In this paper we report the latest results of exact diagonalizations of SU (2) invariant models on various lattices (square, triangular, hexagonal, checkerboard and kagomé lattices) and revisit critically in this light some of our previous analysis. We focus on the low-lying levels in each S sector. The differences in behavior between gapless systems and gapped ones are exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on the kagomé lattice is discussed. A rough estimate of the spin susceptibility in such an hypothesis is given. The evolution of the intra- S -channel spectra under the effect of a small perturbation is consistent with the proximity of a quantum critical point. We reemphasize that the very small intra- S -channel energy scale observed in exact spectra is a very interesting information to understand the low- T dynamics of this model.
In this paper we report the latest results of exact diagonalizations of SU (2) invariant models on various lattices (square, triangular, hexagonal, checkerboard and kagomé lattices) and revisit critically in this light some of our previous analysis. We focus on the low-lying levels in each S sector. The differences in behavior between gapless systems and gapped ones are exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on the kagomé lattice is discussed. A rough estimate of the spin susceptibility in such an hypothesis is given. The evolution of the intra- S -channel spectra under the effect of a small perturbation is consistent with the proximity of a quantum critical point. We reemphasize that the very small intra- S -channel energy scale observed in exact spectra is a very interesting information to understand the low- T dynamics of this model.
The S=1/2 kagome-lattice antiferromagnet is one of interesting frustrated quantum spin systems. The system is supposed to exhibit the quantum spin liquid in the ground state, which was proposed as a possible origin of the high-temprature superconductivity. The spin gap is an important physical quantity to characterize the spin liquid behavior. Whether the S=1/2 kagome-lattice antiferromagnet is gapless or has a finite spin gap, is still an unsolved issue. Because any recently developped numerical calculation methods are not enough to determine it in the thermodynamic limit. Our large-scale numerical diazonalization up to 42-spin clusters and a finite-size scaling analysis indicated that the S=1/2 kagome-lattice antiferromagnet is gapless in the thremodynamic limit[1]. It is consistent with the U(1) Dirac spin liquid theory of the kagome-lattice antiferromagnet[2,3]. On the other hand, some density matrix renormalization group (DMRG) calculations supported the gapped Z2 topological spin liquid theory[4,5]. Our recent numerical diagonalization analysis on the magnetization process of a distorted kagome-lattice antiferromagnet indicated that the perfect kagome-lattice system is just on a quantum critical point[6]. It would be a possible reason why it is difficult to determine whether the perfect kagome-lattice antiferromagnet is gapless or gapped. In the present study, a field derivative analysis is applied for the spin gap issue of the kagome-lattice antiferromanget, using the numerical diagonalization data up to 42-spin clusters. It is consistent with our previous conclusion that it is gapless[7]. [1]H. Nakano and T. Sakai: J. Phys. Soc. Jpn. 80 (2011) 053704. [2]Y. Ran, M. Hermele, P. A. Lee and X. -G. Wen: Phys. Rev. Lett. 98 (2007) 117205. [3]Y. Iqbal, F. Becca, S. Sorella and D. Poilblanc: Phys. Rev. B 87 (2013) 060405(R). [4]S. Yan, D. A. Huse and S. R. White: Science 332 (2011) 1173. [5]S. Nishimoto, N. Shibata and C. Hotta: Nat. Commun. 4 (2013) 2287. [6]H. Nakano and T. Sakai: J. Phys. Soc. Jpn. 83 (2014) 104710. [7]H. Nakano and T. Sakai: in preparation.
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.
There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near-neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appears to be a plethora of low-energy excitations, predominantly singlets but also spin carrying, which suggests that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-21 Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)-dimensional quantum electrodynamics (QED3) with an emergent SU(8) flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.
We examine the perennial quantum spin liquid candidate S=21 Heisenberg antiferromagnet on the kagome lattice. Our paper is based on achieving Lanczos diagonalization of the Hamiltonian on a 48 site cluster in sectors with dimensions as large as $5\ifmmode\times\else\texttimes\fi{}{10}^{11}$. The results reveal intricate structures in the low-lying energy spectrum. These structures by no means unambiguously support a Z2 spin liquid ground state, but instead appear compatible with several scenarios, including fourfold topological degeneracy, inversion symmetry breaking, and a combination thereof. We discuss finite-size effects, such as the apparent absence of the eigenstate thermalization hypothesis, and note that, while considerably reduced, some are still present for the largest cluster. Finally, we observe that an XXZ model in the Ising limit reproduces remarkably well the most striking features of finite-size spectra.
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.
We study the energy and the static spin structure factor of the ground state of the spin-1/2 quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) U(1) Dirac spin liquid is competitive with previously proposed gapped (topological) Z2 spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site $E/J=\ensuremath{-}0.4365(2)$, which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.