The Bethe Ansatz
Section and equation labellingi.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.
 Except where otherwise noted, all content is licensed under a
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Except where otherwise noted, all content is licensed under a
Creative Commons Attribution 4.0 International License.
Created: 2024-01-18 Thu 14:24