arXiv:cond-mat/0407203 · Journal of Experimental and Theoretical Physics Letters

Quasi-one-dimensional anisotropic Heisenberg model in a transverse magnetic field

Д. В. Дмитриев, V. Ya. Krivnov

Published Sep 1, 2004• 10 citations

Abstract

The phase diagram of weakly coupled XXZ chains in a transverse magnetic field is studied using the mean-field approximation for the interchain coupling and known exact results for an effective one-dimensional model. The results are applied to the quasi-one-dimensional antiferromagnet Cs 2 CoCl 4 , and the value of interchain interaction in this compound is estimated.

DOI: 10.1134/1.1825110

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arXiv:cond-mat/0407203 · Journal of Experimental and Theoretical Physics Letters

Quasi-one-dimensional anisotropic Heisenberg model in a transverse magnetic field

Д. В. Дмитриев, V. Ya. Krivnov

Published Sep 1, 2004• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1134/1.1825110

Related papers

Anisotropic Heisenberg chain in coexisting transverse and longitudinal magnetic fields

Д. В. Дмитриев, V. Ya. Krivnov

The one-dimensional spin-1/2 $XXZ$ model in a mixed transverse and longitudinal magnetic field is studied. Using the specially developed version of the mean-field approximation the order-disorder transition induced by the magnetic field is investigated. The ground-state phase diagram is obtained. The behavior of the model in the low transverse field is studied on the basis of conformal field theory. The relevance of our results to the observed phase transition in the quasi-one-dimensional antiferromagnet ${\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}$ is discussed.The one-dimensional spin-1/2 $XXZ$ model in a mixed transverse and longitudinal magnetic field is studied. Using the specially developed version of the mean-field approximation the order-disorder transition induced by the magnetic field is investigated. The ground-state phase diagram is obtained. The behavior of the model in the low transverse field is studied on the basis of conformal field theory. The relevance of our results to the observed phase transition in the quasi-one-dimensional antiferromagnet ${\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}$ is discussed.

arXiv:cond-mat/0403035Physical Review BOct 25, 200439 citations

Role of the spin anisotropy of the interchain interaction in weakly coupled antiferromagnetic Heisenberg chains*

Yuchen Fan, Rong Yu

In quasi-one-dimensional (q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic (AFM) compound YbAlO3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations, and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave (LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.In quasi-one-dimensional (q1D) quantum antiferromagnets, the complicated interplay of intrachain and interchain exchange couplings may give rise to rich phenomena. Motivated by recent progress on field-induced phase transitions in the q1D antiferromagnetic (AFM) compound YbAlO3, we study the phase diagram of spin-1/2 Heisenberg chains with Ising anisotropic interchain couplings under a longitudinal magnetic field via large-scale quantum Monte Carlo simulations, and investigate the role of the spin anisotropy of the interchain coupling on the ground state of the system. We find that the Ising anisotropy of the interchain coupling can significantly enhance the longitudinal spin correlations and drive the system to an incommensurate AFM phase at intermediate magnetic fields, which is understood as a longitudinal spin density wave (LSDW). With increasing field, the ground state changes to a canted AFM order with transverse spin correlations. We further provide a global phase diagram showing how the competition between the LSDW and the canted AFM states is tuned by the Ising anisotropy of the interchain coupling.

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Within a mean-field theory, the disordered spin-1/2 single-chain state is shown to be unstable towards an antiferromagnetically, long-range ordered one, when any finite transverse coupling, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, is introduced between chains. A mean-field Hamiltonian is derived from the Heisenberg model, using an extension of the Wigner-Jordan transformation in two dimensions. The staggered magnetization and the ground-state energy are calculated for values of transverse couplings ranging from 0 to 1. The main consequence of these calculations is that the value of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, required to have antiferromagnetic long-range order, must only be nonzero. This result is consistent with that of Sakai and Takahashi indicating that the critical transverse coupling should be of order of the inverse of the one-dimensional staggered magnetic susceptibility. Following a qualitative argument, it can also suggest that the Luttinger-liquid state is unstable at least at nearly half-filling for the Hubbard model in the limit of large Coulomb repulsion.Within a mean-field theory, the disordered spin-1/2 single-chain state is shown to be unstable towards an antiferromagnetically, long-range ordered one, when any finite transverse coupling, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, is introduced between chains. A mean-field Hamiltonian is derived from the Heisenberg model, using an extension of the Wigner-Jordan transformation in two dimensions. The staggered magnetization and the ground-state energy are calculated for values of transverse couplings ranging from 0 to 1. The main consequence of these calculations is that the value of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, required to have antiferromagnetic long-range order, must only be nonzero. This result is consistent with that of Sakai and Takahashi indicating that the critical transverse coupling should be of order of the inverse of the one-dimensional staggered magnetic susceptibility. Following a qualitative argument, it can also suggest that the Luttinger-liquid state is unstable at least at nearly half-filling for the Hubbard model in the limit of large Coulomb repulsion.

