Exact analysis of one-dimensional quantum spin models

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

Quantum theory of one-dimensional spin systems

Andrei A. Zvyagin

Jan 1, 201034 citations

Remarks on duality of 1 dimensional quantum spin models

Taku Matsui

Communications in Mathematical PhysicsNov 1, 19920 citations

Excitation spectra of the one-dimensional double-exchange model: An exact solution for one mobile electron

K Nakano, R. Eder, Y. Ohta

We study the one-dimensional double-exchange model with L localized spins and one mobile electron. We solve the Schrödinger equation analytically and obtain the energies and wave functions for all the eigenstates with spin S = ( L − 1)***/2 exactly. As an application, we compute the single-particle Green's function. We show that, for vanishing exchange interactions between localized spins, the single-particle spectrum is entirely incoherent and the lowest band has an infinite band mass, i.e., the single electron is localized due to its interaction with the spin excitations. The analysis of the wave function gives us a particularly simple ground state.We study the one-dimensional double-exchange model with L localized spins and one mobile electron. We solve the Schrödinger equation analytically and obtain the energies and wave functions for all the eigenstates with spin S = ( L − 1)***/2 exactly. As an application, we compute the single-particle Green's function. We show that, for vanishing exchange interactions between localized spins, the single-particle spectrum is entirely incoherent and the lowest band has an infinite band mass, i.e., the single electron is localized due to its interaction with the spin excitations. The analysis of the wave function gives us a particularly simple ground state.

Journal of Physics Conference SeriesDec 17, 20120 citations

Exact results for the dynamics of one-dimensional spin-systems

U. Brandt, K. Jacoby

The European Physical Journal BJun 1, 197692 citations

Spin dynamics for the one-dimensional XY model at infinite temperature

Amit Sur, David Jasnow, Irving J. Lowe

The infinite-temperature space- and time-dependent spin-correlation functions ${g}_{r}^{x}(t)$ are studied for the one-dimensional $\mathrm{XY}$ model. Numerical calculations are performed to obtain the exact autocorrelation function ${g}_{0}^{x}(t)$ for chains containing 5, 7, and 9 spins ( $S=\frac{1}{2}$ ). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that ${g}_{0}^{x}(t)$ for the infinite chain is identical to $\frac{\mathrm{exp}(\ensuremath{-}{J}^{2}{t}^{2})}{4}$. We show that ${g}_{r}^{x}(t)$ for $r\ensuremath{\ne}0$ vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for ${g}_{0}^{x}(t)$ is compared with that obtained by Huber for the classical ($S=\ensuremath{\infty}$) chain.The infinite-temperature space- and time-dependent spin-correlation functions ${g}_{r}^{x}(t)$ are studied for the one-dimensional $\mathrm{XY}$ model. Numerical calculations are performed to obtain the exact autocorrelation function ${g}_{0}^{x}(t)$ for chains containing 5, 7, and 9 spins ($S=\frac{1}{2}$). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that ${g}_{0}^{x}(t)$ for the infinite chain is identical to $\frac{\mathrm{exp}(\ensuremath{-}{J}^{2}{t}^{2})}{4}$. We show that ${g}_{r}^{x}(t)$ for $r\ensuremath{\ne}0$ vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for ${g}_{0}^{x}(t)$ is compared with that obtained by Huber for the classical ($S=\ensuremath{\infty}$) chain.

Physical review. B, Solid stateNov 1, 1975113 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.

The infinite-temperature space- and time-dependent spin-correlation functions

{g}_{r}^{x}(t)

are studied for the one-dimensional

\mathrm{XY}

model. Numerical calculations are performed to obtain the exact autocorrelation function

{g}_{0}^{x}(t)

for chains containing 5, 7, and 9 spins (

S=\frac{1}{2}

). This yields exact results for the first 16 moments of the frequency autocorrelation function of the infinite chain, and estimates for a few of the higher moments as well. The analysis suggests that

{g}_{0}^{x}(t)

for the infinite chain is identical to $\frac{\mathrm{exp}(\ensuremath{-}{J}^{2}{t}^{2})}{4}$. We show that

{g}_{r}^{x}(t)

for $r\ensuremath{\ne}0$ vanishes identically for all values of time, implying a wave-vector-independent relaxation shape function. Our result for

{g}_{0}^{x}(t)

is compared with that obtained by Huber for the classical ($S=\ensuremath{\infty}$) chain.