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arXiv:1109.6464 · Physical Review B

Dynamical spin structure factors of quantum spin nematic states

Ryuichi Shindou, Seiji Yunoki, Tsutomu Momoi

Published Feb 22, 2013• 25 citations
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Abstract

Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-$\frac{1}{2}$ square-lattice ${J}_{1}$-${J}_{2}$ model with ferromagnetic ${J}_{1}$ and competing antiferromagnetic ${J}_{2}$ interactions. To this end, we use a fermion representation, generalizing it to $N$ flavors. We begin with a spin-triplet pairing state of fermion fields, called ${Z}_{2}$ planar state, which is a stable saddle-point solution in the large-$N$ limit in a finite parameter range where the couplings ${J}_{1}$ and ${J}_{2}$ compete strongly [R. Shindou and T. Momoi, Phys. Rev. B 80, 064410 (2009)]. Using a large-$N$ expansion, we take into account fluctuations around this saddle point up to corrections of order $1/N$. The dynamical spin structure factors thus obtained signify the existence of gapless $q$-linear director-wave (spin-wave) modes at $\mathbit{q}=(0,0)$ and gapped ``gauge-field''-like collective modes at $\mathbit{q}=(\ensuremath{\pi},\ensuremath{\pi})$, whose spectral weight vanishes as a linear and quadratic function of the momentum, respectively. The low-energy collective modes contain fluctuations of nematic-director, spin, and gauge degrees of freedom. Associated with the gapless $q$-linear modes, we evaluate the temperature dependence of the nuclear spin relaxation rate $1/{T}_{1}$ in the low-temperature regime as $1/{T}_{1}\ensuremath{\propto}{T}^{2d\ensuremath{-}1}$, where $d$ is the effective spatial dimension.

