Quantum Spin Chain Problem: An Overview

[genloz]

what is the quantum spin chain problem?
From my research on the net I can see that its solved through exact diagonlization of some sort of matrix, but I can't work out exactly what the problem is...

 

[blechman]

It is the 1D problem of having a line of spins that are allowed to interact with each other. How they interact depends on the details (Ising/XY/Heisenberg). There's the classical spin chain which is the thing you learn in undergrad stat mech, and then the quantum spin chain, which is the same problem but now you allow quantum effects to be important (treat spin as quantum angular momentum rather than a classical angular momentum).

 

[genloz]

That's useful... I didn't do undergrad stat mech but I had a look through some of what google had to say... I'm still interested in how they interact in the heiseneberg model... any thoughts? Thanks again!

 

[blechman]

That's useful... I didn't do undergrad stat mech but I had a look through some of what google had to say... I'm still interested in how they interact in the heiseneberg model... any thoughts? Thanks again!

Check out the textbook by Dan Schroeder on Stat Mech - it's very good. It doesn't do Heisenberg, but it does a good job with Ising, and is a great intro to the ideas of stat mech (partition functions, free energies, etc). First learn to walk before you learn to fly!

As for good refs on Heisenberg: I learned from my old prof's lectures (unfortunately he didn't put his notes on the web) so I don't really have a good reference. I think I'll leave it for someone with more experience than me (I'm a particle theorist, not a condensed matter person).

Good luck!

 

[genloz]

Thanks for that!
I managed to find this:
http://xxx.lanl.gov/PS_cache/cond-mat/pdf/0107/0107399v1.pdf
which gives a good general overview (in simplistic terms) for anyone else interested...