Variational wave functions for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math>Heisenberg model on the anisotropic triangular lattice: Spin liquids and spiral orders

Ghorbani, Elaheh; Tocchio, Luca F.; Becca, Federico

doi:10.1103/physrevb.93.085111

Cited by 35 publications

(42 citation statements)

References 53 publications

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“…But, U eff cancels from the ratio of superexchange parameters, e.g., J SE B /J SE y ∼ 2t 2 B /(t 2 r + t 2 S ), allowing this to be calculated. The values in Table II 3) which gives rise to a gapless spin-liquid state [6][7][8][9][10][11].…”

Section: Supplementary Informationmentioning

confidence: 98%

Frustration, ring exchange, and the absence of long-range order inEtMe3Sb[Pd(dmit)2]2: From first principles to many-body theory

Kenny

David

Ferré

et al. 2020

Phys. Rev. Materials

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We parameterize Hubbard and thence spin models for EtMe3Sb[Pd(dmit)2]2 from broken symmetry density functional calculations. This gives a scalene triangular model where the largest net exchange interaction is three times larger than the mean interchain coupling. The chain random phase approximation shows that the difference in the interchain couplings is equivalent to a bipartite interchain coupling, favoring long-range magnetic order. This competes with ring exchange, which favors quantum disorder. Ring exchange wins.EtMe 3 Sb[Pd(dmit) 2 ] 2 (EtMe 3 Sb) is a quantum spin liquid (QSL) candidate shrouded in mystery. It lacks magnetic ordering down to the lowest temperatures measured [1-3], but the physics that results in a quantum disordered state remains under debate. EtMe 3 Sb shares important structural motifs with the quantum spin liquids κ-(BEDT-TTF) 2 Cu 2 (CN) 3 (κ-Cu) and κ-(BEDT-TTF) 2 Ag 2 (CN) 3 (κ-Ag). A crucial question is: how closely related are their ground states?EtMe 3 Sb, κ-Cu, and κ-Ag all form structures with alternating layers of organic molecules and counter-ions. In all three materials, the organic molecules dimerize with one unpaired electron found on each dimer in the insulating phase. The main structural difference between them is the spacial arrangement the dimers. Within κ-Cu and κ-Ag, neighboring dimers are almost perpendicular to one another, whereas in EtMe 3 Sb, the dimers (gray circles in Fig. 1a) form quasi-onedimensional stacks (along the horizontal in Fig. 1a).κ-Cu and κ-Ag are Mott insulators. In the strong coupling limit, where the Hubbard U is much greater than the largest interdimer hopping integral, t, their insulating phase is described by the isosceles triangular Heisenberg model (Fig. 1c). This model has two candidate QSL phases. Firstly, a QSL has been suggested in the region 0.6 J /J 0.9 [4-6], for which the ground state remains controversial. Secondly, the large J /J limit is adiabatically connected to the Tomonaga-Luttinger liquid (TLL) expected for uncoupled chains, J /J 1.4 [6][7][8][9][10][11]. Theories in this regime show an emergent 'one-dimensionalization' whereby the many-body state is more one-dimensional than the underlying Hamiltonian [12][13][14][15]. However, the validity of the strong coupling limit in these materials is uncertain because both materials undergo a Mott metal-insulator transition under moderate pressures. This motivates the inclusion of higher order terms, most importantly ring exchange, in the spin model. It has been shown that these can also cause QSL phases [16][17][18][19][20].Many early studies explored the possibility that the spin liquid in EtMe 3 Sb can be explained by one of the above theories. However, the lower symmetry of EtMe 3 Sb means that all three exchange interactions are different, i.e., it is described by a scalene triangular lattice, Fig. 1a,b. EtMe 3 Sb is also close to a Mott transition and so ring exchange is likely to be important.

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Section: Supplementary Informationmentioning

confidence: 98%

Frustration, ring exchange, and the absence of long-range order inEtMe3Sb[Pd(dmit)2]2: From first principles to many-body theory

Kenny

David

Ferré

et al. 2020

Phys. Rev. Materials

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“…The antiferromagnetic Heisenberg model on the anisotropic triangular-lattice is widely believed to be well described by Cs 2 CuBr 4 and Cs 2 CuCl 4 [50]. While Cs 2 CuCl 4 exhibits spin-liquid behavior over a broad temperature range [43,51], the Cs 2 CuBr 4 compound exhibits a magnetically ordered ground state with spiral order in zero magnetic field [6].…”

