An order parameter for impurity systems at quantum criticality.

Abolfazl Bayat,Pasquale Sodano,Sougato Bose,Henrik Johannesson

doi:10.1038/ncomms4784

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.

Highlights

A quantum phase transition may occur in the ground state of a system at zero temperature when a controlling field or interaction is varied
We have shown that the Schmidt gap obtained from the entanglement spectrum provides a nonlocal order parameter for a quantum impurity system at criticality
A case study of the two-impurity Kondo model (TIKM) confirms that the Schmidt gap faithfully captures the scaling behaviour by correctly predicting the critical exponent of the dynamically generated length scale at the quantum critical point

Summary

Introduction

A quantum phase transition may occur in the ground state of a system at zero temperature when a controlling field or interaction is varied. While a QPT cannot be accessed directly in the laboratory, it leaves distinct imprints at finite temperature: in the case of a continuous QPT, characterized by an avoided level crossing in the ground state energy, large quantum fluctuations in the neighbourhood of the quantum critical point spawns a ‘quantum critical regime’, where the scaling of observables are encoded in non-integer exponents This is the signature of a non-Fermi liquid[2], exemplified in the physics of heavy fermions materials[3], unconventional superconductors[4] and quantum impurity systems[5]. Could an analogous construction be used to identify an order parameter for iQPTs?

Methods

Results

Conclusion