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arXiv:1512.05381

Kagome spin liquid: a deconfined critical phase driven by $U(1)$ gauge fluctuation

Yin-Chen He, Yohei Fuji, Subhro Bhattacharjee

Published Dec 16, 2015• 9 citations
arXivHTMLPDF

Abstract

We investigate the nature of quantum spin liquid (QSL) phase of the spin-$1/2$ 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 $U(1)$ 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 $U(1)$ 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.

DOI
10.48550/arxiv.1512.05381

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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.
While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well established numerically, a controlled theoretical path from the lattice model leading to a low-energy topological field theory is still lacking. This we provide via an explicit construction starting from reformulating a microscopic model for a CSL as a lattice gauge theory and deriving the low-energy form of its continuum limit. A crucial ingredient is the realization that the bosonic spinons of the gauge theory exhibit a U(1) symmetry protected topological (SPT) phase, which upon promoting its U(1) global symmetry to a local gauge structure ("gauging"), yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of a SPT phase can be applied more generally to understand topological spin liquids.
Quantum spin liquids (QSLs) host exotic fractionalized magnetic and gauge-field excitations whose microscopic origins and experimental verification remain frustratingly elusive. In the absence of static magnetic order, the spin excitation spectrum constitutes the crucial probe of QSL behavior, but its theoretical computation is a serious challenge. Here we employ state-of-the-art tensor-network methods to obtain the full dynamical spectral function of the J1J_1J1​-J2J_2J2​ kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing ∣J2∣/J1|J_2|/J_1∣J2​∣/J1​ causes increasingly strong spin-wave renormalization, flattening these modes then merging them into a continuum characteristic of deconfined spinons at all finite energies in the QSL. The low-energy continuum and the occurrence of gap closure at multiple high-symmetry points identify this gapless QSL as the U(1) Dirac spin liquid. These results establish a unified understanding of spin excitations in highly frustrated quantum magnets and provide clear spectral fingerprints for experimental detection in candidate kagome QSL materials.
Z2_{2}2​ spin liquid phase on the kagome lattice: a new saddle point
We have performed large scale variational search for the best RVB ansatz for the spin-12\frac{1}{2}21​ kagome antiferromagnet with both nearest-neighboring(NN) and next-nearest-neighboring(NNN) exchanges assuming only translational symmetry. We find the best RVB state is always fully symmetric and has an mean field ansatz that is gauge equivalent to a previous proposed Z2_{2}2​ spin liquid ansatz. The Z2_{2}2​ state is found to be slightly more stable than the extensively studied U(1) gapless Dirac spin liquid state in both the J2≠0J_{2}\neq0J2​=0 and the J2=0J_{2}=0J2​=0 case and to possess a small spinon gap for J2<0.2J_{2}<0.2J2​<0.2. The breaking of the U(1) gauge symmetry in the Z2_{2}2​ state is found to increase with J2J_{2}J2​ and to be quite substantial around J2=0.15J_{2}=0.15J2​=0.15. However, we find the Z2_{2}2​ state is always very close to the gapless U(1) Dirac spin liquid state, although they have very different RVB parameters. We argue the kagome antiferromagnet should be better understood as a near critical system, rather than a system deep inside a gapped spin liquid phase with well established Z2_{2}2​ topological order.
Quantum spin liquids, systems in which quantum fluctuations prevent the magnetic ordering of the spin degrees of freedom down to zero temperature, have been the source of much recent theoretical and experimental interest. These systems are characterised by their long ranged entangled states, preserve symmetries down to zero Kelvin, and have been shown to exhibit fascinating properties such as a topological ground state degeneracy and fractionalised spin excitations. In this thesis, we study several of these phases. The first, Kitaev spin liquids, appear in strongly spin-orbit coupled systems, where the SU(2) spin symmetry is broken. Within our mean field approach, we study the quantum phase transition from the gapless Z 2 spin liquid to a magnetically ordered phase within the Heisenberg-Kitaev model. Beyond the mean field theory, we argue that the gauge structure of the spin liquid plays a crucial role in this transition, leading to a confinement of spinons and the generation of magnetic order. We also discuss the three-dimensional iridate compounds, where the Kitaev spin liquid phase has topologically protected bulk and surface excitations. We next discuss spin liquids appearing on the geometrically frustrated kagome lattice. First, we consider non-Kramers spin liquids, in which the spin structure of the theory is protected by lattice, rather than time-reversal, symmetry. As a result, more phases are allowed, which have different properties than those which transform as Kramers doublets. In addition, these may have positive experimental signatures in the Raman scattering intensity, offering a clear path to detect such a state. Finally, we examine possible spin liquid phases on a breathing kagome lattice, where we find a stable Z2 spin liquid to be the ground state. This may help to guide future numerical studies of the kagome lattice Heisenberg model, and may also be relevant to DQVOF, a recently discovered spin liquid candidate compound.
We analyze the antiferromagnetic spin-1/2 XXZ model on the kagome lattice at finite external magnetic field with the help of a non-perturbative zero-temperature renormalization group (RG) technique. The exact nature of the ground and excited state properties (e.g. gapped or gapless spectrum etc) of this system are still debated. Approximate methods have typically been adopted towards understanding the low-energy spectrum. Following the work of Kumar et al (2014 Phys. Rev. B 90 174409), we use a Jordan–Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbor interactions. While the work of Kumar et al was confined mostly to the plateau at 1/3-filling (magnetization per site) in the XY regime, we analyze the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel–Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a SU (2)-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar et al . We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.
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.