关联电子模型中的有限尺度效应

出版时间:2012-12  出版社:兹维亚金 (Zvyagin A. A.) 北京大学出版社 (2012-12出版)  作者:兹维亚金  页数:367  
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内容概要

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作者简介

作者:(乌克兰)兹维亚金(ZVyagin A.A.)

书籍目录

Preface 1.Introduction 1.1 Why is the Topic of the Book Worthwhile Studying? 1.2 Thermodynamics 1.3 Statistical Mechanics:Simple Models. 1.4 Mermin-Hohenberg Theorem 2.Quantum Spin-1/2 Chain with the Nearest-Neighbour Couplings 2.1 0ne—Dimensional Spin Hamiltonian 2.2 Ising Chain. 2.3 Isotropic XY Rin9. 2.4 Ising Chain in a Transverse Magnetic Field 2.5 Dimerized XY Chain 3.Co—ordinate Bethe Ansatz for a Heisenberg-Ising Ring 3.1 Bethe Ansatz 3.2 Simple Solutions of the Bethe Ansatz Equations:Strings. 3.3 Thermodynamic Bethe Ansatz 3.4 The Ground State Behaviour 3.5 Magnetic Field Behaviour in the Ground State:Wiener—Hopf Method 4.Correlated Electron Chains:Co-ordinate Bethe Ansatz 4.1 Hubbard Chain 4.2 t-J Chain 5. Algebraic Bethe Ansatz 5.1 The Algebraic Bethe Ansatz for a Spin-1/2Chain 5.2 su(2)-Symmetric Spin—S Chain 5.3 The Algebraic Bethe Ansatz for Correlated Electron Models 6. Correlated Quantum Chains with Open Boundary Conditions 6.1 Open Boundaries.XY and Ising Chains 6.2 Open Boundaries: C0—ordinate Bethe Ansatz for the Heisenberg——Ising Chain 6.3 Open Boundaries.The Algebraic Bethe Ansatz 6.4 Open Hubbard Chain 6.5 Open Supersymmetric t-J Chain 7. Correlated Quantum Chains with Isolated Impurities 7.1 Impurities in XY Chains 7.2 Impurities in Spin Chains:Bethe Ansatz. 7.3 Impurity in Correlated Electron Chains 8.Correlated Quantum Chains with a Finite Concentration of Impurities 8.1 Impurities'Bands. 8.2 Disodered Ensembles of Impurities in Correlated Chains."Quantum Transfer Matrix"Approach 9.Finite Size Corrections in Quantum Correlated Chains 9.1 Finite Size Corrections for Quantum Spin Chains. 9.2 Finite Size Corrections for Correlated Electron Chains 9.3 Elements of Conformal Field Theory 9.4 Asymptotics of Correlation Functions. 9.5 Persistent Currents in Correlated Electron Rings 10.Beyond the Integrability:Approximate Methods 10.1 Scaling Analysis. 10.2 Bosonization. Bibliography Index

章节摘录

版权页:   插图:   Summarizing, in this chapter we presented the calculation of finite-sizecorrections to characteristics of exactly solvable models of quantum spinsand correlated electrons with periodic and open boundary conditions, withand without inhomogeneities. We reminded the reader the main featuresof the description of critical phenomena and conformal field theory. Thelatter was used to calculate the asymptotic behaviour of low-energy corre-lation functions of considered models. Also, another finite-size effect, thebehaviour of persistent currents for periodic correlated electron chains isstudied. The calculation of finite size corrections for Bethe ansatz-solvable mod-els was pioneered in [de Vega and Woynarovich (1985)]. The reader canfind calculations of finite size corrections for quantum correlated chains,e.g., in [Woynarovich, Eckle and Truong (1989); Woynarovich (1989);Klümper, Batchelor and Pearce (1991); Pearce and Kliimper (1991);Kawakami and Yang (1991); Barley, Klümper, Schadschneider and Zittartz(1993); Bariev (1994)], homogeneous chains with periodic (twisted) bound-ary conditions, in [Alcaraz, Barber, Batchelor, Baxter and Quispel (1987);Asakawa and Suzuki (1995); Frahm and Zvyagin (1997a); Bediirftig andFrahm (1997)] for chains with open boundary conditions, see also [Frahmand Zvyagin (19975); Zvyagin (2002); Zvyagin (2003)] for quantum chainswith impurities. The dressed charge technique was introduced in [Korepin(1979)]. I can suggest the use of, e.g., the well-known books [Ma (1976);Cardy (1996); Kadanoff (2000); Sachdev (1999)] for the description of crit-ical phenomena in the vicinity of a phase transition. The scaling hy-pothesis was introduced in [Widom (1965a); Widom (19655)], see also[Rushbrooke (1963)], and developed in [Griffiths (1965); Kadanoff (1966);Josephson (1967a); Josephson (1967b); Fisher (1969)]. The conformal fieldtheory was pioneered in [Belavin, Polyakov and Zamolodchikov (1984)].

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  •     这本书是乌克兰的一个这方面的专家写的。相比其他这方面的书,其好处是推导比较详细。

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