# Construction of R-matrix

+ 3 like - 0 dislike
159 views

Background:

For a quantum integrable system the aim is, given some Hamiltonian, to write down its spectrum exactly. The canonical example is the Heisenberg XXX spin chain. The most commonly used method is the algebraic Bethe ansatz. However, this method works by pulling a generating object, the R-matrix, which satisfies the Yang-Baxter equation, out of nowhere and using it to construct a tower of commuting operators, one of which is the Hamiltonian we are seeking to diagonalise (even though it isn't, but this is what everything written on the subject says).

Question:

The Hamiltonian in question is generally invariant under some symmetry algebra, or more precisely, commutes with at least some of the elements of the algebra. Is it possible to write down an R-matrix satisfying the Yang-Baxter Equation and producing the Hamiltonian we seek by some method without the guesswork? In other words,  can one go from

Input parameters: Hamiltonian, Lie algebra

to

Output: R-matrix for the system

asked Sep 18, 2016

## Your answer

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysics$\varnothing$verflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.