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arXiv:1703.09220 · Physical review. B./Physical review. B

Fermionic spin liquid analysis of the paramagnetic state in volborthite

Li Ern Chern, Robert Schaffer, Sopheak Sorn, Yong Baek Kim

Published Oct 10, 2017• 10 citations
arXivHTMLPDF

Abstract

Recently, thermal Hall effect has been observed in the paramagnetic state of volborthite, which consists of distorted kagome layers with $S=1/2$ local moments. Despite the appearance of magnetic order below $1\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, the response to external magnetic field and unusual properties of the paramagnetic state above $1\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ suggest possible realization of exotic quantum phases. Motivated by these discoveries, we investigate possible spin liquid phases with fermionic spinon excitations in a nonsymmorphic version of the kagome lattice, which belongs to the two-dimensional crystallographic group $p2gg$. This nonsymmorphic structure is consistent with the spin model obtained in the density functional theory calculation. Using projective symmetry group analysis and fermionic parton mean field theory, we identify twelve distinct ${\mathbb{Z}}_{2}$ spin liquid states, four of which are found to have correspondence in the eight Schwinger boson spin liquid states we classified earlier. We focus on the four fermionic states with bosonic counterpart and find that the spectrum of their corresponding root $U(1)$ states features spinon Fermi surface. The existence of spinon Fermi surface in candidate spin liquid states may offer a possible explanation of the finite thermal Hall conductivity observed in volborthite.

DOI
10.1103/physrevb.96.165117

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Due to strong geometric frustration and quantum fluctuation, the S=1/2S=1/2S=1/2 quantum Heisenberg antiferromagnet on the kagome\text{kagome}kagome lattice has long been considered as an ideal platform to realize a spin liquid (SL), a phase exhibiting fractionalized excitations without any symmetry breaking. A recent numerical study (Yan et al., e-print arXiv:1011.6114) of the Heisenberg S=1/2,kagomeS=1/2,\text{kagome}S=1/2,kagome lattice model (HKLM) shows, in contrast to earlier results, that the ground state is a singlet-gapped SL with signatures of Z2{\mathbb{Z}}_{2}Z2​ topological order. Motivated by this numerical discovery, we use the projective symmetry group to classify all 20 possible Schwinger fermion mean-field states of Z2{\mathbb{Z}}_{2}Z2​ SLs on the kagome\text{kagome}kagome lattice. Among them we found only one gapped Z2{\mathbb{Z}}_{2}Z2​ SL (which we call the ${\mathbb{Z}}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ state) in the neighborhood of the U(1) Dirac SL state. Since its parent state, i.e., the U(1) Dirac SL, was found [Ran et al., Phys. Rev. Lett. 98, 117205 (2007)] to be the lowest among many other candidate U(1) SLs, including the uniform resonating-valence-bond states, we propose this ${\mathbb{Z}}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ state to be the numerically discovered SL ground state of the HKLM.
Motivated by the recent progress in the spin-orbit-coupled triangular lattice spin liquid candidate YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, we carry out a systematic projective symmetry group analysis and mean-field study of candidate U(1)U(1)U(1) spin-liquid ground states. Due to the spin-orbital entanglement of the Yb moments, the space-group symmetry operation transforms both the position and the orientation of the local moments, and hence it brings different features for the projective realization of the lattice symmetries from the cases with spin-only moments. Among the eight U(1)U(1)U(1) spin liquids that we find with the fermionic parton construction, only one spin-liquid state, which was proposed and analyzed by Yao Shen et al. [Nature (London) 540, 559 (2016)] and labeled as U1A00 in the present work, stands out and gives a large spinon Fermi surface and provides a consistent explanation for the spectroscopic results in YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​. Further connection of this spinon Fermi surface U(1)U(1)U(1) spin liquid with YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ and the future directions are discussed. Finally, our results may apply to other spin-orbit-coupled triangular lattice spin-liquid candidates, and more broadly, our general approach can be well extended to spin-orbit-coupled spin-liquid candidate materials.
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Motivated by recent experiments on the Heisenberg S=1/2S=1/2S=1/2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled antiferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.
Recent numerical studies have provided strong evidence for a gapped Z2{Z}_{2}Z2​ quantum spin liquid in the kagome lattice spin-1/2 Heisenberg model. A special feature of spin liquids is that symmetries can be fractionalized, and different patterns of symmetry fractionalization imply distinct phases. The symmetry fractionalization pattern for the kagome spin liquid remains to be determined. A popular approach to studying spin liquids is to decompose the physical spin into partons obeying either Bose (Schwinger bosons) or Fermi (Abrikosov fermions) statistics, which are then treated within mean-field theory. A long-standing question has been whether these two approaches are truly distinct, or describe the same phase in complementary ways. Here we show that all 8Z28{Z}_{2}8Z2​ spin liquid phases in the Schwinger-boson mean-field (SBMF) construction can also be described in terms of Abrikosov fermions, unifying pairs of theories that seem rather distinct. The key idea is that for Z2{Z}_{2}Z2​ spin liquid states that admit a SBMF description on the kagome lattice, the symmetry fractionalization of visions is uniquely fixed. Two promising candidate states for the kagome Heisenberg model, Sachdev's Q1=Q2{Q}_{1}={Q}_{2}Q1​=Q2​ SBMF state and the Lu-Ran-Lee ${Z}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ Abrikosov-fermion state, are found to describe the same symmetric spin liquid phase. We expect these results to aid in a complete specification of the numerically observed spin liquid phase. We also discuss a set of Z2{Z}_{2}Z2​ spin liquid phases in the fermionic parton approach, where spin rotation and lattice symmetries protect gapless edge states that do not admit a SBMF description.
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.