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Fabian H. L. Eßler, Alexei M. Tsvelik, Gesualdo Delfino A

We study weakly coupled antiferromagnetic spin chains in their ordered phase by combining an exact solution of the single-chain problem with a random-phase-approximation analysis of the interchain interaction. A single chain is described by a quantum Sine-Gordon model and dynamical staggered susceptibilities are determined by employing the form-factor approach to quantum correlation functions. We consider both antiferromagnetic order encountered in quasi-one-dimensional materials such as ${\mathrm{KCuF}}_{3}$ and spin-Peierls order as found in ${\mathrm{CuGeO}}_{3}.$ We study weakly coupled antiferromagnetic spin chains in their ordered phase by combining an exact solution of the single-chain problem with a random-phase-approximation analysis of the interchain interaction. A single chain is described by a quantum Sine-Gordon model and dynamical staggered susceptibilities are determined by employing the form-factor approach to quantum correlation functions. We consider both antiferromagnetic order encountered in quasi-one-dimensional materials such as ${\mathrm{KCuF}}_{3}$ and spin-Peierls order as found in ${\mathrm{CuGeO}}_{3}.$

arXiv:cond-mat/9705196Physical review. B, Condensed matterNov 1, 199787 citations

The one-dimensional spin-1/2

XXZ

model in a mixed transverse and longitudinal magnetic field is studied. Using the specially developed version of the mean-field approximation the order-disorder transition induced by the magnetic field is investigated. The ground-state phase diagram is obtained. The behavior of the model in the low transverse field is studied on the basis of conformal field theory. The relevance of our results to the observed phase transition in the quasi-one-dimensional antiferromagnet

{\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}

is discussed.

{\mathit{H}}_{\mathit{c}1}

(=\ensuremath{\Delta}), where \ensuremath{\Delta} is the Haldane gap. It is also found that the transverse spin correlation has the asymptotic form 〈

{\mathit{S}}_{0}^{\mathit{x}}

{\mathit{S}}_{\mathit{r}}^{\mathit{x}}

〉\ensuremath{\sim}(-1

{)}^{\mathit{r}}

${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}}}$, and the transverse staggered susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{st}}^{\mathit{x}\mathit{x}}$ diverges between

{\mathit{H}}_{\mathit{c}1}

and

{\mathit{H}}_{\mathit{c}2}

(=4). The exponent \ensuremath{\eta} has a minimum (\ensuremath{\eta}\ensuremath{\simeq}0.3) at magnetization m\ensuremath{\simeq}1/3 and \ensuremath{\eta}\ensuremath{\simeq}0.5 at

{\mathit{H}}_{\mathit{c}1}

and

{\mathit{H}}_{\mathit{c}2}

. If the system is quasi-one-dimensional, even small interchain couplings can create a canted N\'eel order, within a mean-field approximation for interchain interactions. This is consistent with a recent NMR measurement for Ni(

{\mathrm{C}}_{2}

{\mathrm{H}}_{8}

{\mathrm{N}}_{2}

{)}_{2}

{\mathrm{NO}}_{2}

(

{\mathrm{ClO}}_{4}

) (NENP) at low temperature.

{\mathrm{Cs}}_{2}{\mathrm{CoCl}}_{4}.

{\mathrm{KCuF}}_{3}

and spin-Peierls order as found in

{\mathrm{CuGeO}}_{3}.