First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized $XXZ$ spin chain is obtained within the propagator approach suggested by E. W. Montroll and J. C. Ward. All the calculations employ only one- and two-magnon infinite-chain spectrums. In the $XXX$ -point the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized $XXZ$ spin chain is obtained within the propagator approach suggested by E. W. Montroll and J. C. Ward. All the calculations employ only one- and two-magnon infinite-chain spectrums. In the $XXX$-point the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.

arXiv:1408.4586Aug 20, 20142 citations

Dynamical correlation functions of the XXZ spin- 1/2 chain

N Kitanine, Jean Michel Maillet, N. A. Slavnov +1 more

arXiv:hep-th/0407108Nuclear Physics BSep 17, 200583 citations

Infinite temperature spin dc conductivity of the spin-1/2 XXZ chain

Shinya Ae

Using the Bethe ansatz method and the TBA equations for the higher spin integrable XXZ chain, the regular zero frequency contribution to the spin current correlation (spin dc conductivity) is analyzed for the spin-1/2 XXZ chain with an anisotropy $0 \le Δ<1$ . In the high temperature limit, we write down the dressed scattering kernels by one quasi-particle bare energies, which allows the exact evaluation of the infinite temperature spin dc conductivity $\mathcal{L}$ . We find that $\mathcal{L}$ is discontinuous at all rational numbers of the anisotropy parameter $p_0=π/\cos^{-1}Δ$ in the region $p_0 \ge 2$ with the gap increasing larger than the second power of growing magnetization on one quasi-particle. The isotropic $Δ=1$ point is exceptional. Close to this point, $\mathcal{L}$ slowly increases in proportion to the first power of the magnetization. On the other hand $\mathcal{L}$ is proportional to the second power of the magnetization when $p_0$ approaches irrational numbers.Using the Bethe ansatz method and the TBA equations for the higher spin integrable XXZ chain, the regular zero frequency contribution to the spin current correlation (spin dc conductivity) is analyzed for the spin-1/2 XXZ chain with an anisotropy $0 \le Δ<1$. In the high temperature limit, we write down the dressed scattering kernels by one quasi-particle bare energies, which allows the exact evaluation of the infinite temperature spin dc conductivity $\mathcal{L}$. We find that $\mathcal{L}$ is discontinuous at all rational numbers of the anisotropy parameter $p_0=π/\cos^{-1}Δ$ in the region $p_0 \ge 2$ with the gap increasing larger than the second power of growing magnetization on one quasi-particle. The isotropic $Δ=1$ point is exceptional. Close to this point, $\mathcal{L}$ slowly increases in proportion to the first power of the magnetization. On the other hand $\mathcal{L}$ is proportional to the second power of the magnetization when $p_0$ approaches irrational numbers.

arXiv:2310.04790Oct 7, 20230 citations

Spectral Gaps in the XXZ Quantum Spin Chain

Hans-Peter Eckle

Journal of Mathematical SciencesApr 1, 20010 citations

First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized

XXZ

spin chain is obtained within the propagator approach suggested by E. W. Montroll and J. C. Ward. All the calculations employ only one- and two-magnon infinite-chain spectrums. In the

XXX

-point the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.

0 \le Δ<1

. In the high temperature limit, we write down the dressed scattering kernels by one quasi-particle bare energies, which allows the exact evaluation of the infinite temperature spin dc conductivity

\mathcal{L}

. We find that

\mathcal{L}

is discontinuous at all rational numbers of the anisotropy parameter

p_0=π/\cos^{-1}Δ

in the region

p_0 \ge 2

with the gap increasing larger than the second power of growing magnetization on one quasi-particle. The isotropic

Δ=1

point is exceptional. Close to this point,

\mathcal{L}

slowly increases in proportion to the first power of the magnetization. On the other hand

\mathcal{L}

is proportional to the second power of the magnetization when

p_0

approaches irrational numbers.