Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model

Recent developments in the theory of exactly solvable models are reviewed. Particular attention is paid to the finite size corrections to the Bethe ansatz equations. Baxter’s formula which relates a 2-dimensional statistical model with a 1-dimensional spin model is extended into the finite temperature case. A combination of this extension and the theory of finite size corrections gives a systematic method to evaluate low temperature expansions of physical quantities. Applications of the method to 1-dimensional quantum spin models are discussed. Throughout this paper, the usefulness of the soliton theory should be observed.

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Exactly solvable quantum spin model with alternating and multiple spin exchange interactions

Physical Review B ◽

10.1103/physrevb.73.024427 ◽

2006 ◽

Vol 73 (2) ◽

Cited By ~ 23

Author(s):

A. A. Zvyagin ◽

G. A. Skorobagat'ko

Keyword(s):

Spin Exchange ◽

Exchange Interactions ◽

Spin Model ◽

Quantum Spin ◽

Exactly Solvable ◽

Solvable Quantum ◽

Quantum Spin Model

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Classical stochasticity and quantum uncertainty in a simple quantum spin model

Journal of Magnetism and Magnetic Materials ◽

10.1016/0304-8853(86)90784-5 ◽

1986 ◽

Vol 54-57 ◽

pp. 1203-1204

Author(s):

H. Frahm ◽

H.J. Mikeska

Keyword(s):

Spin Model ◽

Quantum Spin ◽

Quantum Uncertainty ◽

Simple Quantum ◽

Quantum Spin Model

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Finite Heisenberg Quantum Spin Chain

Models of Quantum Matter ◽

10.1093/oso/9780199678839.003.0020 ◽

2019 ◽

pp. 667-686

Author(s):

Hans-Peter Eckle

Keyword(s):

Bethe Ansatz ◽

Conformal Symmetry ◽

Finite Size ◽

Quantum Spin ◽

Ansatz Method ◽

Finite Sums ◽

Mathematical Techniques ◽

Higher Order Corrections ◽

Finite Size Corrections ◽

Maclaurin Formula

The Bethe ansatz genuinely considers a finite system. The extraction of finite-size results from the Bethe ansatz equations is of genuine interest, especially against the background of the results of finite-size scaling and conformal symmetry in finite geometries. The mathematical techniques introduced in chapter 19 permit a systematic treatment in this chapter of finite-size corrections as corrections to the thermodynamic limit of the system. The application of the Euler-Maclaurin formula transforming finite sums into integrals and finite-size corrections transforms the Bethe ansatz equations into Wiener–Hopf integral equations with inhomogeneities representing the finite-size corrections solvable using the Wiener–Hopf technique. The results can be compared to results for finite systems obtained from other approaches that are independent of the Bethe ansatz method. It briefly discusses higher-order corrections and offers a general assessment of the finite-size method.

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One-dimensional quantum spin heterojunction as a thermal switch

International Journal of Modern Physics B ◽

10.1142/s0217979216500272 ◽

2016 ◽

Vol 30 (07) ◽

pp. 1650027

Author(s):

Chuan-Jing Yang ◽

Li-Hui Jin ◽

Wei-Jiang Gong

Keyword(s):

Thermal Transport ◽

Structural Parameters ◽

Finite Size ◽

Quantum Spin ◽

Spin Interaction ◽

Heat Current ◽

Spin Hamiltonian ◽

One Dimensional ◽

Thermal Switch ◽

Wigner Transformation

We study the thermal transport through a quantum spin-[Formula: see text] heterojunction, which consists of a finite-size chain with two-site anisotropic XY interaction and three-site XZX+YZY interaction coupled at its ends to two semi-infinite isotropic XY chains. By performing the Jordan–Wigner transformation, the original spin Hamiltonian is mapped onto a fermionic Hamiltonian. Then, the fermionic structure is discussed, and the heat current as a function of structural parameters is evaluated. It is found that the magnetic fields applied at respective chains play different roles in adjusting the heat current in this heterojunction. Moreover, the interplay between the anisotropy of the XY interaction and the three-site spin interaction assists to further control the thermal transport. In view of the numerical results, we propose this heterojunction to be an alternate candidate for manipulating the heat current in one-dimensional (1D) systems.

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Thermodynamic properties of a finite one-dimensional system of bosons with repulsive delta-function interaction

Canadian Journal of Physics ◽

10.1139/p95-033 ◽

1995 ◽

Vol 73 (3-4) ◽

pp. 245-247

Author(s):

K. L. Poon ◽

K. Young ◽

D. Kiang

Keyword(s):

Thermodynamic Properties ◽

Thermodynamic Limit ◽

General Model ◽

Finite Size ◽

Delta Function ◽

One Dimension ◽

Dimensional System ◽

One Dimensional ◽

Finite Size Corrections

The thermodynamics of N bosons in a length L in one dimension, with repulsive delta-function interaction, is studied numerically for finite N, L. The results show the nature of finite-size corrections and how the thermodynamic limit is approached, and hopefully will be of some guidance in seeking the solution of a more general model.

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Critical exponents for the Reggeon quantum spin model

Physics Letters B ◽

10.1016/0370-2693(78)90279-4 ◽

1978 ◽

Vol 76 (2) ◽

pp. 213-219 ◽

Cited By ~ 141

Author(s):

Richard C. Brower ◽

Miguel A. Furman ◽

Moshe Moshe

Keyword(s):

Critical Exponents ◽

Spin Model ◽

Quantum Spin ◽

Quantum Spin Model

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Investigation of the Finite Size Properties of the Ising Model Under Various Boundary Conditions

Zeitschrift für Naturforschung A ◽

10.1515/zna-2019-0227 ◽

2020 ◽

Vol 75 (2) ◽

pp. 175-182

Author(s):

Magdy E. Amin ◽

Mohamed Moubark ◽

Yasmin Amin

Keyword(s):

Magnetic Field ◽

Ising Model ◽

Boundary Conditions ◽

Finite Size ◽

Scaling Functions ◽

Finite Size Scaling ◽

One Dimensional ◽

Various Boundary Conditions ◽

The One ◽

Bulk Case

AbstractThe one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.

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