Physical review. B, Condensed matter

Spin-liquid state of Wigner-Jordan fermions of the quantum antiferromagnetic Heisenberg model on a triangular lattice

Y. R. Wang

Published Jun 1, 1992• 15 citations

Abstract

A disordered spin state, the nearest-neighbor virtual bonding state of Wigner-Jordan fermions, of the quantum antiferromagnetic Heisenberg model on a triangular lattice is found to have a zero-temperature energy -1.106J per spin, lower than that calculated from spin-wave theories, and in excellent agreement with that from numerical calculations, (-1.094\ifmmode\pm\else\textpm\fi{}0.018)J per spin. The excitations of the state are Wigner-Jordan fermions with a gapless spectrum. The low-temperature specific heat is predicted to be proportional to ${\mathit{T}}^{\ensuremath{\nu}}$, with \ensuremath{\nu} between 2/3 and 1, significantly deviating from the spin-wave prediction, ${\mathit{T}}^{2}$. At higher temperature, a broad peak in the specific heat near T/2J\ensuremath{\approxeq}0.75 is also predicted.

DOI: 10.1103/physrevb.45.12604

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Physical review. B, Condensed matter

Spin-liquid state of Wigner-Jordan fermions of the quantum antiferromagnetic Heisenberg model on a triangular lattice

Y. R. Wang

Published Jun 1, 1992• 15 citations

Publisher

Abstract

{\mathit{T}}^{\ensuremath{\nu}}

, with \ensuremath{\nu} between 2/3 and 1, significantly deviating from the spin-wave prediction,

{\mathit{T}}^{2}

. At higher temperature, a broad peak in the specific heat near T/2J\ensuremath{\approxeq}0.75 is also predicted.

DOI: 10.1103/physrevb.45.12604

Related papers

Low-dimensional quantum antiferromagnetic Heisenberg model studied using Wigner-Jordan transformations

Y. R. Wang

A Wigner-Jordan (WJ) transformation is used to study the one-dimensional (1D) and two-dimensional (2D) quantum antiferromagnetic Heisenberg model. The advantage of using the Wigner-Jordan transformation is that it preserves all spin-commutation relations as well as the spin on-site exclusion principle. In the 1D case a nearest-neighbor covalent-bonding state of the WJ fermions is found to have a ground-state energy (-0.4351J per site) comparable with that from the Bethe-ansatz solution (-0.4431J per site), and a linear energy spectrum at low energies with velocity 1.6366J, in close agreement with the velocity obtained by Haldane for the quantum antiferromagnetic Heisenberg model with 1/ ${\mathit{d}}^{2}$ interaction (1.5708J). The method used for studying the 1D model is then applied to the 2D Heisenberg model in a square lattice. The resulting state at finite temperature is the in-phase flux state, i.e., a flux state of the Wigner-Jordan spinless fermions with an in-phase fermion orbital current circulating around each elementary plaquette.The single-particle excitation spectrum, i.e., the energy dispersion of reversing orientation of a spin in the system, of the in-phase flux state is overall similar to that of spin waves, with significant difference near the edge point k=(\ensuremath{\pi},0), at which the excitation energy of the WJ fermion is zero, whereas that of the spin-wave excitation is 2J. The specific heat of the in-phase flux state predicts a correct temperature dependence over the entire temperature range, namely a ${\mathit{T}}^{2}$ dependence at low temperature, a peak near T/J=0.6, and a 1/ ${\mathit{T}}^{2}$ decreasing at high temperature. It also gives excellent agreement with the specific heat calculated from numerical methods. In contrast, the spin-wave theory only correctly predicts a ${\mathit{T}}^{2}$ dependence at low temperature. The Raman spectrum of the in-phase flux state is calculated and shows significant improvement over that from spin-wave theories compared with the experimental spectrum of ${\mathrm{La}}_{2}$ ${\mathrm{CuO}}_{4}$ . The exchange parameter, J, obtained from the comparison is 1060 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in agreement with that obtained from analyzing the neutron-scattering data.A Wigner-Jordan (WJ) transformation is used to study the one-dimensional (1D) and two-dimensional (2D) quantum antiferromagnetic Heisenberg model. The advantage of using the Wigner-Jordan transformation is that it preserves all spin-commutation relations as well as the spin on-site exclusion principle. In the 1D case a nearest-neighbor covalent-bonding state of the WJ fermions is found to have a ground-state energy (-0.4351J per site) comparable with that from the Bethe-ansatz solution (-0.4431J per site), and a linear energy spectrum at low energies with velocity 1.6366J, in close agreement with the velocity obtained by Haldane for the quantum antiferromagnetic Heisenberg model with 1/${\mathit{d}}^{2}$ interaction (1.5708J). The method used for studying the 1D model is then applied to the 2D Heisenberg model in a square lattice. The resulting state at finite temperature is the in-phase flux state, i.e., a flux state of the Wigner-Jordan spinless fermions with an in-phase fermion orbital current circulating around each elementary plaquette.The single-particle excitation spectrum, i.e., the energy dispersion of reversing orientation of a spin in the system, of the in-phase flux state is overall similar to that of spin waves, with significant difference near the edge point k=(\ensuremath{\pi},0), at which the excitation energy of the WJ fermion is zero, whereas that of the spin-wave excitation is 2J. The specific heat of the in-phase flux state predicts a correct temperature dependence over the entire temperature range, namely a ${\mathit{T}}^{2}$ dependence at low temperature, a peak near T/J=0.6, and a 1/${\mathit{T}}^{2}$ decreasing at high temperature. It also gives excellent agreement with the specific heat calculated from numerical methods. In contrast, the spin-wave theory only correctly predicts a ${\mathit{T}}^{2}$ dependence at low temperature. The Raman spectrum of the in-phase flux state is calculated and shows significant improvement over that from spin-wave theories compared with the experimental spectrum of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. The exchange parameter, J, obtained from the comparison is 1060 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in agreement with that obtained from analyzing the neutron-scattering data.

