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低温下自旋为1/2的海森伯亚铁磁棱型链的1/3磁化平台

成泰民, 王金刚

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

本文利用Jordan-Wigner变换和不变本征算符法计算了低温下自旋为1／2的海森伯亚铁磁棱型链系统的元激发谱，得到了三支没有简并的元激发谱．利用不变本征算符法对系统的哈密顿量进行了对角化，并导出有限温度和外磁场下的系统的配分函数及磁化强度．在绝对零度与有限温度下，通过分析诸交换积分（J1，J2，J3，Jm）对系统的磁化强度随外磁场的变化规律，得到了系统的三个临界磁场强度（HOB，Hce，Hcs），并从三支元激发的性质说明了三个临界磁场强度起源及系统的磁化强度随外磁场变化出现1／3磁化平台的起因．

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一维自旋1/2的 J1-J2 海森堡 XXZ 链的精确对角化研究

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铁磁—反铁磁—反铁磁三聚自旋链的磁化特性

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采用Jordan-Wigner变换,讨论自旋-1/2铁磁—反铁磁—反铁磁三聚海森堡链系统在外磁场作用下的磁化过程,数值计算了零温下系统的磁化强度随反铁磁相互作用和外磁场的变化关系,结果发现有1/3磁化平台出现,且遵循OYA理论。此外,分析了系统的能隙及磁化平台产生的原因。

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Ground State of the S=1/2 Distorted Diamond Chain --- Model of Cu_3_Cl_6_(H_2_O)_2_・2H_8_C_4_SO_2_

Kiyomi Okamoto, Taskashi Tonegawa, Yutaka Takahashi +1 more

Abstract. We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu3Cl6(H2O)2 · 2H8C4SO2 in which the non-magnetic ground state is observed recently. This model consists of stacked trimers and has three kinds of coupling constants between spins; the intra-trimer coupling constant J1 and the inter-trimer coupling constants J2 and J3. All of these constants are assumed to be antiferromagnetic. By use of the analytical method and physical considerations, we show that there are three phases on the ˜ J2 − ˜ J3 plane ( ˜ J2 ≡ J2/J1, ˜ J3 ≡ J3/J1), the dimer phase, the spin fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists the excitation gap between the twofold degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu3Cl6(H2O)2 ·2H8C4SO2. We also obtain the phase diagram on the ˜ J2 − ˜ J3 plane from the numerical diagonalization data for finite systems. PACS numbers: 75.10.Jm, 75.40.Cx, 75.50.Ee, 75.50.GgGround state of an S = 1/2 distorted diamond chain 2 1.

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"Haunted" quantum contextuality

Karl Svozil

Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables $\{J_1^2,J_2^2,J_3^2\}$ and $\{\bar J_1^2, \bar J_2^2,J_3^2\}$ with $[J_1^2,\bar J_1^2]\neq 0$ are measured. The outcomes of measurements of $J_3^2$ (via $J_1^2,J_2^2$) and $J_3^2$ (via $\bar J_1^2,\bar J_2^2$) are compared. Although formally $J_3^2$ is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether $J_1^2$ or $\bar J_1^2$ is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.

arXiv:quant-ph/9907015•Jul 5, 1999•4 citations

低温下自旋为1/2的X-Y亚铁磁棱型链的元激发谱

成泰民, 王蕴鹏

利用Jordan-Wigner变换和不变本征算符法计算低温下自旋为1/2的一维X-Y模型亚铁磁棱型链系统的元激发谱和对应的本征态.得到3支没有简并的元激发谱,其对应的本征态函数之间又相互正交归一.利用不变本征算符法对系统的Hamiltonian进行了退耦,其退耦合过程比常规的幺正变换法便捷,而且直接在系统的能量自表象上自动退耦,因此,这对计算系统的配分函数而言非常便捷.并讨论了不变本征算符法的优缺点.

•Jan 1, 2012•0 citations

SPIN-2 ISING MODEL ON THE BILAYER BETHE LATTICE

Erhan Albayrak, Seyma Akkaya, Saban Yilmaz

A spin-2 system consisting of two layers of Bethe lattices each with a branching ratio of q Ising spins was analyzed by the use of the exact recursion relations in a pairwise approach. The upper layer interacting with nearest-neighbor (NN) bilinear interaction J1 is laid over the top of the lower layer interacting with bilinear NN interaction J2, and the two layers are tied together via the bilinear interaction between the vertically aligned adjacent NN spins denoted as J3. The study of the ground state phase diagrams on the (J2/|J3|, J1/|J3|) plane with J3>0 and J3<0 and on the (J2/J1, J3/q J1) plane with J1>0 has yielded five distinct ground state configurations. The temperature dependent phase diagrams are obtained for the case with intralayer coupling constants of the two layers with ferromagnetic type J1 and J2>0, and the interlayer coupling constant of the layers with either ferromagnetic J3>0 or antiferromagnetic type J3<0 on the (kT/J1, J3/J1) planes for given values of the J2/J1 for various values of the coordination numbers. As a result, we have found that the model presents both second- and first-order phase transitions, therefore, tricritical points.

