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Finite-size scaling studies of massive one-dimensional lattice models
Liu, YC; Dai, JH; Qin, SJ; Yu, L; Liu, YC , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
2001
发表期刊PHYSICAL REVIEW B
ISSN0163-1829
卷号64期号:10页码:-
摘要In this paper we propose an efficient routine to carry out finite size scaling studies of one-dimensional massive lattice models. Unlike massless systems, for which the lattice and continuum models yield the same results for low-lying excitations due to the infinite correlation length, the massive continuum models can at best approximate their lattice counterparts because of the intrinsic length scale xi similar to Delta -1, where Delta is the mass gap. On examples of antiferromagnetic gapped spin-1/2 XXZ chains we show explicitly that several relations between physical quantities like the mass gap, spin-wave velocity upsilon, and the correlation length xi, derived from the continuum models deviate significantly from the numerical results obtained for finite chains, when xi is comparable with the lattice spacing ao. On the other hand, we find if the dispersion for elementary excitations is modified from the "Lorentz invariant" form root Delta (2)+upsilon (2)p(2) to root Delta (2)+upsilon (2)sub(2)p, the spin-wave velocity upsilon becomes almost size independent, and the appropriately defined correlation length using that dispersion agrees very well with numerical results. In fact, this follows from the Bethe ansatz solution for the spin-1/2 XXZ chains. Based on our previous experience and these considerations we propose scaling equations to obtain the a-state energy, mass gap, correlation length, spin-wave velocity and scattering length between the massive elementary excitations. Only three low energy levels are needed in this method. Although the method is illustrated on the gapped XXZ quantum spins, it is applicable to all one-dimensional lattice models with massive relativistic low energy dispersions. To substantiate our statement we show explicitly that the numerical data for the Ising model in a transverse magnetic field fully agree with the finite-size scaling based on the correlation length newly defined from the exact analytic solution.
部门归属Acad Sinica, Inst Theoret Phys, Beijing 100080, Peoples R China; Zhejiang Univ, Zhejiang Inst Modern Phys, Hangzhou 310027, Peoples R China; Kyushu Univ, Dept Phys, Higashi Ku, Fukuoka 8128581, Japan; Abdus Salam Int Ctr Theoret Phys, I-34100 Trieste, Italy
关键词Antiferromagnetic Heisenberg Chain Spin Chains Field-theory Magnetization
学科领域Physics
收录类别SCI
WOS记录号WOS:000170978400057
引用统计
被引频次:1[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/13677
专题1978-2010年知识产出
通讯作者Liu, YC , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
推荐引用方式
GB/T 7714
Liu, YC,Dai, JH,Qin, SJ,et al. Finite-size scaling studies of massive one-dimensional lattice models[J]. PHYSICAL REVIEW B,2001,64(10):-.
APA Liu, YC,Dai, JH,Qin, SJ,Yu, L,&Liu, YC , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China..(2001).Finite-size scaling studies of massive one-dimensional lattice models.PHYSICAL REVIEW B,64(10),-.
MLA Liu, YC,et al."Finite-size scaling studies of massive one-dimensional lattice models".PHYSICAL REVIEW B 64.10(2001):-.
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