We present the magnetic phase diagram of the $\ensuremath{\nu}=2$ quantum Hall system on the whole $({r}_{s},{E}_{Z})$ plane. We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin-density excitations in the time-dependent Hartree-Fock theory. A nontrivial phase is obtained in the self-consistent Hartree-Fock theory for ${r}_{s}\ensuremath{\sim}2$ and ${E}_{Z}\ensuremath{\lesssim}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where both the paramagnetic and ferromagnetic states show spin instability. We show that the obtained phase is the spin-density wave (SDW) state, and explain the mechanism how the SDW stabilizes.We present the magnetic phase diagram of the $\ensuremath{\nu}=2$ quantum Hall system on the whole $({r}_{s},{E}_{Z})$ plane. We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin-density excitations in the time-dependent Hartree-Fock theory. A nontrivial phase is obtained in the self-consistent Hartree-Fock theory for ${r}_{s}\ensuremath{\sim}2$ and ${E}_{Z}\ensuremath{\lesssim}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where both the paramagnetic and ferromagnetic states show spin instability. We show that the obtained phase is the spin-density wave (SDW) state, and explain the mechanism how the SDW stabilizes.

Physical Review BMar 24, 20092 citations

Spin waves in linear magnetic chains

Martin Blume, George H. Vineyard, Richard E. Watson

Physics Letters AJan 1, 197515 citations

Triangular-lattice anisotropic dimerized Heisenberg antiferromagnet: Stability and excitations of the quantum paramagnetic phase

R. L. Doretto, Matthias Vojta C

Motivated by experiments on nonmagnetic triangular-lattice Mott insulators, we study one candidate paramagnetic phase, namely the columnar dimer (or valence-bond) phase. We apply variants of the bond-operator theory to a dimerized and spatially anisotropic spin-1/2 Heisenberg model and determine its zero-temperature phase diagram and the spectrum of elementary triplet excitations (triplons). Depending on model parameters, we find that the minimum of the triplon energy is located at either a commensurate or an incommensurate wave vector. Condensation of triplons at this commensurate-incommensurate transition defines a quantum Lifshitz point, with effective dimensional reduction that possibly leads to nontrivial paramagnetic (e.g., spin-liquid) states near the closing of the triplet gap. We also discuss the two-particle decay of high-energy triplons, and we comment on the relevance of our results for the organic Mott insulator EtMe ${}_{3}$ P[Pd(dmit) ${}_{2}$ ] ${}_{2}$ .Motivated by experiments on nonmagnetic triangular-lattice Mott insulators, we study one candidate paramagnetic phase, namely the columnar dimer (or valence-bond) phase. We apply variants of the bond-operator theory to a dimerized and spatially anisotropic spin-1/2 Heisenberg model and determine its zero-temperature phase diagram and the spectrum of elementary triplet excitations (triplons). Depending on model parameters, we find that the minimum of the triplon energy is located at either a commensurate or an incommensurate wave vector. Condensation of triplons at this commensurate-incommensurate transition defines a quantum Lifshitz point, with effective dimensional reduction that possibly leads to nontrivial paramagnetic (e.g., spin-liquid) states near the closing of the triplet gap. We also discuss the two-particle decay of high-energy triplons, and we comment on the relevance of our results for the organic Mott insulator EtMe${}_{3}$P[Pd(dmit)${}_{2}$]${}_{2}$.

arXiv:1111.4327Physical Review BMar 26, 201216 citations

On the theory of spin paramagnetism

Annals of PhysicsJun 1, 19610 citations

Power-law correlated phase in random-field XY models and randomly pinned charge-density waves

