Physical review. B, Condensed matter

Complete solution of theXXZmodel on finite rings: Finite-temperature structure factors

K. Fabricius, U. Löw, K.-H. Mütter

Published Apr 1, 1995• 3 citations

Abstract

The transverse and longitudinal structure factors of the spin-1/2 XXZ model are determined from a complete diagonalization of the Hamiltonian on rings with N=4,...,16 sites. At fixed critical momentum p=\ensuremath{\pi}, we observe the critical low-temperature behavior as it is predicted by scaling arguments. Finite-size scaling works well for the transverse structure factors. However, it breaks down for the longitudinal structure factors if the anisotropy is too large (\ensuremath{\gamma}>0.3\ensuremath{\pi}). We also investigate the low-temperature behavior of the uniform susceptibility.

DOI: 10.1103/physrevb.51.8270

Related papers

Complete solution of the XXZ-model on finite rings; dynamical structure factors at zero temperature

K Fabricius, K -H Mutter, U Low

The finite-size effects of the dynamical structure factors in the XXZ-model are studied in the euclidean time ( tau -) representation. Away from the critical momentum p= pi finite-size effects rum out to be small except for in large- tau limit. The large finite-size effects at the critical momentum p= pi signal the emergence of infrared singularities in the spectral ( omega ) representation of the dynamical structure factors.

arXiv:cond-mat/9502072Journal of Physics Condensed MatterJul 10, 19952 citations

Finite-size analysis of the structure factors in the one-dimensional spin-1/2 antiferromagneticXXZmodel

Michael Karbach, K.-H. Mütter, M. Schmidt

arXiv:cond-mat/9403005Physical review. B, Condensed matterOct 1, 199417 citations

Static structure factors of the XXZ-model in the presence of a uniform field

Michael Karbach, K -H Mutter, M Schmidt

The static structure factors of the XXZ-model in the presence of a uniform field are determined from an exact computation of the ground states at given total spin on rings with N=4,6,...,28 sites. Against the naive expectation, a weak uniform field strengthens the antiferromagnetic order in the transverse structure factor for the isotropic case.

arXiv:cond-mat/9410105Journal of Physics Condensed MatterApr 3, 19956 citations

Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization

K. Fabricius, U. Löw, Joachim Stolze

arXiv:cond-mat/9611077Physical review. B, Condensed matterMar 1, 199771 citations

Magnetic properties of a spin-1/2 Heisenberg XXZ model in the presence of longitudinal, transverse and transverse staggered magnetic fields: effect of inhomogeneity property

Hamid Arian Zad, Moones Sabeti, Azam Zoshki

Dec 30, 20180 citations

The antiferromagnetic spin- 1/2 -XXZ model on rings with an odd number of sites

Michael Karbach, K -H Mutter

The ground-state energies of the antiferromagnetic XXZ model at a given spin are determined on chains with an odd number N of sites. Analytical and numerical solutions of the Bethe ansatz equations are compared for the N-even and N-odd case. The scaling properties of the ground-state energies enable the determination of the zero-temperature susceptibility. For the isotropic case, we analyse the logarithmic terms in the low-field limit.

Journal of Physics A Mathematical and GeneralAug 21, 199522 citations

Physical review. B, Condensed matter

Complete solution of theXXZmodel on finite rings: Finite-temperature structure factors

K. Fabricius, U. Löw, K.-H. Mütter

Published Apr 1, 1995• 3 citations

Publisher

Abstract

DOI: 10.1103/physrevb.51.8270

Related papers

Complete solution of the XXZ-model on finite rings; dynamical structure factors at zero temperature

K Fabricius, K -H Mutter, U Low

arXiv:cond-mat/9502072Journal of Physics Condensed MatterJul 10, 19952 citations

Finite-size analysis of the structure factors in the one-dimensional spin-1/2 antiferromagneticXXZmodel

Michael Karbach, K.-H. Mütter, M. Schmidt

We perform a finite-size analysis of the longitudinal and transverse structure factors ${\mathit{S}}_{\mathit{j}}$ (p,\ensuremath{\gamma},N),j=1,3 in the ground state of the one-dimensional spin-1/2 XXZ model. Comparison with the exact results of Tonegawa for the XX model yields excellent agreement.We perform a finite-size analysis of the longitudinal and transverse structure factors ${\mathit{S}}_{\mathit{j}}$(p,\ensuremath{\gamma},N),j=1,3 in the ground state of the one-dimensional spin-1/2 XXZ model. Comparison with the exact results of Tonegawa for the XX model yields excellent agreement.

