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arXiv:0806.4395 · Physical Review Letters

Gapless Spin Liquids on the Three-Dimensional Hyperkagome Lattice of Na4Ir3O8

Michael J. Lawler, Arun Paramekanti, Yong Baek Kim, Leon Balents

Published Nov 3, 2008• 132 citations
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Abstract

Recent experiments indicate that Na4Ir3O8, a material in which s=1/2 Ir local moments live on a three-dimensional "hyperkagome" lattice of corner-sharing triangles, may have a quantum spin liquid ground state with gapless spin excitations. Using a combination of exact diagonalization, symmetry analysis of fermionic mean field ground states and Gutzwiller projected variational wave functions studies, we propose a quantum spin liquid with spinon Fermi surfaces as a favorable candidate for the ground state of the Heisenberg model on this lattice. We point out implications of this proposal for thermodynamic properties and discuss possible weak instabilities of the spinon Fermi surfaces.

DOI
10.1103/physrevlett.101.197202

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Motivated by the recent synthesis of $\ensuremath{\beta}$-Li2{}_{2}2​IrO3{}_{3}3​---a spin-orbit entangled j=1/2j=1/2j=1/2 Mott insulator with a three-dimensional lattice structure of the Ir4+{}^{4+}4+ ions---we consider generalizations of the Kitaev model believed to capture some of the microscopic interactions between the iridium moments on various trivalent lattice structures in three spatial dimensions. Of particular interest is the so-called hyperoctagon lattice---the premedial lattice of the hyperkagome lattice, for which the ground state is a gapless quantum spin liquid where the gapless Majorana modes form an extended two-dimensional Majorana Fermi surface. We demonstrate that this Majorana Fermi surface is inherently protected by lattice symmetries and discuss possible instabilities. We thus provide the first example of an analytically tractable microscopic model of interacting SU(2) spin-12\frac{1}{2}21​ degrees of freedom in three spatial dimensions that harbors a spin liquid with a two-dimensional spinon Fermi surface.
Motivated by recent experiments on Ba3{}_{3}3​NiSb2{}_{2}2​O9{}_{9}9​, we investigate possible quantum spin liquid ground states for spin S=1S=1S=1 Heisenberg models on the triangular lattice. We use variational Monte Carlo techniques to calculate the energies of microscopic spin liquid wave functions where spin is represented by three flavors of fermionic spinon operators. These energies are compared with the energies of various competing three-sublattice ordered states. Our approach shows that the antiferromagnetic Heisenberg model with biquadratic term and single-ion anisotropy does not have a low-temperature spin liquid phase. However, for an SU(3)-invariant model with sufficiently strong ring-exchange terms, we find a paired chiral quantum spin liquid with a Fermi surface of deconfined spinons that is stable against all types of ordering patterns we considered. We discuss the physics of this exotic spin liquid state in relation to the recent experiment and suggest new ways to test this scenario.
The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-one-dimensional strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge c=2c=2c=2 and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors. We argue that this intriguing spin liquid phase can be understood as a marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field, an interpretation which we substantiate via bosonization analysis and Monte Carlo calculations on model Gutzwiller variational wave functions. Our results represent one of the first numerical demonstrations of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly one-dimensional (Bethe chain) limit.
The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-one-dimensional strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge c = 2 and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors. We argue that this intriguing spin liquid phase can be understood as a marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field, an interpretation which we substantiate via bosonization analysis and Monte Carlo calculations on model Gutzwiller variational wave functions. Our results represent one of the first numerical demonstrations of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly one-dimensional (Bethe chain) limit.
We study fermionic quantum spin liquids (QSLs) on the three-dimensional trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frustration. Using the framework of projective symmetry groups (PSG), we obtain a classification of all symmetric Z 2 and U ( 1 ) QSLs on the trillium lattice. We find two Z 2 spin-liquids, and a single U ( 1 ) spin-liquid that is proximate to one of the Z 2 states. The small number of solutions reflects the constraints imposed by the nonsymmorphic symmetries in the space group of the trillium lattice. Using self-consistency conditions of the mean-field equations, we obtain the spinon band-structure and spin structure factors corresponding to these states. All three of our spin liquids are gapless at their saddle points: one of the two Z 2 QSLs is nodal, while the U ( 1 ) case hosts a spinon Fermi surface. One of our Z 2 spin liquids hosts a stable gapless nodal star that is protected by projective symmetries against additions of further neighbor terms in the mean-field ansatz. We comment on directions for further work.