Ronald Fisch

Monte Carlo simulations have been used to study the ${\mathrm{Z}}_{\mathrm{N}}$ ferromagnet in a random field on simple cubic lattices for N=6 and N=12. The random field is chosen to have infinite strength and random direction on a fraction x of the sites of the lattice, and to be zero on the remaining sites. For N=6 and x=1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the sixfold nonrandom anisotropy. The intermediate temperature phase is characterized by a |k${\mathrm{|}}^{\mathrm{\ensuremath{-}}3}$ decay of two-spin correlations, but no true ferromagnetic order. At the transition between the power-law correlated phase and the paramagnetic phase the magnetic susceptibility diverges, and the two-spin correlations decay approximately as |k${\mathrm{|}}^{\mathrm{\ensuremath{-}}2.87}$. There is no evidence for a latent heat at either transition, but the magnetization seems to disappear discontinuously. For N=6 and x=1/8 the correlation length never exceeds 12, and the paramagnetic phase goes directly into the ferromagnetic phase; the two-spin correlation function is peaked at small |k|, but the only divergence is the ferromagnetic \ensuremath{\delta} function at |k|=0. Results in the paramagnetic and power-law correlated phases for N=12 are essentially identical to those for N=6, so the power-law correlated phase should exist in the limit N\ensuremath{\rightarrow}\ensuremath{\infty}. The ferromagnetic phase terminates near x=1/6 for N=6, but the limit of ferromagnetic stability for N=12 is less than x=1/16.Monte Carlo simulations have been used to study the ${\mathrm{Z}}_{\mathrm{N}}$ ferromagnet in a random field on simple cubic lattices for N=6 and N=12. The random field is chosen to have infinite strength and random direction on a fraction x of the sites of the lattice, and to be zero on the remaining sites. For N=6 and x=1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the sixfold nonrandom anisotropy. The intermediate temperature phase is characterized by a |k${\mathrm{|}}^{\mathrm{\ensuremath{-}}3}$ decay of two-spin correlations, but no true ferromagnetic order. At the transition between the power-law correlated phase and the paramagnetic phase the magnetic susceptibility diverges, and the two-spin correlations decay approximately as |k${\mathrm{|}}^{\mathrm{\ensuremath{-}}2.87}$. There is no evidence for a latent heat at either transition, but the magnetization seems to disappear discontinuously. For N=6 and x=1/8 the correlation length never exceeds 12, and the paramagnetic phase goes directly into the ferromagnetic phase; the two-spin correlation function is peaked at small |k|, but the only divergence is the ferromagnetic \ensuremath{\delta} function at |k|=0. Results in the paramagnetic and power-law correlated phases for N=12 are essentially identical to those for N=6, so the power-law correlated phase should exist in the limit N\ensuremath{\rightarrow}\ensuremath{\infty}. The ferromagnetic phase terminates near x=1/6 for N=6, but the limit of ferromagnetic stability for N=12 is less than x=1/16.

arXiv:cond-mat/9608036Physical review. B, Condensed matterApr 1, 199712 citations

We present the magnetic phase diagram of the $\ensuremath{\nu}=2$ quantum Hall system on the whole

({r}_{s},{E}_{Z})

plane. We fix the phase boundaries of the paramagnetic and ferromagnetic states by looking for a softening of spin-density excitations in the time-dependent Hartree-Fock theory. A nontrivial phase is obtained in the self-consistent Hartree-Fock theory for ${r}_{s}\ensuremath{\sim}2$ and ${E}_{Z}\ensuremath{\lesssim}0.06\ensuremath{\hbar}{\ensuremath{\omega}}_{c}$, where both the paramagnetic and ferromagnetic states show spin instability. We show that the obtained phase is the spin-density wave (SDW) state, and explain the mechanism how the SDW stabilizes.

{}_{3}

P[Pd(dmit)

{}_{2}

]

{}_{2}

Monte Carlo simulations have been used to study the

{\mathrm{Z}}_{\mathrm{N}}

ferromagnet in a random field on simple cubic lattices for N=6 and N=12. The random field is chosen to have infinite strength and random direction on a fraction x of the sites of the lattice, and to be zero on the remaining sites. For N=6 and x=1/16 there are two phase transitions. At low temperature there is a ferromagnetic phase, which is stabilized by the sixfold nonrandom anisotropy. The intermediate temperature phase is characterized by a |k${\mathrm{|}}^{\mathrm{\ensuremath{-}}3}$ decay of two-spin correlations, but no true ferromagnetic order. At the transition between the power-law correlated phase and the paramagnetic phase the magnetic susceptibility diverges, and the two-spin correlations decay approximately as |k${\mathrm{|}}^{\mathrm{\ensuremath{-}}2.87}$. There is no evidence for a latent heat at either transition, but the magnetization seems to disappear discontinuously. For N=6 and x=1/8 the correlation length never exceeds 12, and the paramagnetic phase goes directly into the ferromagnetic phase; the two-spin correlation function is peaked at small |k|, but the only divergence is the ferromagnetic \ensuremath{\delta} function at |k|=0. Results in the paramagnetic and power-law correlated phases for N=12 are essentially identical to those for N=6, so the power-law correlated phase should exist in the limit N\ensuremath{\rightarrow}\ensuremath{\infty}. The ferromagnetic phase terminates near x=1/6 for N=6, but the limit of ferromagnetic stability for N=12 is less than x=1/16.