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 behavior 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 which exhibits scaling at the critical point is generically missing in these systems. We here 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 behavior by correctly predicting the critical exponent of the dynamically generated length scale at the critical point.

6 pages, 5 figures

References in corpus (4)

• "Deconfined" quantum critical points
• Entanglement spectrum in one-dimensional systems
• Quantum criticality in a double quantum-dot system
• Universal low-temperature crossover in two-channel Kondo models

Cited by in corpus (12)

• Quantum coherence and uncertainty in the anisotropic XY chain
• Negativity spectrum of one-dimensional conformal field theories
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Explicit Hamiltonians Inducing Volume Law for Entanglement Entropy in Fermionic Lattices
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Fluctuations and Entanglement spectrum in quantum Hall states
• Pulse and quench induced dynamical phase transition in a chiral multiferroic spin chain
• Natural Orbitals Renormalization Group Approach to the Two-Impurity Kondo Critical Point
• Entanglement entropy scaling in solid-state spin arrays via capacitance measurements
• Nonclassicality and criticality in symmetry-protected magnetic phases
• Dynamics of Entanglement and the Schmidt Gap in a Driven Light-Matter System
• Entanglement of magnetic impurities through electron scattering in an electric field