Non-Abelian fermionization and fractional quantum Hall transitions

Article

关键词: SINE-GORDON EQUATION;    FILLED LANDAU-LEVEL;    INSULATOR TRANSITION;    GAUGE-THEORIES;    FIELD-THEORY;    WZW MODELS;    DUALITY;    SUPERCONDUCTIVITY;    PHYSICS;    LIQUID;   

DOI  :  10.1103/PhysRevB.97.085112

来源: SCIE

【 摘 要 】

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent nu approximate to 2.3 and that nu is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi et al., Rev. Mod. Phys. 69, 315 (1997)]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U(N-c) gauge group coupled to N-f = 1 fermion. We study one class of theories in a controlled limit where N-f >> N-c and calculate nu to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent. within the large N-f >> N-c expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993); Chen et al., Phys. Rev. B 48, 13749 (1993)].

【 授权许可】

Free