Physical review. B, Condensed matterJul 1, 199252 citations

Excitation spectrum of the two-dimensional quantum antiferromagnetic Heisenberg model: Wigner-Jordan fermions or spin waves

Y. R. Wang, M. J. Rice, Han-Yong Choi

The excitation spectrum of the quantum antiferromagnetic Heisenberg model for a square lattice, as predicted from the in-phase flux state of Wigner-Jordan fermions, is calculated and compared with that calculated from conventional spin-wave theory. While the two spectra are overall similar, there are significant differences for short-wavelength excitations. The ratio of the excitation energy at wave vector (\ensuremath{\pi}/2,\ensuremath{\pi}/2) to that at (\ensuremath{\pi}/2,0) is predicted to be \ensuremath{\surd}2 for the Wigner-Jordan fermion excitations, and 2/ \ensuremath{\surd}3 for the spin-wave excitations. At long wavelengths, in contrast to the gapped spin-wave spectrum of Auerbach and Arovas, the excitation spectrum of Wigner-Jordan fermions is gapless at any finite temperature. Possible experimental examination of the excitation spectrum is discussed.The excitation spectrum of the quantum antiferromagnetic Heisenberg model for a square lattice, as predicted from the in-phase flux state of Wigner-Jordan fermions, is calculated and compared with that calculated from conventional spin-wave theory. While the two spectra are overall similar, there are significant differences for short-wavelength excitations. The ratio of the excitation energy at wave vector (\ensuremath{\pi}/2,\ensuremath{\pi}/2) to that at (\ensuremath{\pi}/2,0) is predicted to be \ensuremath{\surd}2 for the Wigner-Jordan fermion excitations, and 2/ \ensuremath{\surd}3 for the spin-wave excitations. At long wavelengths, in contrast to the gapped spin-wave spectrum of Auerbach and Arovas, the excitation spectrum of Wigner-Jordan fermions is gapless at any finite temperature. Possible experimental examination of the excitation spectrum is discussed.

