase.

DOI
10.1103/physrevb.106.064428

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Whereas a quantum spin liquid (QSL) phase has been identified in the J1\ensuremath-J2{J}_{1}\text{\ensuremath{-}}{J}_{2}J1​\ensuremath-J2​ Heisenberg model on a triangular lattice via numerical calculations, debate persists about whether or not such a QSL is gapped or gapless with contradictory conclusions from different techniques. Moreover, information about excitations and dynamics is crucial for the experimental detection of such a phase. In this paper, we use exact diagonalization to characterize signatures of a QSL phase on the triangular lattice through the dynamical spin structure factor S(q,\ensuremathω)\mathcal{S}(q,\ensuremath{\omega})S(q,\ensuremathω) and Raman susceptibility \ensuremathχ(\ensuremathω)\ensuremath{\chi}(\ensuremath{\omega})\ensuremathχ(\ensuremathω). We find that spectra for the QSL phase show distinct features compared to those of neighboring phases; and both the Raman spectra and spin structure factor show gapped behavior in the QSL phase. Interestingly, there is a prominent excitation mode in the Raman A2{A}_{2}A2​ channel, indicating a strong subleading tendency toward a chiral spin liquid phase.
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We study the interplay of competing interactions in spin-12\frac{1}{2}21​ triangular Heisenberg model through tuning the first- (J1{J}_{1}J1​), second- (J2{J}_{2}J2​), and third-neighbor (J3{J}_{3}J3​) couplings. Based on a large-scale density-matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a gapless chiral spin-liquid (CSL) phase in the intermediate J2{J}_{2}J2​ and J3{J}_{3}J3​ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin-liquid state, the U(1)U(1)U(1) staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the U(1)U(1)U(1) Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero J2{J}_{2}J2​ and J3{J}_{3}J3​, which naturally explains the numerical results. This realizes an example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of interesting quantum phases emergent from competing interactions in triangular-lattice magnets.
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Dynamics and stability of U(1) spin liquids beyond mean-field theory: Triangular-lattice J1J_1J1​-J2J_2J2​ Heisenberg model
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