scholarly journals A distribution approach to finite-size corrections in Bethe Ansatz solvable models

2018 ◽  
Vol 934 ◽  
pp. 96-117 ◽  
Author(s):  
Etienne Granet ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Bethe Ansatz ◽  
Finite Size ◽  
Solvable Models ◽  
Finite Size Corrections

Finite Heisenberg Quantum Spin Chain

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.

EXACTLY SOLVABLE MODELS AND FINITE SIZE CORRECTIONS

1992 ◽  
Vol 06 (08) ◽  
pp. 1119-1180 ◽  
Author(s):  
JUNJI SUZUKI ◽  
TARO NAGAO ◽  
MIKI WADATI
Keyword(s):  
Finite Size ◽  
Spin Model ◽  
Quantum Spin ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Soliton Theory ◽  
Exactly Solvable ◽  
Recent Developments ◽  
Quantum Spin Models ◽  
Finite Size Corrections

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.

THE CRITICAL BEHAVIOR OF SINE-GORDON MODEL

1992 ◽  
Vol 06 (11) ◽  
pp. 665-674
Author(s):  
YI-MIN LIU ◽  
FU-CHO PU ◽  
HANG SU
Keyword(s):  
Bethe Ansatz ◽  
Excited States ◽  
Critical Behavior ◽  
Coupling Parameter ◽  
Finite Size ◽  
Conformal Anomaly ◽  
Critical Coupling ◽  
Sine Gordon Model ◽  
Energy And Momentum ◽  
Finite Size Corrections

Using the algebraic Bethe Ansatz and Euler-Maclaurin formulae, we calculate the finite-size corrections to the energy and momentum of ground and excited states for the sine-Gordon model. The conformal anomaly, operator dimension and critical coupling parameter are given in the ultraviolet limit.

scholarly journals SU(2) FUSION HIERARCHIES OF DILUTE MODELS

1996 ◽  
Vol 10 (25) ◽  
pp. 3481-3503 ◽  
Author(s):  
YU-KUI ZHOU
Keyword(s):  
Bethe Ansatz ◽  
Finite Size ◽  
Transfer Matrices ◽  
Fusion Rules ◽  
Finite Size Corrections

The dilute AL models have been studied by analyzing their adjacency conditions, face weights and transfer matrices. The new results including two su(2) fusion rules and Bethe ansatz solutions of the fused transfer matrices are presented. Some relevant physics aspects such as the finite-size corrections to transfer matrices are also discussed.

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