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理论物理通讯：英文版

A Quantum Monte Carlo Study on Mixed-Spin Chains of 1／2-1／2-1-1 and 3／2-3／2-1-1

XUZhao-Xin, ZHANGJun, YINGHe-Ping

Published Jan 1, 2003• 0 citations
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Abstract

The ground-state and thermodynamic properties of quantum mixed-spin chains of1/2-1/2-1-1and 3/2-3/2-1-1are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameterα=J2/J1.

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We investigate both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1/2-1-1 chain described by the Hamiltonian $H=\sum_{\ell=1}^{N/4} (J_1\vecs_{4\ell-3}\cdot \vecs_{4\ell-2}+J_2\vecs_{4\ell-2}\cdot\vecS_{4\ell-1}+J_3\vecS_{4\ell-1}\cdot \vecS_{4\ell}+J_2\vecS_{4\ell}\cdot\vecs_{4\ell+1})$, where two $S=1/2$ spins ($\vecs_{4\ell-3}$ and $\vecs_{4\ell-2}$) and two S=1 spins ($\vecS_{4\ell-1}$ and $\vecS_{4\ell}$) are arranged alternatively. Inseveral limiting cases of $J_1$, $J_2$, and $J_3$ we apply the Wigner-Eckart theorem and carry out a perturbation calculation to examine the behavior of the massless lines where the energy gap vanishes. Performing a quantum Monte Carlo calculation without global flips at a sufficiently low temperature for the case where $J_1=J_3=1.0$ and $J_2>0$, we find that the ground state of the present system in this case undergoes a second-order phase transition accompanying the vanishing of the energy gap at $J_2=J_{2c$ with $J_{2 c} = 0.77 \pm 0.01$. We also find that the ground states for both $J_2 < J_{2 c$ and $J_2 > J_{2c$ can be understood by means of the valence-bond-solid picture. A quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account is carried out to elucidate the temperature dependences of the specific heat and the magnetic susceptibility. In particular, it is found that the susceptibility per unit cell for $J_2=0.77$ with $J_1=J_3=1.0$ takes a finite value at absolute zero temperature and that the specific heat per unit cell versus temperature curve for $J_2=5.0$ with $J_1=J_3=1.0$ has a double peak.

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We investigate the ground-state phase diagram of the quantum mixed spin chain in which two \(S\!=\!\frac{1}{2}\) and two S =1 spins are arranged alternatively and isotropic exchange interactions between nearest-neighboring pairs of spins are assumed. Guided by our previous results [J. Phys. Soc. Jpn. 67 (1998) 1000] for a few limiting cases of the exchange interactions, we carry out a density-matrix renormalization-group calculation to determine the ground-state phase diagram in detail. From the gapless points of the singlet-triplet energy gap, five boundary lines are determined, which divide the phase diagram into six regions. In three regions the ground states with the Haldane-phase character appear, while in the remaining three regions those with the dimer character appear. We also present a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. Making use of the matrix-product wave function, we classify the VBS pictures and interpret the ground-state phase diagram in terms of symmetries schematically related to the VBS pictures. We investigate the ground-state nearest-neighboring two-spin correlation functions and a kind of string order parameters, by which we confirm the validity of the characterization.

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Shangbin Li, Zhaoxin Xu, Jianhui Dai +1 more

The ground entanglement and thermal entanglement in quantum mixed spin chains consisting of two integer spins 1 and two half-integer spins $\frac{1}{2}$ arrayed as $\frac{1}{2}\text{\ensuremath{-}}\frac{1}{2}\text{\ensuremath{-}}1\text{\ensuremath{-}}1$ in a unit cell with antiferromagnetic nearest-neighbor couplings ${J}_{1}$ $({J}_{2})$ between the spins of equal (different) magnitudes are investigated by employing the logarithmic negativity as entanglement measure. The ground entanglement transition found here is closely related to the valence-bond-solid phase transition, and the thermal entanglement near the critical point is calculated and it is shown that two distinct behaviors exist in the nearest-neighbor same kind of spins and different kind of spins, respectively.

