ITP OpenIR  > SCI期刊论文
Liu, YC; Dai, JH; Qin, SJ; Yu, L; Liu, YC , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
Finite-size scaling studies of massive one-dimensional lattice models
Source PublicationPHYSICAL REVIEW B
KeywordAntiferromagnetic Heisenberg Chain Spin Chains Field-theory Magnetization
AbstractIn 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.
2001
ISSN0163-1829
Volume64Issue:10Pages:-
Subject AreaPhysics
Indexed BySCI
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/13677
CollectionSCI期刊论文
Corresponding AuthorLiu, YC , Acad Sinica, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.
Recommended Citation
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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