Inequalities between ground-state energies of Heisenberg models

被引：0

作者：

Wojtkiewicz, Jacek ^{[1
]}

Skolasinski, Rafal ^{[1
]}

机构：

[1] Univ Warsaw, Fac Phys, Dept Math Methods Phys, PL-00682 Warsaw, Poland

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2015年 / 419卷

关键词：

Heisenberg model; Quantum spin systems; Matrix inequalities; Exact diagonalization; Density matrix renormalization group; SPIN SYSTEMS; HUBBARD-MODEL; ORDER;

D O I：

10.1016/j.physa.2014.09.042

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The Lieb-Schupp inequality is the inequality between ground state energies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb-Schupp inequality has been tested for spin systems in various geometries: chains, ladders and quasi-two-dimensional lattices. It turned out that this energy difference was strongly dependent on the class of the system. The relation between this difference and a fall-off of a correlation function has been empirically found and formulated as a conjecture. (C) 2014 Elsevier B.V. All rights reserved.

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页码：134 / 144

页数：11

相关论文

共 17 条

[1] The ALPS project release 2.0: open source software for strongly correlated systems [J].

Bauer, B. ;

Carr, L. D. ;

Evertz, H. G. ;

Feiguin, A. ;

Freire, J. ;

Fuchs, S. ;

Gamper, L. ;

Gukelberger, J. ;

Gull, E. ;

Guertler, S. ;

Hehn, A. ;

Igarashi, R. ;

Isakov, S. V. ;

Koop, D. ;

Ma, P. N. ;

Mates, P. ;

Matsuo, H. ;

Parcollet, O. ;

Pawlowski, G. ;

Picon, J. D. ;

Pollet, L. ;

Santos, E. ;

Scarola, V. W. ;

Schollwoeck, U. ;

Silva, C. ;

Surer, B. ;

Todo, S. ;

Trebst, S. ;

Troyer, M. ;

Wall, M. L. ;

Werner, P. ;

Wessel, S. .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2011,

[2]

Caspers W.J., 1989, Spin Systems

[3] NON-LINEAR FIELD-THEORY OF LARGE-SPIN HEISENBERG ANTI-FERROMAGNETS - SEMI-CLASSICALLY QUANTIZED SOLITONS OF THE ONE-DIMENSIONAL EASY-AXIS NEEL STATE [J].

HALDANE, FDM .

PHYSICAL REVIEW LETTERS, 1983, 50 (15) :1153-1156

[4] EXISTENCE OF NEEL ORDER IN SOME SPIN-1/2 HEISENBERG ANTIFERROMAGNETS [J].

KENNEDY, T ;

LIEB, EH ;

SHASTRY, BS .

JOURNAL OF STATISTICAL PHYSICS, 1988, 53 (5-6) :1019-1030

[5] EQUIVALENCE AND SOLUTION OF ANISOTROPIC SPIN-1 MODELS AND GENERALIZED T-J FERMION MODELS IN ONE DIMENSION [J].

KLUMPER, A ;

SCHADSCHNEIDER, A ;

ZITTARTZ, J .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (16) :L955-L959

[6] GROUND-STATE PROPERTIES OF A GENERALIZED VBS-MODEL [J].

KLUMPER, A ;

SCHADSCHNEIDER, A ;

ZITTARTZ, J .

ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1992, 87 (03) :281-287

[7] Singlets and reflection symmetric spin systems [J].

Lieb, EH ;

Schupp, P .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2000, 279 (1-4) :378-385

[8] 2 THEOREMS ON THE HUBBARD-MODEL [J].

LIEB, EH .

PHYSICAL REVIEW LETTERS, 1989, 62 (10) :1201-1204

[9] Ground state properties of a fully frustrated quantum spin system [J].

Lieb, EH ;

Schupp, P .

PHYSICAL REVIEW LETTERS, 1999, 83 (25) :5362-5365

[10] THE SPIN-1/2 HEISENBERG-ANTIFERROMAGNET ON A SQUARE LATTICE AND ITS APPLICATION TO THE CUPROUS OXIDES [J].

MANOUSAKIS, E .

REVIEWS OF MODERN PHYSICS, 1991, 63 (01) :1-62