What Are Ring Exchanges in Quantum Systems?

[iibewegung]

Hello condensed matter gurus out there,

I'm a new graduate student who's been trying to understand some sentences in a review article that reads:
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... One of Feynman's early successes with path integrals is often neglected, his mapping with path integrals of a quantum system onto a classical model of interacting "polymers." The polymers are ring exchanges of bosons in imaginary time. ...
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Now I have no clue what "ring exchanges" are... can anyone briefly explain it to me or point me to a reference? Google wasn't too helpful when I fed it ring, exchange, interaction, etc.
Thanks in advance.




PS. by the way, this article is Rev.Mod.Phys., v67 p279 by D.M. Ceperley

 

[Gokul43201]

Ceperley has written some papers on (super)solid He, where he talks about ring exchanges. I think the idea, (from a talk he gave here some years ago, so my recollection is foggy) at least in that context, is that if you have a model based on a lattice, then the partition function of an N-particle system (living in this lattice) can be written as a sum over various arrangements of particle positions. These positions can be permuted about in N! ways, and I think, each permutation can be represented as a sum of "ring exchanges" - where you move one particle to a nearest-neighbor site, that one to one of its nearest neighbors, and so on, till the n'th particle is moved into the site vacated by the first particle.

 

[charng]

Ring exchanges refer to a type of interaction between particles in a quantum system, specifically bosons, that can be described using path integrals. In this context, "ring" refers to a closed loop or circle that the particles follow in imaginary time. The exchange part refers to the swapping of positions between particles along this loop, which is a key component in understanding the behavior of the system. This concept was first introduced by physicist Richard Feynman and has been used to map quantum systems onto classical models. For a more in-depth understanding, you can refer to the review article by D.M. Ceperley mentioned in the question.