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arXiv:1902.11301 · Physical Review A

Flux-driven quantum spin liquids in kagome optical lattices

Hoi-Yin Hui, Mengsu Chen, Sumanta Tewari, V. W. Scarola

Published Nov 14, 2019• 2 citations
arXivHTMLPDF

Abstract

Quantum spin liquids (QSLs) define an exotic class of quantum ground states where spins are disordered down to zero temperature. We propose routes to QSLs in kagome optical lattices using applied flux. An optical flux lattice can be applied to induce a uniform flux and chiral three-spin interactions that drive the formation of a gapped chiral spin liquid. A different approach based on recent experiments using laser-assisted tunneling and lattice tilt implements a staggered flux pattern which can drive a gapless spin liquid with symmetry protected nodal lines. Our proposals, therefore, establish kagome optical lattices with effective flux as a powerful platform for exploration of QSLs.

DOI
10.1103/physreva.100.053614

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Quantum spin liquids (QSLs) define an exotic class of quantum ground states where spins are disordered down to zero temperature. We propose routes to QSLs in kagome optical lattices using applied flux. An optical flux lattice can be applied to induce a uniform flux and chiral three-spin interactions that drive the formation of a gapped chiral spin liquid. A different approach based on recent experiments using laser-assisted tunneling and lattice tilt implements a staggered flux pattern which can drive a gapless spin liquid with symmetry protected nodal lines. Our proposals, therefore, establish kagome optical lattices with effective flux as a powerful platform for exploration of QSLs.
We argue that a relatively simple model containing only SU(2)-invariant chiral three-spin interactions on a Kagome lattice of S=1/2 spins can give rise to both a gapped and a gapless quantum spin liquid. Our arguments are rooted in a formulation in terms of network models of edge states and are backed up by a careful numerical analysis. For a uniform choice of chirality on the lattice, we realize the Kalmeyer-Laughlin state, i.e. a gapped spin liquid which is identified as the nu=1/2 bosonic Laughlin state. For staggered chiralities, a gapless spin liquid emerges which exhibits gapless spin excitations along lines in momentum space, a feature that we probe by studying quasi-two-dimensional systems of finite width. We thus provide a single, appealingly simple spin model (i) for what is probably the simplest realization of the Kalmeyer-Laughlin state to date, as well as (ii) for a non-Fermi liquid state with lines of gapless SU(2) spin excitations.
We present a comprehensive analytical theory of quantum spin liquids (QSLs) on the kagome lattice with Heisenberg exchange J1, next-nearest-neighbor exchange J2, Dzyaloshinskii-Moriya interaction D, and scalar spin chirality interaction λ. The work contains three principal contributions. First, we derive new mean-field analytic relations connecting the chiral interaction λ to the spinon gap, low-temperature thermodynamics, and thermal Hall response, with explicit spin-S dependence and generalization across kagome, triangular, and honeycomb lattices. The central result is Δspinon ∝ S³λ/J12 with lattice-dependent prefactors derived from self-consistent mean-field equations. Second, we derive a controlled effective model by projecting the kagome Hamiltonian onto the triangle-doublet subspace, obtaining an effective spin-chirality model on the triangular lattice with complex-valued interactions arising from the C3 symmetry of the chirality eigenstates. We compute all matrix elements of the effective spin operator in the chirality basis and characterize the inter-chirality coupling mediated by shared lattice sites. Third, we provide a rigorous map of obstructions to exact analytical solutions, systematically examining eight classes of proof techniques and identifying the precise mathematical reason each fails for the kagome Hamiltonian. The Lieb-Schultz-Mattis theorem provides the single rigorous exact result: any gapped ground state on the kagome lattice with spin-1/2 per site must exhibit topological order. All other results are classified by derivation category with explicit uncertainty quantification. AI-Generated Content Statement: This manuscript was generated primarily with the assistance of artificial intelligence language models, including ChatGPT. The work represents an exploratory demonstration of AI-assisted knowledge generation and prompt engineering methods rather than traditional experimental research.
Using a perturbative renormalization group approach, we show that the extended ( J_1-J_2-J_d J 1 − J 2 − J d ) Heisenberg model on the kagome lattice with a staggered chiral interaction ( J_\chi J χ ) can exhibit a gapless chiral quantum spin liquid phase. Within a coupled-chain construction, this phase can be understood as a chiral sliding Luttinger liquid with algebraic decay of spin correlations along the chain directions. We calculate the low-energy properties of this gapless chiral spin liquid using the effective field theory and show that they are compatible with the predictions from parton mean-field theories with symmetry-protected line Fermi surfaces. These results may be relevant to the state observed in the kapellasite material.
Inspired by the recent discovery of a new instability towards a chiral phase of the classical Heisenberg model on the kagome lattice, we propose a specific chiral spin liquid that reconciles different, well-established results concerning both the classical and quantum models. This proposal is analyzed in an extended mean-field Schwinger boson framework encompassing time reversal symmetry breaking phases, which allows both a classical and a quantum phase description. At low temperatures, we find that quantum fluctuations favor this chiral phase, which is stable against small perturbations of second- and third-neighbor interactions. For spin-1/2, this phase may be, beyond the mean field, a chiral gapped spin liquid. Such a phase is consistent with the density matrix renormalization group results of Yan et al. [Science 332, 1173 (2011)]. Mysterious features of the low-lying excitations of exact diagonalization spectra also find an explanation in this framework. Moreover, thermal fluctuations compete with quantum ones and induce a transition from this flux phase to a planar zero flux phase at a nonzero value of the renormalized temperature (T/S2), reconciling these results with those obtained for the classical system.
Kagome spin liquid: a deconfined critical phase driven by U(1)U(1)U(1) gauge fluctuation
We investigate the nature of quantum spin liquid (QSL) phase of the spin-1/21/21/2 nearest-neighbor XXZ antiferromagnet on the kagome lattice. Recent numerical calculations suggest that such a kagome spin liquid is insensitive to the XXZ anisotropy and is adjacent to a chiral spin liquid phase. Reformulating the problem in terms of a U(1)U(1)U(1) lattice gauge theory with dynamical bosonic spinons, we propose that the kagome spin liquid can be understood as a deconfined critical phase extended by the U(1)U(1)U(1) gauge fluctuation from a deconfined critical point between a symmetry-protected topological phase and a superfluid phase. Crucially, the stability of this QSL is ensured by the gauge fluctuation and hence our description necessarily falls beyond the conventional mean-field constructions of QSLs. Our work also makes an interesting connection between the critical spin liquid, deconfined criticality, symmetry protected topological phase and topological order.
The realization of non-Abelian anyons in topological phases is a crucial step toward topological quantum computation. We propose a scheme to realize a non-Abelian quantum spin liquid (QSL) phase in a three-component Bose gas with contact interaction on optical kagome lattices. In the strong coupling regime, the system is described by an effective spin-1 model with two- and three-body interactions between neighboring spins. By mapping out the phase diagram via the variational Monte Carlo method, we find a non-Abelian chiral spin-liquid phase in which the Ising-type anyons obey non-Abelian braiding statistics. The gapless chiral edge states can be detected by measuring the spin-spin correlation from atomic population. Furthermore, an interesting Z2{Z}_{2}Z2​ QSL phase is observed exhibiting both topological order and lattice symmetry-breaking order. Our scheme can be implemented in cold quantum gases of bosonic atoms.