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四川师范大学学报：自然科学版

变形的一维半满t-J⊥-Jz-V模型的量子相图研究

林二印, 丁汉芹, Jun Zhang

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

借助于变形玻色算符手段、费米-玻色转化技术及重整化技术,研究了在依赖自旋的最近邻磁交换作用下,一维半满t-J扩展模型（t-J⊥-Jz-V）的弱耦合量子相图.相图显示,来自最近邻格点间各向向异性自旋交换作用（J⊥-Jz）和库仑斥力作用（V）的相互竞争使得此扩展模型基态总呈现绝缘密度波的关联行为,并且此模型量子相图的拓扑结构可通过特征参数（V/tδ^2）c=4/π来刻画,这里参数δ∈（0,1]表征玻色算符形变程度.一旦甩掉作用V（较弱的库仑作用,以致可略去）,此模型基态则会呈现绝缘相向金属相间的转变.有望此结果能为理解一维强关联t-J系统及其扩展提供了一种图景和参考.

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借助于变形玻色算符手段、费米-玻色转化技术及重整化技术,研究了在依赖自旋的最近邻磁交换作用下,一维半满t-J扩展模型（t-J⊥-Jz-V）的弱耦合量子相图.相图显示,来自最近邻格点间各向向异性自旋交换作用（J⊥-Jz）和库仑斥力作用（V）的相互竞争使得此扩展模型基态总呈现绝缘密度波的关联行为,并且此模型量子相图的拓扑结构可通过特征参数（V/tδ^2）c=4/π来刻画,这里参数δ∈（0,1]表征玻色算符形变程度.一旦甩掉作用V（较弱的库仑作用,以致可略去）,此模型基态则会呈现绝缘相向金属相间的转变.有望此结果能为理解一维强关联t-J系统及其扩展提供了一种图景和参考.
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The thermodynamics of the one-dimensional Heisenberg-Ising model for |Δ| ≪ 1 as well as of the X-Y-Z model is reduced to a set of non-linear integral equations under some plausible assumptions. It is remarkable that the number of unknown functions involved in them becomes finite when π/ cos -1Δ is a rational number for the Heisenberg-Ising model and when Kl /ζ is a rational number for the X-Y-Z model (where coupling constants Jx, Jy and Jz are parametrized by ζ, l, and Jz as Jx = Jz cn(2ζ, l) and Jy = Jz dn(2ζ, l); 1 ≥l ≥0, Kl ≥2ζ≥0 and Kl is the complete elliptic integral of the first kind of modulus l). The validity of our theory has been confirmed by the high-temperature expansion of the free energy through the second term for a general value of Δ and through the fourth them for Δ= ½.
Low-temperature specific heat of Heisenberg-Ising ring at | Δ| ≪ 1 is calculated by the method of non-linear integral equations. Specific heat in constant magnetic field (CH) is proportional to temperature (T) at |2µ0H| ≪ (1+Δ)J. In particular lim H →0 lim T →0CH/T is 2θ/(3Jsin θ) where θ= cos -1Δ, ≤θ≪ π. It is conjectured that lim T→0 lim H→0CH/T = lim H→0 lim T→0CH/T from the result of numerical calculation. Low-temperature specific heat of the one-dimensional X-Y-Z model is proportional to T-3/2 exp (-α/T) in the case of Jz > Jy > 0, Jy ≧Jx > -Jy.
Correlation inequalities <σAz>≥0, <σAzσBz>≥<σAz><σBz>, ∂<σAz>/∂JBz≥0, and ∂<σAz>/∂JBx≤0 are proved for the generalized X-Y model with the Hamiltonian of the form H=−Σ(JAzσAz+JAxσAx), where σAz=ΠjεAσjz, σAx=ΠjεAσjx, JAz≥0,JAx≥0, A denotes an arbitrary subset of the N lattice points, and σjx, σjz are the Pauli matrices. This yields a simple extension of the Griffiths-Kelly-Sherman inequalities to the above quantal system. Applications to phase transitions are also discussed briefly.