A Line of Critical Points in 2+1 Dimensions: Quantum Critical Loop Gases and Non-Abelian Gauge Theory

Details A Line of Critical Points in 2+1 Dimensions: Quantum Critical Loop Gases and Non-Abelian Gauge Theory A Line of Critical Points in 2+1 Dimensions: Quantum Critical Loop Gases and Non-Abelian Gauge Theory

2004-08-11

arxiv.org/abs/cond-mat/0408257v1

Phys.Rev.Lett. 94 (2005) 147205

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1103/PhysRevLett.94.147205

We (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ground states to O(n) loop gases; (4) show that the models are critical for $d\leq \sqrt{2}$, where $d$ parametrizes the models; (5) note that for the special values $d=2\cos(\pi/(k+2))$, they are related to doubled level-$k$ SU(2) Chern-Simons theory; (6) conjecture that they are in the universality class of a non-relativistic SU(2) gauge theory; and (7) show that its one-loop $\beta$-function vanishes for all values of the coupling constant, implying that it is also on a critical line.

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