arXiv:cond-mat/9403005Physical review. B, Condensed matterOct 1, 199417 citations

Static structure factors of the XXZ-model in the presence of a uniform field

Michael Karbach, K -H Mutter, M Schmidt

arXiv:cond-mat/9410105Journal of Physics Condensed MatterApr 3, 19956 citations

Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization

K. Fabricius, U. Löw, Joachim Stolze

All eigenstates and eigenvalues are determined for the spin- XXZ chain H=2J${\ensuremath{\sum}}_{\mathrm{i}}$( ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{x}}$ ${\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{x}}$ + ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{y}}$ ${\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{y}}$ +\ensuremath{\Delta} ${\mathrm{S}}_{\mathrm{i}}^{\mathrm{z}}$ ${\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{z}}$ ) for rings with up to N=16 spins, for anisotropies \ensuremath{\Delta}=0, cos (0.3\ensuremath{\pi}), and 1. The dynamic spin pair correlations 〈${\mathrm{S}}_{\mathrm{l}+\mathrm{n}}^{\mathrm{\ensuremath{\mu}}}$(t)${\mathrm{S}}_{\mathrm{l}}^{\mathrm{\ensuremath{\mu}}}$〉, (\ensuremath{\mu}=x,z), the dynamic structure factors ${\mathrm{S}}^{\mathrm{\ensuremath{\mu}}}$(q,\ensuremath{\omega}), and the intermediate structure factors ${\mathrm{I}}^{\mathrm{\ensuremath{\mu}}}$(q,t) are calculated for arbitrary temperature T. It is found that for all T, ${\mathrm{S}}^{\mathrm{z}}$ (q,\ensuremath{\omega}) is mainly concentrated on the region |\ensuremath{\omega}|${\mathrm{\ensuremath{\varepsilon}}}_{2}$(q), where ${\mathrm{\ensuremath{\varepsilon}}}_{2}$(q) is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors ${\mathrm{I}}^{\mathrm{\ensuremath{\mu}}}$(q,t) for \ensuremath{\Delta}\ensuremath{\ne}0 show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin-correlation functions do not display the long-time signatures of spin diffusion.All eigenstates and eigenvalues are determined for the spin- XXZ chain H=2J${\ensuremath{\sum}}_{\mathrm{i}}$(${\mathrm{S}}_{\mathrm{i}}^{\mathrm{x}}$${\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{x}}$+${\mathrm{S}}_{\mathrm{i}}^{\mathrm{y}}$${\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{y}}$+\ensuremath{\Delta}${\mathrm{S}}_{\mathrm{i}}^{\mathrm{z}}$${\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{z}}$) for rings with up to N=16 spins, for anisotropies \ensuremath{\Delta}=0, cos (0.3\ensuremath{\pi}), and 1. The dynamic spin pair correlations 〈${\mathrm{S}}_{\mathrm{l}+\mathrm{n}}^{\mathrm{\ensuremath{\mu}}}$(t)${\mathrm{S}}_{\mathrm{l}}^{\mathrm{\ensuremath{\mu}}}$〉, (\ensuremath{\mu}=x,z), the dynamic structure factors ${\mathrm{S}}^{\mathrm{\ensuremath{\mu}}}$(q,\ensuremath{\omega}), and the intermediate structure factors ${\mathrm{I}}^{\mathrm{\ensuremath{\mu}}}$(q,t) are calculated for arbitrary temperature T. It is found that for all T, ${\mathrm{S}}^{\mathrm{z}}$(q,\ensuremath{\omega}) is mainly concentrated on the region |\ensuremath{\omega}|${\mathrm{\ensuremath{\varepsilon}}}_{2}$(q), where ${\mathrm{\ensuremath{\varepsilon}}}_{2}$(q) is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors ${\mathrm{I}}^{\mathrm{\ensuremath{\mu}}}$(q,t) for \ensuremath{\Delta}\ensuremath{\ne}0 show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin-correlation functions do not display the long-time signatures of spin diffusion.

arXiv:cond-mat/9611077Physical review. B, Condensed matterMar 1, 199771 citations

