Universität zu Köln

Ihrig, Bernhard, Zerf, Nikolai, Marquard, Peter, Herbut, Igor F. and Scherer, Michael M. (2019). Abelian Higgs model at four loops, fixed-point collision, and deconfined criticality. Phys. Rev. B, 100 (13). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9969

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Abstract

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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ihrig, Bernhard UNSPECIFIED UNSPECIFIED UNSPECIFIED Zerf, Nikolai UNSPECIFIED UNSPECIFIED UNSPECIFIED Marquard, Peter UNSPECIFIED UNSPECIFIED UNSPECIFIED Herbut, Igor F. UNSPECIFIED UNSPECIFIED UNSPECIFIED Scherer, Michael M. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-130967
DOI:	10.1103/PhysRevB.100.134507
Journal or Publication Title:	Phys. Rev. B
Volume:	100
Number:	13
Date:	2019
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9969
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NONLINEAR SIGMA-MODEL; FIELD PENETRATION DEPTH; CRITICAL FLUCTUATIONS; PHASE-TRANSITIONS; BETA-FUNCTION; QUANTUM CRITICALITY; RENORMALIZATION-GROUP; SYMMETRY-BREAKING; SUPERCONDUCTORS; ELECTRODYNAMICS Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/13096