Method for calculating finite size corrections in Bethe ansatz systems: Heisenberg chain and six-vertex model

1985 ◽  
Vol 251 ◽  
pp. 439-456 ◽  
Author(s):  
H.J. de Vega ◽  
F. Woynarovich
Keyword(s):  
Bethe Ansatz ◽  
Finite Size ◽  
Vertex Model ◽  
Heisenberg Chain ◽  
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.

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

A crash course on the simple Bethe Ansatz

2008 ◽  
Vol 86 (3) ◽  
pp. 413-446
Author(s):  
Jeffrey R Schmidt
Keyword(s):  
Bethe Ansatz ◽  
Lattice Models ◽  
Wave Functions ◽  
Vertex Model ◽  
Heisenberg Chain ◽  
Many Body ◽  
Full Wave

The simple Bethe Ansatz is illustrated step by step in great detail for a variety of many-body quantum problems and lattice models. The focus is on a constructive presentation in which the problems of determining the spectral conditions and full wave functions are completely and transparently solved for the cases of the isotropic Heisenberg chain, N bosons or spin ħ/2 fermions with δ-function interactions, the XX-Heisenberg chain, and the six-vertex model. PACS Nos.: 05.50.+q, 05.30.Fk, 03.65.Fd, 75.10.Hk, 71.10.Fd

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