DOI
10.1103/physrevb.87.054429

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Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-12\frac{1}{2}21​ square-lattice J1{J}_{1}J1​-J2{J}_{2}J2​ model with ferromagnetic J1{J}_{1}J1​ and competing antiferromagnetic J2{J}_{2}J2​ interactions. To this end, we use a fermion representation, generalizing it to NNN flavors. We begin with a spin-triplet pairing state of fermion fields, called Z2{Z}_{2}Z2​ planar state, which is a stable saddle-point solution in the large-NNN limit in a finite parameter range where the couplings J1{J}_{1}J1​ and J2{J}_{2}J2​ compete strongly [R. Shindou and T. Momoi, Phys. Rev. B 80, 064410 (2009)]. Using a large-NNN expansion, we take into account fluctuations around this saddle point up to corrections of order 1/N1/N1/N. The dynamical spin structure factors thus obtained signify the existence of gapless qqq-linear director-wave (spin-wave) modes at \mathbitq=(0,0)\mathbit{q}=(0,0)\mathbitq=(0,0) and gapped ``gauge-field''-like collective modes at \mathbitq=(\ensuremathπ,\ensuremathπ)\mathbit{q}=(\ensuremath{\pi},\ensuremath{\pi})\mathbitq=(\ensuremathπ,\ensuremathπ), whose spectral weight vanishes as a linear and quadratic function of the momentum, respectively. The low-energy collective modes contain fluctuations of nematic-director, spin, and gauge degrees of freedom. Associated with the gapless qqq-linear modes, we evaluate the temperature dependence of the nuclear spin relaxation rate 1/T11/{T}_{1}1/T1​ in the low-temperature regime as 1/T1\ensuremath∝T2d\ensuremath−11/{T}_{1}\ensuremath{\propto}{T}^{2d\ensuremath{-}1}1/T1​\ensuremath∝T2d\ensuremath−1, where ddd is the effective spatial dimension.
We investigate the dynamical quadrupole structure factor of a spin-1/2 J1-J2 Heisenberg chain with competing ferromagnetic J1 and antiferromagnetic J2 in a magnetic field by exploiting density-matrix renormalization group techniques. In a field-induced spin nematic regime, we observe gapless excitations at q=π according to quasi-long-range antiferro-quadrupole correlations. The gapless excitation mode has a quadratic form at the saturation, while it changes into a linear dispersion as the magnetization decreases.
We investigate the quantum spin-1/2 zigzag chain with frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\mathrm{\ensuremath{\Gamma}}$ term, both with and without an applied magnetic field. Based on the density-matrix renormalization group calculation, we map out the ground-state phase diagram that shows a variety of magnetic and nonmagnetic phases including multicritical points and several exactly solvable points. Upon introducing a finite $\mathrm{\ensuremath{\Gamma}}$ term, we observe the persistent dimer-singlet state of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model, sustaining a nonzero spin gap, while also hosting a gapless nonmagnetic excitation that manifests in the substantial zero-energy peak in the nematic dynamical structure factor. This gapless peak-mode, remaining almost as a fluctuation to the ground state, induces a dilute but robust concentration of nematicity on top of singlets on dimers, which we call the nematic singlet-dimer phase. When the whole nematic excited mode condenses and replaces the singlet, the nematic-dimer phase transforms into the Ising-type ferromagnetic or antiferromagnetic long-range orders. The $\mathrm{\ensuremath{\Gamma}}$ term spontaneously selects magnetic easy axes, and their orientations dictate the type of magnetic order under geometric frustration effects as predicted by Landau's mean-field theory. These theoretical findings provide insights into the exotic low-temperature phase observed in YbCuS2{\mathrm{YbCuS}}_{2}YbCuS2​, characterized by gapless excitations and seemingly nonmagnetic behavior.
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The dynamical spin structure factor is computed within a variational framework to study the one-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. Starting from Gutzwiller-projected fermionic wave functions, the low-energy spectrum is constructed from two-spinon excitations. The direct comparison with Lanczos calculations on small clusters demonstrates the excellent description of both gapless and gapped (dimerized) phases, including incommensurate structures for J2/J1>0.5{J}_{2}/{J}_{1}>0.5J2​/J1​>0.5. Calculations on large clusters show how the intensity evolves when increasing the frustrating ratio and give an unprecedented accurate characterization of the dynamical properties of (nonintegrable) frustrated spin models.
We consider the effective model of H=−J1∑Si⋅Sj−J2∑(Si⋅Sj)2H=-J_{1}\sum_{}\mathbf{S}_{i}\cdot \mathbf{S}_{j}-J_{2}\sum_{}(\mathbf{S}_{i}\cdot \mathbf{S}_{j}) ^{2}H=−J1​∑​Si​⋅Sj​−J2​∑​(Si​⋅Sj​)2, describing the Mott insulating phase with odd number of spin-1 bosons in optical lattices (J2>J1>0J_{2}>J_{1}>0J2​>J1​>0). In terms of an SU(3) boson representation, a valence bond mean field theory is developed. In 1D, a \textit{first-order} quantum phase transition from a spin singlet to a spin nematic phase with \textit{gapful} excitations is identified at $ J_{1}/J_{2}=0.19833$, while on a 2D square lattice a spin nematic ordered phase with gapless excitations prevails. In both 1D and 2D cases, we predict that the spin structure factor displays dominant antiferromagnetic fluctuations, while the quadrupole structure factor exhibits strong ferroquadrupolar correlations.
We compute the zero temperature dynamical structure factor S(q,ω)S({\bf q},\omega)S(q,ω) of the triangular lattice Heisenberg model using a Schwinger Boson approach that includes the Gaussian fluctuations (1/N1/N1/N correction) of the saddle point solution. While the ground state of this model exhibits a well-known 120∘^{\circ}∘ magnetic ordering, the excitation spectrum revealed by S(q,ω)S({\bf q},\omega)S(q,ω) has a strong quantum character that is not captured by low-order 1/S1/S1/S expansions. The low-energy magnons consist of two spinon bound states confined by gauge fluctuations of the auxiliary fields, which can produce internal structure of the magnon peaks. In addition, the high-energy continuum of spinon modes extends up to about three times the single-magnon bandwidth.