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

Abstract

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.

9 pages, 5 figures

References in corpus (5)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Interacting anyons in topological quantum liquids: The golden chain
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Collective states of interacting Fibonacci anyons
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Cited by in corpus (7)

• The $Z_2$ staggered vertex model and its applications
• The "not-A", RSPT and Potts phases in an $S_3$-invariant chain
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• Integrable boundary conditions in the antiferromagnetic Potts model
• The antiferromagnetic Potts model
• Self-dual $S_3$-invariant quantum chains
• Integrability in anyonic quantum spin chains via a composite height model