The Bethe Ansatz

Section and equation labelling i.n.l

For labelling sections and equations, I've preferred to use a semantic format instead of traditional numbers.

This has a number of advantages: the labelling is

  • meaningful (at least occasionally)
  • easier to remember in the long run
  • stable under tree structure modifications

but also come with some things which need getting used to:

  • the loss of clear notion of ordering
  • abbreviations being as short as possible, thus sometimes obfuscating their original meaning

Section labelling: floated right next to the title of any section, you will see the label together with a permalink (pointing to the main site's version of that particular section). Under a section's headline, you will also sometimes see references (in small gray letters) to corresponding sections in complementary literature.

Parts identification: each part of the notes has a single-letter identifier, given in the following table:

Part Identifier
Introduction i
Exact eigenstates: the Coordinate Bethe Ansatz c
Ground states g
Equilibrium thermodynamics e
The Algebraic Bethe Ansatz a
Dynamical correlation functions d
Out of equilibrium o
Literature l

Model identification: each model which is treated is given a one- or two-letter identifier according to the following table:

Class Model   Identifier
Fundamental   f  
  Lieb-Liniger   l
  Heisenberg spin-1/2 isotropic antiferromagnet   h
Further spin chains   sc  
  Ising   i
  Heisenberg spin-1/2 isotropic ferromagnet   f
  Heisenberg spin-1/2 planar model (XXZ with -1 < Δ < 1)   p
  Heisenberg spin-1/2 axial antiferromagnet (XXZ with Δ > 1)   a
  Heisenberg spin-1/2 axial ferromagnet (XXZ with Δ < -1)   af
  Haldane-Shastry   hs
  Inozemtsev   in
  Babujian-Takhtajan   bt
  Integrable spin-S   s
Further continuum   cm  
  Attractive Lieb-Liniger   al
  Two-component Bose gas   b2
  Yang permutation   y
Fermions on a lattice   fl  
  t-J   tj
  Hubbard   hu
Impurity models   im  
  Kondo or s-d   k
  Anderson impurity   ai
Gaudin magnets   gm  
  Richardson   r
  Gaudin magnets   g

Equation labelling: similarly to sections, some (but not all) equations also carry a semantic label, given in parentheses to the right of the equation. As per sections, a permalink is also given, together with corresponding equation numbers in complementary literature.

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Author: Jean-Sébastien Caux

Created: 2023-06-07 Wed 16:02