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Theory of the spin liquid state of the Heisenberg antiferromagnet

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We propose that the disordered state of a two-dimensional spin-1/2 Heisenberg antiferromagnet is physically equivalent to the incompressible liquid state of the fractional quantum Hall system. The fractional quantum Hall state for bosons is shown to be an exact spin singlet and to possess a low variational energy for the near-neighbor Heisenberg model on a triangular lattice. Variational wave functions for neutral spin-1/2 excitations are constructed and shown to form an exact spin doublet. Variational energies of these states are calculated, and their spin density profiles are determined. We find that a localized spin-1/2 quaisparticle has a size comparable to a lattice bond length and an excitation energy \ensuremath{\Delta}=1.3J. The energy-momentum dispersion of quasiparticles and spin-1 collective modes, obtained variationally, supports the hypothesis that the spin liquid state has a finite energy gap. The 1/2 fractional statistics exhibited by the quasiparticle excitations is explicitly demonstrated.We propose that the disordered state of a two-dimensional spin-1/2 Heisenberg antiferromagnet is physically equivalent to the incompressible liquid state of the fractional quantum Hall system. The fractional quantum Hall state for bosons is shown to be an exact spin singlet and to possess a low variational energy for the near-neighbor Heisenberg model on a triangular lattice. Variational wave functions for neutral spin-1/2 excitations are constructed and shown to form an exact spin doublet. Variational energies of these states are calculated, and their spin density profiles are determined. We find that a localized spin-1/2 quaisparticle has a size comparable to a lattice bond length and an excitation energy \ensuremath{\Delta}=1.3J. The energy-momentum dispersion of quasiparticles and spin-1 collective modes, obtained variationally, supports the hypothesis that the spin liquid state has a finite energy gap. The 1/2 fractional statistics exhibited by the quasiparticle excitations is explicitly demonstrated.

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Quantum Spin-Liquid Behavior in the Spin-1/2 Random Heisenberg Antiferromagnet on the Triangular Lattice

Ken Watanabe, Hikaru Kawamura, Hiroki Nakano +1 more

Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this observation, we propose as a minimal model of the observed quantum spin-liquid behavior the S=1/2 antiferromagnetic Heisenberg on the triangular lattice with a quenched randomness in the exchange interaction. We study both zero- and finite-temperature properties of the model by an exact diagonalization method, to find that when the randomness exceeds a critical value the model exhibits a quantum spin-liquid ground state. This randomness-induced quantum spin-liquid state exhibits gapless behaviors including the temperature-linear specific heat. The results provide a consistent explanation of the recent experimental observations on organic salts.Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this observation, we propose as a minimal model of the observed quantum spin-liquid behavior the S=1/2 antiferromagnetic Heisenberg on the triangular lattice with a quenched randomness in the exchange interaction. We study both zero- and finite-temperature properties of the model by an exact diagonalization method, to find that when the randomness exceeds a critical value the model exhibits a quantum spin-liquid ground state. This randomness-induced quantum spin-liquid state exhibits gapless behaviors including the temperature-linear specific heat. The results provide a consistent explanation of the recent experimental observations on organic salts.

arXiv:1309.6309Journal of the Physical Society of JapanFeb 25, 2014142 citations

Marginal-Fermi-liquid behavior of charge carriers scattered by two-dimensional quantum antiferromagnetic spin fluctuations

Y. R. Wang, M. J. Rice, Han-Yong Choi

In the Wigner-Jordan (WJ) fermion representation of quantum spins with antiferromagnetic interaction, the WJ fermions always fill half of the total available states, and their energy spectrum possesses a particle-hole symmetry. These two intrinsic properties of the WJ representation, together with a finite density of states at small WJ-fermion excitation energy, give rise to the marginal-Fermi-liquid behavior of the charge carriers when they are scattered by the WJ fermions. The finite density of states of the WJ fermions at zero excitation energy is demonstrated for the defected quantum antiferromagnetic Heisenberg model in a square lattice.In the Wigner-Jordan (WJ) fermion representation of quantum spins with antiferromagnetic interaction, the WJ fermions always fill half of the total available states, and their energy spectrum possesses a particle-hole symmetry. These two intrinsic properties of the WJ representation, together with a finite density of states at small WJ-fermion excitation energy, give rise to the marginal-Fermi-liquid behavior of the charge carriers when they are scattered by the WJ fermions. The finite density of states of the WJ fermions at zero excitation energy is demonstrated for the defected quantum antiferromagnetic Heisenberg model in a square lattice.

