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

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

Michael Freedman, Chetan Nayak, and Kirill Shtengel

Phys. Rev. Lett. 94, 147205 – Published 14 April 2005

Abstract

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 $d \leq \sqrt{2}$ , where $d$ parametrizes the models; (5) note that, for the special values $d = 2 \cos [π / (k + 2)]$ , 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.

Received 23 August 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.147205

Authors & Affiliations

Michael Freedman¹, Chetan Nayak^1,2, and Kirill Shtengel^1,3

¹Microsoft Research, One Microsoft Way, Redmond, Washington 98052, USA
²Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547, USA
³Department of Physics, California Institute of Technology, Pasadena, California 91125, USA

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Vol. 94, Iss. 14 — 15 April 2005

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