Finite-temperature Drude weight (spin stiffness) $D(T)$ is evaluated within the anisotropic spin- $1/2$ Heisenberg model on a chain using the exact diagonalization for small systems. It is shown that odd-side chains allow for more reliable scaling and results, in particular, if one takes into account corrections due to low-frequency finite-size anomalies. At high $T$ and zero magnetization $D$ is shown to scale to zero approaching the isotropic point $\ensuremath{\Delta}=1$. On the other hand, for $\ensuremath{\Delta}>2$ at all magnetizations $D$ is nearly exhausted with the overlap with the conserved energy current. Results for the $T$ variation $D(T)$ are also presented.Finite-temperature Drude weight (spin stiffness) $D(T)$ is evaluated within the anisotropic spin-$1/2$ Heisenberg model on a chain using the exact diagonalization for small systems. It is shown that odd-side chains allow for more reliable scaling and results, in particular, if one takes into account corrections due to low-frequency finite-size anomalies. At high $T$ and zero magnetization $D$ is shown to scale to zero approaching the isotropic point $\ensuremath{\Delta}=1$. On the other hand, for $\ensuremath{\Delta}>2$ at all magnetizations $D$ is nearly exhausted with the overlap with the conserved energy current. Results for the $T$ variation $D(T)$ are also presented.

arXiv:1107.3027Physical Review BOct 17, 201176 citations

String Order Parameters in the Haldane Gap Phase of the Spin-1/2 Alternating Heisenberg Chain –Numerical Diagonalization and Variational Study–

Kazuo Hida, Satoshi Takada

Two possible extensions of the string order parameter originally defined for the spin-1 Heisenberg chain to the spin-1/2 alternating Heisenberg chain are examined by comparing the numerical diagonalization results of finite size systems and the variational results. It is suggested that the naive extension in which the spin-1 operator is simply replaced by the sum of two spin-1/2 operators can be regarded as the valence bond solid (VBS) order parameter while another extension proposed by Hida corresponds to the measure of the strength of the localized singlet taking the full value for the completely localized singlet state.Two possible extensions of the string order parameter originally defined for the spin-1 Heisenberg chain to the spin-1/2 alternating Heisenberg chain are examined by comparing the numerical diagonalization results of finite size systems and the variational results. It is suggested that the naive extension in which the spin-1 operator is simply replaced by the sum of two spin-1/2 operators can be regarded as the valence bond solid (VBS) order parameter while another extension proposed by Hida corresponds to the measure of the strength of the localized singlet taking the full value for the completely localized singlet state.

Journal of the Physical Society of JapanJun 1, 199224 citations

Critical Behavior of Quantum Heisenberg Chains

P. Schlottmann, Kong-Ju-Bock Lee

Springer proceedings in physicsJan 1, 19901 citation

S=1/2 Heisenberg Chain with Bond Alternation in theSz-SzCoupling

Kiyomi Okamoto

The effect of bond alternation in the S z - S z coupling ( z -alternation) on the dimerization in an S =1/2 Heisenberg chain is investigated both analytically and numerically. The spin Hamiltonian is transformed into the phase Hamiltonian, and the variational method is used. An analytical study shows that the z -alternation plays an important role and brings about the dimerization when there is no bond alternation in the S x - S x and S y - S y couplings. The results of numerical diagonalization for finite systems support the above analytical conclusion.The effect of bond alternation in the S z - S z coupling ( z -alternation) on the dimerization in an S =1/2 Heisenberg chain is investigated both analytically and numerically. The spin Hamiltonian is transformed into the phase Hamiltonian, and the variational method is used. An analytical study shows that the z -alternation plays an important role and brings about the dimerization when there is no bond alternation in the S x - S x and S y - S y couplings. The results of numerical diagonalization for finite systems support the above analytical conclusion.

Journal of the Physical Society of JapanOct 15, 19924 citations

Finite-temperature Drude weight (spin stiffness)

D(T)

is evaluated within the anisotropic spin-

1/2

Heisenberg model on a chain using the exact diagonalization for small systems. It is shown that odd-side chains allow for more reliable scaling and results, in particular, if one takes into account corrections due to low-frequency finite-size anomalies. At high

T

and zero magnetization

D

is shown to scale to zero approaching the isotropic point $\ensuremath{\Delta}=1$. On the other hand, for $\ensuremath{\Delta}>2$ at all magnetizations

D

is nearly exhausted with the overlap with the conserved energy current. Results for the

T

variation

D(T)

are also presented.