title: An order parameter for impurity systems at quantum criticality.
abstract: A quantum phase transition may occur in the ground state of a system at zero temperature when a controlling field or interaction is varied. The resulting quantum fluctuations which trigger the transition produce scaling behaviour of various observables, governed by universal critical exponents. A particularly interesting class of such transitions appear in systems with quantum impurities where a non-extensive term in the free energy becomes singular at the critical point. Curiously, the notion of a conventional order parameter that exhibits scaling at the critical point is generically missing in these systems. Here we explore the possibility to use the Schmidt gap, which is an observable obtained from the entanglement spectrum, as an order parameter. A case study of the two-impurity Kondo model confirms that the Schmidt gap faithfully captures the scaling behaviour by correctly predicting the critical exponent of the dynamically generated length scale at the critical point.
authors.affiliation: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
authors.forename: Abolfazl
authors.initials: A
authors.lastname: Bayat
authors.affiliation: Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden.
authors.forename: Henrik
authors.initials: H
authors.lastname: Johannesson
authors.affiliation: Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK.
authors.forename: Sougato
authors.initials: S
authors.lastname: Bose
authors.affiliation: 1] International Institute of Physics, Universidade Federal do Rio Grande do Norte, 59078-400 Natal-RN, Brazil [2] Departamento de Fisica Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN, Brazil [3] INFN, Sezione di Perugia, Via A. Pascoli, 06123 Perugia, Italy.
authors.forename: Pasquale
authors.initials: P
authors.lastname: Sodano