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.
Created: 2024-01-18 Thu 14:24