Understanding Strongly Correlated Systems: From Atoms to Chaos Theory

[leoant]

I am no familiar with this area, and I want to know whether can we say that materials including atoms with d electrons are strongly correltated sysytem?

 

[ZapperZ]

I am no familiar with this area, and I want to know whether can we say that materials including atoms with d electrons are strongly correltated sysytem?

You do know that you're asking a question that is the topic of whole books.

The term "strongly correlated" is often a vague term. More often than not, it is reflected in the ratio of t/U, or W/U, where t is the hopping integral, U is the on-site Coulomb repulsion, and W is the bandwidth. If you have done tight-binding approximation, you would have noticed that the s-orbital tends to be highly localized around the ions. Compare this to the d-orbital that is more spread out, and you can see why transition atoms and oxides will create more overlap between neighboring sites. So the hopping integral will become more dominant and electrons from each ions can no longer ignore each other's presence. This, essentially, is a handwaving argument why transition metal/oxides tend to be considered as strongly-correlated systems.

One of the most important classifications in strongly correlated electron system is the Zaanen-Sawatzky-Allen scheme[1]. This scheme tries to delineate between a Mott-Hubbard system and a charge-transfer system in the transition metal/oxides. You may want to read on this also.

Zz.

[1] J. Zaanen, et al. Phys. Rev. Lett. v.55, p.418 (1985).

 

[ZapperZ]

Here's possibly additional useful information on this topic:

http://arxiv.org/abs/cond-mat/0508631

Caveat: I did only a quick glance at this preprint, so I cannot vouch for its accuracy (it looked good on that quick glance). I seldom recommend preprints on Arxiv based on a flimsy review such as this, but I'm pressed for time right now (have to complete as much stuff this week as possible before my Disney World vacation).

Zz.

 

[leoant]

Thank you very much, dear Zapperz. And May you a good journey.

 

[ZapperZ]

More relevant material on this topic from a very well-known source. This is a review article that appeared in Science a couple of months ago.

http://arxiv.org/abs/cond-mat/0509041

Zz.

 

[leoant]

Ohh, it's an exciting paper while makes me frustrated. One can interpret 'the complex system' intuitively, however, how can we describe it mathematically?
Using Hubbard mode or t-J mode? Or even chaos theory?

 

[ZapperZ]

Ohh, it's an exciting paper while makes me frustrated. One can interpret 'the complex system' intuitively, however, how can we describe it mathematically?
Using Hubbard mode or t-J mode? Or even chaos theory?

But that is a central research work in condensed matter. What model one can use it extremely important. One model that works in one situation may not work in another. It very much depends on the nature of the problem. If you have, for example, a Kondo system, then even perturbative approach may fail since for this system, one of the higher order interaction is LARGE.

Zz.