International Journal of Modern Physics B•Sep 30, 2008•5 citations
本文利用Jordan-Wigner变换和不变本征算符法计算了低温下自旋为1／2的海森伯亚铁磁棱型链系统的元激发谱，得到了三支没有简并的元激发谱．利用不变本征算符法对系统的哈密顿量进行了对角化，并导出有限温度和外磁场下的系统的配分函数及磁化强度．在绝对零度与有限温度下，通过分析诸交换积分（J1，J2，J3，Jm）对系统的磁化强度随外磁场的变化规律，得到了系统的三个临界磁场强度（HOB，Hce，Hcs），并从三支元激发的性质说明了三个临界磁场强度起源及系统的磁化强度随外磁场变化出现1／3磁化平台的起因．
在一维小尺寸强关联电子体系中，使用精确对角化数值算法能够得到体系精确的物理结果。本文应用该方法研究了具有周期性边界条件并且自旋1/2的一维反铁磁 J1-J2 海森堡XXZ链。我们利用模型的基态相图选择变量 α(α=J2/J1, J1、J2 为系统原子间的耦合系数)和 delta (Z方向上的各向异性参数)，计算有限温下系统在不同相中的比热和磁化率(零磁场)。由低温下不同相中系统的比热和磁化率随温度的变化可知，它们在有能隙相和无能隙相中的行为很不同：当系统温度降低时，比热在有能隙相中以指数方式衰减到零，在无能隙相中以幂次关系减小到零；磁化率在有能隙相和无能隙相中都随系统温度的降低而趋于零。但是在无能隙相中，磁化率的这种行为是因为系统存在有限尺寸效应(本文所计算系统的最大格点数为20)，如果链长继续增加，系统的磁化率可以外推到一个有限值。
Abstract. We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu3Cl6(H2O)2 · 2H8C4SO2 in which the non-magnetic ground state is observed recently. This model consists of stacked trimers and has three kinds of coupling constants between spins; the intra-trimer coupling constant J1 and the inter-trimer coupling constants J2 and J3. All of these constants are assumed to be antiferromagnetic. By use of the analytical method and physical considerations, we show that there are three phases on the ˜ J2 − ˜ J3 plane ( ˜ J2 ≡ J2/J1, ˜ J3 ≡ J3/J1), the dimer phase, the spin fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists the excitation gap between the twofold degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu3Cl6(H2O)2 ·2H8C4SO2. We also obtain the phase diagram on the ˜ J2 − ˜ J3 plane from the numerical diagonalization data for finite systems. PACS numbers: 75.10.Jm, 75.40.Cx, 75.50.Ee, 75.50.GgGround state of an S = 1/2 distorted diamond chain 2 1.
Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables {J12,J22,J32}\{J_1^2,J_2^2,J_3^2\}{J12​,J22​,J32​} and {Jˉ12,Jˉ22,J32}\{\bar J_1^2, \bar J_2^2,J_3^2\}{Jˉ12​,Jˉ22​,J32​} with [J12,Jˉ12]≠0[J_1^2,\bar J_1^2]\neq 0[J12​,Jˉ12​]=0 are measured. The outcomes of measurements of J32J_3^2J32​ (via J12,J22J_1^2,J_2^2J12​,J22​) and J32J_3^2J32​ (via Jˉ12,Jˉ22\bar J_1^2,\bar J_2^2Jˉ12​,Jˉ22​) are compared. Although formally J32J_3^2J32​ is associated with the same projection operator, a strong form of quantum contextuality states that an outcome depends on the complete disposition of the measurement apparatus, in particular whether J12J_1^2J12​ or Jˉ12\bar J_1^2Jˉ12​ is measured alongside. It is argued that in this case it is impossible to measure contextuality directly, a necessary condition being a non-operational counterfactuality of the argument.
利用Jordan-Wigner变换和不变本征算符法计算低温下自旋为1/2的一维X-Y模型亚铁磁棱型链系统的元激发谱和对应的本征态.得到3支没有简并的元激发谱,其对应的本征态函数之间又相互正交归一.利用不变本征算符法对系统的Hamiltonian进行了退耦,其退耦合过程比常规的幺正变换法便捷,而且直接在系统的能量自表象上自动退耦,因此,这对计算系统的配分函数而言非常便捷.并讨论了不变本征算符法的优缺点.
A spin-2 system consisting of two layers of Bethe lattices each with a branching ratio of q Ising spins was analyzed by the use of the exact recursion relations in a pairwise approach. The upper layer interacting with nearest-neighbor (NN) bilinear interaction J1 is laid over the top of the lower layer interacting with bilinear NN interaction J2, and the two layers are tied together via the bilinear interaction between the vertically aligned adjacent NN spins denoted as J3. The study of the ground state phase diagrams on the (J2/|J3|, J1/|J3|) plane with J3>0 and J3<0 and on the (J2/J1, J3/q J1) plane with J1>0 has yielded five distinct ground state configurations. The temperature dependent phase diagrams are obtained for the case with intralayer coupling constants of the two layers with ferromagnetic type J1 and J2>0, and the interlayer coupling constant of the layers with either ferromagnetic J3>0 or antiferromagnetic type J3<0 on the (kT/J1, J3/J1) planes for given values of the J2/J1 for various values of the coordination numbers. As a result, we have found that the model presents both second- and first-order phase transitions, therefore, tricritical points.