Physical review. B, Condensed matterOct 1, 19927 citations

Exotic S=1 spin-liquid state with fermionic excitations on the triangular lattice

Maksym Serbyn, T. Senthil, Patrick A. Lee

Motivated by recent experiments on the material Ba ${}_{3}$ NiSb ${}_{2}$ O ${}_{9}$ , we consider a spin-one quantum antiferromagnet on a triangular lattice with the Heisenberg bilinear and biquadratic exchange interactions and a single-ion anisotropy. Using a fermionic ``triplon'' representation for spins, we study the phase diagram within mean-field theory. In addition to a fully gapped spin-liquid ground state, we find a state where one gapless triplon mode with a Fermi surface coexists with $d+id$ topological pairing of the other triplons. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Such a state has linear in-temperature specific heat and constant in-plane spin susceptibility, with an unusually high Wilson ratio.Motivated by recent experiments on the material Ba${}_{3}$NiSb${}_{2}$O${}_{9}$, we consider a spin-one quantum antiferromagnet on a triangular lattice with the Heisenberg bilinear and biquadratic exchange interactions and a single-ion anisotropy. Using a fermionic ``triplon'' representation for spins, we study the phase diagram within mean-field theory. In addition to a fully gapped spin-liquid ground state, we find a state where one gapless triplon mode with a Fermi surface coexists with $d+id$ topological pairing of the other triplons. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Such a state has linear in-temperature specific heat and constant in-plane spin susceptibility, with an unusually high Wilson ratio.

arXiv:1108.3070Physical Review BNov 3, 201149 citations

{\mathit{T}}^{\ensuremath{\nu}}

, with \ensuremath{\nu} between 2/3 and 1, significantly deviating from the spin-wave prediction,

{\mathit{T}}^{2}

. At higher temperature, a broad peak in the specific heat near T/2J\ensuremath{\approxeq}0.75 is also predicted.

{\mathit{d}}^{2}

interaction (1.5708J). The method used for studying the 1D model is then applied to the 2D Heisenberg model in a square lattice. The resulting state at finite temperature is the in-phase flux state, i.e., a flux state of the Wigner-Jordan spinless fermions with an in-phase fermion orbital current circulating around each elementary plaquette.The single-particle excitation spectrum, i.e., the energy dispersion of reversing orientation of a spin in the system, of the in-phase flux state is overall similar to that of spin waves, with significant difference near the edge point k=(\ensuremath{\pi},0), at which the excitation energy of the WJ fermion is zero, whereas that of the spin-wave excitation is 2J. The specific heat of the in-phase flux state predicts a correct temperature dependence over the entire temperature range, namely a

{\mathit{T}}^{2}

dependence at low temperature, a peak near T/J=0.6, and a 1/

{\mathit{T}}^{2}

decreasing at high temperature. It also gives excellent agreement with the specific heat calculated from numerical methods. In contrast, the spin-wave theory only correctly predicts a

{\mathit{T}}^{2}

dependence at low temperature. The Raman spectrum of the in-phase flux state is calculated and shows significant improvement over that from spin-wave theories compared with the experimental spectrum of

{\mathrm{La}}_{2}

{\mathrm{CuO}}_{4}

. The exchange parameter, J, obtained from the comparison is 1060 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, in agreement with that obtained from analyzing the neutron-scattering data.

Motivated by recent experiments on the material Ba

{}_{3}

NiSb

{}_{2}

{}_{9}

, we consider a spin-one quantum antiferromagnet on a triangular lattice with the Heisenberg bilinear and biquadratic exchange interactions and a single-ion anisotropy. Using a fermionic ``triplon'' representation for spins, we study the phase diagram within mean-field theory. In addition to a fully gapped spin-liquid ground state, we find a state where one gapless triplon mode with a Fermi surface coexists with

d+id

topological pairing of the other triplons. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Such a state has linear in-temperature specific heat and constant in-plane spin susceptibility, with an unusually high Wilson ratio.