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arXiv:1406.7205 · Physical Review B

Nematic and supernematic phases in kagome quantum antiferromagnets under the influence of a magnetic field

Thibaut Picot, Didier Poilblanc

Published Feb 17, 2015• 41 citations
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Abstract

Optimizing translationally invariant infinite-projected entangled pair states, we investigate the spin-2 Affleck-Kennedy-Lieb-Tasaki and spin-1 Heisenberg models on the kagome lattice as a function of magnetic field. We found that the magnetization curves offer a wide variety of compressible and incompressible phases. Incompressible nematic phases breaking the lattice ${C}_{3}$ rotation, for which we propose simple qualitative pictures, give rise to magnetization plateaus at reduced magnetization ${m}_{z}=\frac{5}{6}$ and $\frac{1}{3}$ for spin-2 and -1, respectively, in addition to the ${m}_{z}=0$ plateaus characteristic of zero-field gapped spin liquids. Moving away from the plateaus, we observe a rich variety of compressible superfluid nematic, named ``supernematic,'' phases breaking spontaneously both point group and spin-U(1) symmetries, as well as a superfluid phase preserving lattice symmetries. We also identify the nature, continuous or first order, of the various phase transitions. Possible connections to experimental spin-1 systems are discussed.

DOI
10.1103/physrevb.91.064415

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Spin-12\frac{1}{2}21​ kagome Heisenberg antiferromagnet with strong breathing anisotropy
We study the zero-temperature phase diagram of the spin-1/2 Heisenberg model with breathing anisotropy (i.e., with different coupling strength on the upward and downward triangles) on the kagome lattice. Our study relies on large scale tensor network simulations based on infinite projected entangled-pair state and infinite projected entangled-simplex state methods adapted to the kagome lattice. Our energy analysis suggests that the U(1) algebraic quantum spin-liquid (QSL) ground-state of the isotropic Heisenberg model is stable up to very large breathing anisotropy until it breaks down to a critical lattice-nematic phase that breaks rotational symmetry in real space through a first-order quantum phase transition. Our results also provide further insight into the recent experiment on vanadium oxyfluoride compounds which has been shown to be relevant platforms for realizing QSL in the presence of breathing anisotropy.
We study numerically the spin-1/2 XXZ model in a field on an infinite kagome lattice. We use different algorithms based on infinite projected entangled pair states (iPEPSs) for this, namely, (i) an approach with simplex tensors and a 9-site unit cell, and (ii) an approach based on coarse-graining three spins in the kagome lattice and mapping it to a square-lattice model with local and nearest-neighbor interactions, with the usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emergence of magnetization plateaus as a function of the magnetic field, at mz=13{m}_{z}=\frac{1}{3}mz​=31​ using 6-, 9-, and 12-site PEPS unit cells, and at mz=19,59{m}_{z}=\frac{1}{9},\phantom{\rule{0.28em}{0ex}}\frac{5}{9}mz​=91​,95​, and 79\frac{7}{9}97​ using a 9-site PEPS unit cell, the latter setup being able to accommodate $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ solid order. We also find that, at mz=13{m}_{z}=\frac{1}{3}mz​=31​, (lattice) nematic and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ VBC-order states are degenerate within the accuracy of the nine-site simplex method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and $1\ifmmode\times\else\texttimes\fi{}2$ VBC-solid orders. We also find that, within our accuracy, the six-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even in cases where the PEPS unit cell is not commensurate with the expected ground-state unit cell. Furthermore, we do not observe chiral spin liquid behaviors at and close to the XY point, as has been recently proposed. Our results are the first tensor network investigations of the XXZ model in a field and reveal the subtle competition between nearby magnetic orders in numerical simulations of frustrated quantum antiferromagnets, as well as the delicate interplay between energy optimization and symmetry in tensor network numerical simulations.
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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.