Section: Model Hamiltonianmentioning

confidence: 99%

Torque equilibrium spin wave theory study of anisotropy and Dzyaloshinskii-Moriya interaction effects on the indirect K -edge RIXS spectrum of a triangular lattice antiferromagnet

et al. 2019

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We apply the recently formulated torque equilibrium spin wave theory (TESWT) to compute the 1/S -order interacting K -edge bimagnon resonant inelastic x-ray scattering (RIXS) spectra of an anisotropic triangular lattice antiferromagnet with Dzyaloshinskii-Moriya (DM) interaction. We extend the interacting torque equilibrium formalism, incorporating the effects of DM interaction, to appropriately account for the zero-point quantum fluctuation that manifests as the emergence of spin Casimir effect in a noncollinear spin spiral state. Using inelastic neutron scattering data from Cs 2 CuCl 4 we fit the 1/S corrected TESWT dispersion to extract exchange and DM interaction parameters. We use these new fit coefficients alongside other relevant model parameters to investigate, compare, and contrast the effects of spatial anisotropy and DM interaction on the RIXS spectra at various points across the magnetic Brillouin zone. We highlight the key features of the bi-and trimagnon RIXS spectrum at the two inequivalent rotonlike points, M(0, 2π/ √3) and M (π, π/ √ 3), whose behavior is quite different from an isotropic triangular lattice system. While the roton RIXS spectrum at the M point undergoes a spectral downshift with increasing anisotropy, the peak at the M location loses its spectral strength without any shift. With the inclusion of DM interaction the spiral phase is more stable and the peak at both M and M point exhibits a spectral upshift. Our calculation offers a practical example of how to calculate interacting RIXS spectra in a non-collinear quantum magnet using TESWT. Our findings provide an opportunity to experimentally test the predictions of interacting TESWT formalism using RIXS, a spectroscopic method currently in vogue. PACS number(s): 78.70. Ck, 75.10.Jm

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“…For antiferromagnetic xy-coupling with spatial anisotropy there has been a controversial discussion on a possible spin liquid phase [28][29][30][31][32][33][34][35][36][37][38][39][40] or an incommensurate phase [42,43]. For hard-core bosons in optical lattices the hopping parameter plays the role of a ferromagnetic xy-coupling.…”

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confidence: 99%

Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

Zhang

Pelster

et al. 2016

Phys. Rev. Lett.

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We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both hopping and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstrate that this intermediate phase results from the proliferation of topological defects in the form of quantum bosonic domain walls. Accordingly, the structure factor has peaks at wave vectors, which are linearly related to the number of domain walls in a finite system in agreement with extensive quantum Monte Carlo simulations. We discuss possible connections with the supersolid behavior in the high-temperature superconducting striped phase. [42,43]. For hard-core bosons in optical lattices the hopping parameter plays the role of a ferromagnetic xy-coupling. In this case, nearest neighbor interacting bosons are realizable, for instance, with magnetic erbium atoms [48]. On the triangular lattice [49,50] they have been predicted to show supersolid behavior [12][13][14][15][16][17][18][19][20][21], which is characterized by two independent spontaneously broken symmetries -U(1) and translation -with corresponding superfluid and density order. For an anisotropic triangular lattice the commensurate supersolid phase is found to be unstable [26,27], and the solid order turns out to be incommensurate [41].Supersolid phases with two independently broken order parameters were first discussed for solid He [51,52] and were more recently shown to exist theoretically [12][13][14][15][16][17][18][19][20][21] and experimentally [53,54] in optical lattices for ultracold gases. Although high-temperature superconductors [55][56][57] are not often mentioned in this context, the coexistence of superconductivity and anti-ferromagnetic density order, so-called superstripes, are the defining characteristics of an incommensurate supersolid. Remarkably, the analogous physical phenomenon of incommensurate density order together with a finite superfluid density can be observed in a simple hard-core boson model. In the following we present a quantitative analytical model for this behavior in terms of topological defects in their simplest form, namely an increasing number of domain walls. Obviously the microscopic model of high-temperature superconductors is quite different, but the detailed understanding of the underlying mechanism via a spontaneous appearance of domain walls [55-57] is a helpful unifying feature of these many-body phenomena.In this paper we analyze the quantum phase diagram of hard-core bosons with anisotropic hopping t, t ′ ≥ 0 and nearest neighbor interactions V, V ′ ≥ 0 on a triangular latticê H =

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Variational wave functions for theS=12Heisenberg model on the anisotropic triangular lattice: Spin liquids and spiral orders

Cited by 35 publications

References 53 publications

Frustration, ring exchange, and the absence of long-range order inEtMe3Sb[Pd(dmit)2]2: From first principles to many-body theory

Frustration, ring exchange, and the absence of long-range order inEtMe3Sb[Pd(dmit)2]2: From first principles to many-body theory

Torque equilibrium spin wave theory study of anisotropy and Dzyaloshinskii-Moriya interaction effects on the indirect K -edge RIXS spectrum of a triangular lattice antiferromagnet

Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

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