Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9507062 · Journal of Physics Condensed Matter

Computation of dynamical structure factors with the recursion method

Andreas Fledderjohann, Michael Karbach, K -H Mutter, P. Wielath

Published Nov 20, 1995• 10 citations
arXivHTMLPDF

Abstract

We compute the energies and transition probabilities for low excitations in the one-dimensional antiferromagnetic spin- 1/2 Heisenberg model by means of the recursion method. We analyse finite-size effects in the Euclidean time ( tau -) representation and compare the resulting estimate for the thermodynamical limit with two parametrizations for the dynamical structure factors in the spectral ( omega -) representation.

DOI
10.1088/0953-8984/7/47/018

Related papers

Two-spinon dynamic structure factor of the one-dimensional s= Heisenberg antiferromagnet

Michael Karbach, Gerhard H. Muller, A. Hamid Bougourzi +2 more

The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q,\ensuremath{\omega}) of the one-dimensional s=1/2 Heisenberg antiferromagnet at T=0 is evaluated for direct comparison with finite-chain transition rates (N\ensuremath{\leqslant}28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q,\ensuremath{\omega}). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and q dependent susceptibility are determined via sum rules. The impact of the non-two-spinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q,\ensuremath{\omega}) is studied on the basis of finite-size data.

arXiv:cond-mat/9606068•Physical review. B, Condensed matter•May 1, 1997•165 citations

Dynamics of the one-dimensional spin-1 Heisenberg antiferromagnet with exchange and single-site anisotropy

Shu Zhang, Yongmin Yu, V. S. Viswanath +2 more

The T=0 dynamical properties of the one-dimensional s=1 XXZ model with an additional single-site term are investigated by means of the recursion method. The dynamic structure factors Sμμ(q=π,ω), μ=x,z bear the characteristic signatures of several different phase transitions. In the s=1 Heisenberg antiferromagnet, the intrinsic linewidth (at fixed q) of Sμμ(q,ω) is larger for small q than for q near π, in contrast to well-established results for the corresponding s=1/2 model.

Journal of Applied Physics•May 15, 1994•0 citations

Numerical evaluation of frequency-moment sum rules for dynamical structure factors

Andreas Fledderjohann, Michael Karbach, K.-H. Mütter

The frequency moments of the zero-temperature dynamical structure factor in the antiferromagnetic Heisenberg model are computed on rings up to 28 sites. Finite-size effects are analyzed and the estimate of the thermodynamical limit is compared with the two-spinon ansatz of M\"uller and with a modification of this ansatz for the dynamical structure factor. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•May 1, 1996•5 citations

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/9502072•Journal of Physics Condensed Matter•Jul 10, 1995•2 citations

Ordering and fluctuations in the ground state of the one-dimensional and two-dimensional S =1/2 XXZ antiferromagnets: A study of dynamical properties based on the recursion method

V. S. Viswanath, Shu Zhang, Joachim Stolze +1 more

The recursion method is applied to the T=0 dynamics of the S=1/2 XXZ model on a linear chain and a square lattice. By means of new calculational techniques for the analysis of the continued-fraction coefficients pertaining to specific dynamical quantities, we obtain reliable information on the type of ordering in the ground state, on the size of gaps in the dynamically relevant excitation spectrum, on the bandwidths of dominant structures in spectral densities, on the exponents of infrared singularities, and on the detailed shape of spectral-weight distributions. We investigate some characteristic properties of the dynamic structure factors ${\mathit{S}}_{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{\mu}}}$(q,\ensuremath{\omega}) and the spin autocorrelation functions ${\mathit{S}}^{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{\mu}}}$(\ensuremath{\omega})=${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$ t${sum}_{\mathbf{q}}$${\mathit{S}}_{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{\mu}}}$(q,\ensuremath{\omega}), specifically their dependence on the uniaxial anisotropy, i.e., on the parameter which controls the type of ordering and the amount of quantum fluctuations in the ground state. We find, for example, that the different degrees of ordering in the planar regime of the one-dimensional and two-dimensional systems (criticality versus antiferromagnetic long-range order) have characteristic signatures in the dynamical properties which are conspicuously displayed in our results.

Physical review. B, Condensed matter•Apr 1, 1994•36 citations

Impact of criticality and phase separation on the spin dynamics of the one-dimensional t–J model

Shu Zhang, Gerhard Müller, Joachim Stolze

The recursion method is used to determine the T=0 spin dynamic structure factor Szz(q,ω) in the Luttinger liquid state and in the phase-separated state of the one-dimensional t–J model. As the exchange coupling increases from zero, the dispersions and line shapes of the dominant spin excitations are observed to undergo a major metamorphosis between the free-fermion limit and the onset of phase separation. The familiar two-spinon spectrum of the Heisenberg antiferromagnetic chain emerges gradually in the strongly phase-separated state.

arXiv:cond-mat/9508134•Journal of Applied Physics•Apr 15, 1996•1 citation
We compute the energies and transition probabilities for low excitations in the one-dimensional antiferromagnetic spin- 1/2 Heisenberg model by means of the recursion method. We analyse finite-size effects in the Euclidean time ( tau -) representation and compare the resulting estimate for the thermodynamical limit with two parametrizations for the dynamical structure factors in the spectral ( omega -) representation.
The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q,\ensuremath{\omega}) of the one-dimensional s=1/2 Heisenberg antiferromagnet at T=0 is evaluated for direct comparison with finite-chain transition rates (N\ensuremath{\leqslant}28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q,\ensuremath{\omega}). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and q dependent susceptibility are determined via sum rules. The impact of the non-two-spinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q,\ensuremath{\omega}) is studied on the basis of finite-size data.
The recursion method is applied to the T=0 dynamics of the S=1/2 XXZ model on a linear chain and a square lattice. By means of new calculational techniques for the analysis of the continued-fraction coefficients pertaining to specific dynamical quantities, we obtain reliable information on the type of ordering in the ground state, on the size of gaps in the dynamically relevant excitation spectrum, on the bandwidths of dominant structures in spectral densities, on the exponents of infrared singularities, and on the detailed shape of spectral-weight distributions. We investigate some characteristic properties of the dynamic structure factors ${\mathit{S}}_{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{\mu}}}$(q,\ensuremath{\omega}) and the spin autocorrelation functions ${\mathit{S}}^{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{\mu}}}$(\ensuremath{\omega})=${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$ tsumq{sum}_{\mathbf{q}}sumq​${\mathit{S}}_{\mathrm{\ensuremath{\mu}}\mathrm{\ensuremath{\mu}}}$(q,\ensuremath{\omega}), specifically their dependence on the uniaxial anisotropy, i.e., on the parameter which controls the type of ordering and the amount of quantum fluctuations in the ground state. We find, for example, that the different degrees of ordering in the planar regime of the one-dimensional and two-dimensional systems (criticality versus antiferromagnetic long-range order) have characteristic signatures in the dynamical properties which are conspicuously displayed in our results.
The recursion method is used to determine the T=0 spin dynamic structure factor Szz(q,ω) in the Luttinger liquid state and in the phase-separated state of the one-dimensional t–J model. As the exchange coupling increases from zero, the dispersions and line shapes of the dominant spin excitations are observed to undergo a major metamorphosis between the free-fermion limit and the onset of phase separation. The familiar two-spinon spectrum of the Heisenberg antiferromagnetic chain emerges gradually in the strongly phase-separated state.