A Temperley-Lieb quantum chain with two- and three-site interactions

Details A Temperley-Lieb quantum chain with two- and three-site interactions A Temperley-Lieb quantum chain with two- and three-site interactions

2009-01-29

arxiv.org/abs/0901.4685v2

J. Phys. A: Math. Theor. 42, 292002 (2009)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 5 figures

Scientific paper

We study a quantum chain of spin-1/2 particles whose world lines form a loop gas. In addition to the usual interaction that projects a pair of neighboring spins onto quantum-group spin 0, we introduce a three-site interaction that projects onto spin 3/2. Changing the relative strengths of these interactions leads to a rich phase diagram containing gapped and critical phases, and exactly solvable points. For loop weight $n=2 \cos [\pi/(p+1)]$, the model corresponds to N=p-3 species of interacting anyons, of which only the Fibonacci case N=1 was studied previously. Our study applies to real n, and provides further exact results which were unnoticed even for the special case N=1.

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