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

In this Letter, 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≤√2, where d parametrizes the models; (5) note that, for the special values d=2cos⁡[π/(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 nonrelativistic SU(2) gauge theory; and (7) show that its one-loop β function vanishes for all values of the coupling constant, implying that it is also on a critical line.