arXiv:quant-ph/0508115•Physical Review B•May 10, 2006•16 citations
The ground-state and thermodynamic properties of quantum mixed-spin chains of1/2-1/2-1-1and 3/2-3/2-1-1are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameterα=J2/J1.
The ground-state and thermodynamic properties of quantum mixed-spin chains of 1/2-1/2-1-1 and 3/2-3/2-1-1 are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameter .
The ground-state and thermodynamic properties of quantum mixed-spin chains of1/2-1/2-1-1and 3/2-3/2-1-1are investigated by a quantum Monte Carlo simulation with the loop-cluster algorithm. For 1/2-1/2-1-1 chain, we find it has two phases separated by an energy-gap vanishing point in the ground-state. For 3/2-3/2-1-1 chain, the numerical results show two energy-gap vanishing points isolated by different phases in its ground-state. Our calculations indicate that all these ground state phases can be understood by means of valence-bond-solid picture, and the thermodynamic behavior at finite temperatures is continuous as a function of parameterα=J2/J1.
We investigate both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1/2-1-1 chain described by the Hamiltonian $H=\sum_{\ell=1}^{N/4} (J_1\vecs_{4\ell-3}\cdot \vecs_{4\ell-2}+J_2\vecs_{4\ell-2}\cdot\vecS_{4\ell-1}+J_3\vecS_{4\ell-1}\cdot \vecS_{4\ell}+J_2\vecS_{4\ell}\cdot\vecs_{4\ell+1})$, where two S=1/2S=1/2S=1/2 spins ($\vecs_{4\ell-3}$ and $\vecs_{4\ell-2}$) and two S=1 spins ($\vecS_{4\ell-1}$ and $\vecS_{4\ell}$) are arranged alternatively. Inseveral limiting cases of J1J_1J1​, J2J_2J2​, and J3J_3J3​ we apply the Wigner-Eckart theorem and carry out a perturbation calculation to examine the behavior of the massless lines where the energy gap vanishes. Performing a quantum Monte Carlo calculation without global flips at a sufficiently low temperature for the case where J1=J3=1.0J_1=J_3=1.0J1​=J3​=1.0 and J2>0J_2>0J2​>0, we find that the ground state of the present system in this case undergoes a second-order phase transition accompanying the vanishing of the energy gap at $J_2=J_{2c$ with J2c=0.77±0.01J_{2 c} = 0.77 \pm 0.01J2c​=0.77±0.01. We also find that the ground states for both $J_2 < J_{2 c$ and $J_2 > J_{2c$ can be understood by means of the valence-bond-solid picture. A quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account is carried out to elucidate the temperature dependences of the specific heat and the magnetic susceptibility. In particular, it is found that the susceptibility per unit cell for J2=0.77J_2=0.77J2​=0.77 with J1=J3=1.0J_1=J_3=1.0J1​=J3​=1.0 takes a finite value at absolute zero temperature and that the specific heat per unit cell versus temperature curve for J2=5.0J_2=5.0J2​=5.0 with J1=J3=1.0J_1=J_3=1.0J1​=J3​=1.0 has a double peak.
We study quantum mixed-spin chains consisting of two integer spins S1{S}^{1}S1 and two half integer spins S2{S}^{2}S2 arrayed as ${S}^{1}\ensuremath{-}{S}^{1}\ensuremath{-}{S}^{2}\ensuremath{-}{S}^{2}$ in a unit cell with antiferromagnetic nearest-neighbor couplings J1{J}_{1}J1​ (J2){(J}_{2})(J2​) between the spins of equal (different) magnitudes. By varying the ratio of two competing couplings, $\ensuremath{\alpha}{=J}_{2}{/J}_{1},$ the systems undergo successive quantum phase transitions between different valence-bond-solid (VBS) states accompanied by the vanishing of the energy gap. By a quantum Monte Carlo simulation with an improved loop cluster algorithm, we find one critical point ${\ensuremath{\alpha}}_{c}=0.762(1)$ in a $1\ensuremath{-}1\ensuremath{-}\frac{1}{2}\ensuremath{-}\frac{1}{2}$ chain and two critical points ${\ensuremath{\alpha}}_{c1}=0.479(1)$ and ${\ensuremath{\alpha}}_{c2}=1.318(1)$ in a $1\ensuremath{-}1\ensuremath{-}\frac{3}{2}\ensuremath{-}\frac{3}{2}$ chain, respectively. The calculated expectation values of the Lieb-Shultz-Mattis twist operator show the characteristic features of the single VBS transition in the $1\ensuremath{-}1\ensuremath{-}\frac{1}{2}\ensuremath{-}\frac{1}{2}$ chain and two successive VBS transitions in the $1\ensuremath{-}1\ensuremath{-}\frac{3}{2}\ensuremath{-}\frac{3}{2}$ chain at these critical points.
Ground-State Phase Diagram of the Spin-12\frac{\bf 1}{\bf 2}21​-12\frac{\bf 1}{\bf 2}21​-1-1 Chain
We investigate the ground-state phase diagram of the quantum mixed spin chain in which two S ⁣= ⁣12S\!=\!\frac{1}{2}S=21​ and two S =1 spins are arranged alternatively and isotropic exchange interactions between nearest-neighboring pairs of spins are assumed. Guided by our previous results [J. Phys. Soc. Jpn. 67 (1998) 1000] for a few limiting cases of the exchange interactions, we carry out a density-matrix renormalization-group calculation to determine the ground-state phase diagram in detail. From the gapless points of the singlet-triplet energy gap, five boundary lines are determined, which divide the phase diagram into six regions. In three regions the ground states with the Haldane-phase character appear, while in the remaining three regions those with the dimer character appear. We also present a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. Making use of the matrix-product wave function, we classify the VBS pictures and interpret the ground-state phase diagram in terms of symmetries schematically related to the VBS pictures. We investigate the ground-state nearest-neighboring two-spin correlation functions and a kind of string order parameters, by which we confirm the validity of the characterization.
The ground entanglement and thermal entanglement in quantum mixed spin chains consisting of two integer spins 1 and two half-integer spins 12\frac{1}{2}21​ arrayed as $\frac{1}{2}\text{\ensuremath{-}}\frac{1}{2}\text{\ensuremath{-}}1\text{\ensuremath{-}}1$ in a unit cell with antiferromagnetic nearest-neighbor couplings J1{J}_{1}J1​ (J2)({J}_{2})(J2​) between the spins of equal (different) magnitudes are investigated by employing the logarithmic negativity as entanglement measure. The ground entanglement transition found here is closely related to the valence-bond-solid phase transition, and the thermal entanglement near the critical point is calculated and it is shown that two distinct behaviors exist in the nearest-neighbor same kind of spins and different kind of spins, respectively.