Magnetic properties of a spin-1/2 Heisenberg XXZ model in the presence of longitudinal, transverse and transverse staggered magnetic fields: effect of inhomogeneity property

Hamid Arian Zad, Moones Sabeti, Azam Zoshki

Magnetic and thermodynamic properties of the anisotropic Heisenberg XXZ spin=1/2 chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at finite low temperature. To this end, we rigorously study the magnetization, magnetic susceptibility and specific heat of the model in the vicinity of three different magnetic fields including longitudinal, transverse and transverse staggered magnetic fields. The thermodynamic parameters of the model are investigated under two conditions separately: I) when the model is putted in the presence of homogeneous magnetic fields; II) when a finite inhomogeneity is considered for all applied magnetic fields in the Hamiltonian. We show that at low temperature, independent of the chain size, the magnetization curve versus longitudinal field has some plateaus, which convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization, susceptibility, and specific heat is reported in detail. We find that the inhomogeneity has a substantial effect on the thermodynamic parameters of the model under consideration.Magnetic and thermodynamic properties of the anisotropic Heisenberg XXZ spin=1/2 chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at finite low temperature. To this end, we rigorously study the magnetization, magnetic susceptibility and specific heat of the model in the vicinity of three different magnetic fields including longitudinal, transverse and transverse staggered magnetic fields. The thermodynamic parameters of the model are investigated under two conditions separately: I) when the model is putted in the presence of homogeneous magnetic fields; II) when a finite inhomogeneity is considered for all applied magnetic fields in the Hamiltonian. We show that at low temperature, independent of the chain size, the magnetization curve versus longitudinal field has some plateaus, which convert to their counterpart quasi-plateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization, susceptibility, and specific heat is reported in detail. We find that the inhomogeneity has a substantial effect on the thermodynamic parameters of the model under consideration.

Dec 30, 20180 citations

The antiferromagnetic spin- 1/2 -XXZ model on rings with an odd number of sites

Michael Karbach, K -H Mutter

Journal of Physics A Mathematical and GeneralAug 21, 199522 citations

We perform a finite-size analysis of the longitudinal and transverse structure factors

{\mathit{S}}_{\mathit{j}}

(p,\ensuremath{\gamma},N),j=1,3 in the ground state of the one-dimensional spin-1/2 XXZ model. Comparison with the exact results of Tonegawa for the XX model yields excellent agreement.

All eigenstates and eigenvalues are determined for the spin- XXZ chain H=2J${\ensuremath{\sum}}_{\mathrm{i}}$(

{\mathrm{S}}_{\mathrm{i}}^{\mathrm{x}}

{\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{x}}

{\mathrm{S}}_{\mathrm{i}}^{\mathrm{y}}

{\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{y}}

+\ensuremath{\Delta}

{\mathrm{S}}_{\mathrm{i}}^{\mathrm{z}}

{\mathrm{S}}_{\mathrm{i}+1}^{\mathrm{z}}

) for rings with up to N=16 spins, for anisotropies \ensuremath{\Delta}=0, cos (0.3\ensuremath{\pi}), and 1. The dynamic spin pair correlations 〈${\mathrm{S}}_{\mathrm{l}+\mathrm{n}}^{\mathrm{\ensuremath{\mu}}}$(t)${\mathrm{S}}_{\mathrm{l}}^{\mathrm{\ensuremath{\mu}}}$〉, (\ensuremath{\mu}=x,z), the dynamic structure factors ${\mathrm{S}}^{\mathrm{\ensuremath{\mu}}}$(q,\ensuremath{\omega}), and the intermediate structure factors ${\mathrm{I}}^{\mathrm{\ensuremath{\mu}}}$(q,t) are calculated for arbitrary temperature T. It is found that for all T,

{\mathrm{S}}^{\mathrm{z}}

(q,\ensuremath{\omega}) is mainly concentrated on the region |\ensuremath{\omega}|${\mathrm{\ensuremath{\varepsilon}}}_{2}$(q), where ${\mathrm{\ensuremath{\varepsilon}}}_{2}$(q) is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors ${\mathrm{I}}^{\mathrm{\ensuremath{\mu}}}$(q,t) for \ensuremath{\Delta}\ensuremath{\ne}0 show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin-correlation functions do not display the long-time signatures of spin diffusion.