Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality

Article

关键词: NONLINEAR SIGMA-MODEL;    FIELD PENETRATION DEPTH;    CRITICAL FLUCTUATIONS;    PHASE-TRANSITIONS;    BETA-FUNCTION;    QUANTUM CRITICALITY;    RENORMALIZATION-GROUP;    SYMMETRY-BREAKING;    SUPERCONDUCTORS;    ELECTRODYNAMICS;   

DOI  :  10.1103/PhysRevB.100.134507

来源: SCIE

【 摘 要 】

The Abelian Higgs model is the textbook example for the superconducting transition and the Anderson-Higgs mechanism, and has become pivotal in the description of deconfined quantum criticality. We study the Abelian Higgs model with n complex scalar fields at unprecedented four-loop order in the 4 - epsilon expansion and find that the annihilation of the critical and bicritical points occurs at a critical number of n(c) approximate to 182.95(1 - 1.752 epsilon + 0.798 epsilon(2) + 0.362 epsilon(3)) + O(epsilon(4)). Consequently, below n(c), the transition turns from second to first order. Resummation of the series to extract the result in three dimensions provides strong evidence for a critical n(c) (d = 3) which is significantly below the leading-order value, but the estimates for n(c) are widely spread. Conjecturing the topology of the renormalization group flow between two and four dimensions, we obtain a smooth interpolation function for n(c)(d) and find n(c)(3) approximate to 12.2 +/- 3.9 as our best estimate in three dimensions. Finally, we discuss Miransky scaling occurring below n(c) and comment on implications for weakly first-order behavior of deconfined quantum transitions. We predict an emergent hierarchy of length scales between deconfined quantum transitions corresponding to different n.

【 授权许可】

Free