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Characterizing and quantifying frustration in quantum many-body systems.

S M Giampaolo1, G Gualdi, A Monras

  • 1Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy.

Physical Review Letters
|January 17, 2012
PubMed
Summary
This summary is machine-generated.

We introduce a universal measure for quantum frustration, linking it to entanglement. This framework unifies geometric and quantum frustration in quantum spin systems.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Quantum information theory

Background:

  • Frustration is a key concept in condensed matter physics, particularly in spin systems.
  • Understanding frustration is crucial for designing novel quantum materials and devices.
  • Existing criteria for frustration are primarily classical and do not fully capture quantum effects.

Purpose of the Study:

  • To develop a general theoretical framework for studying frustration in quantum systems.
  • To introduce a universal measure of frustration applicable to any quantum system.
  • To establish criteria for identifying quantum systems that are "inequality saturating" and to connect these to geometric and quantum frustration.

Main Methods:

  • Introduction of a universal measure of frustration for arbitrary quantum systems.
  • Relating the frustration measure to entanglement monotones via an exact inequality.
  • Defining and deriving sufficient conditions for quantum spin systems to be inequality saturating.
  • Extensive numerical tests to confirm the derived conditions.

Main Results:

  • A universal measure of frustration is introduced and related to entanglement monotones.
  • A precise inequality is established, and its saturation defines "inequality saturating" systems.
  • Sufficient conditions for inequality saturation in quantum spin systems are derived.
  • These conditions generalize classical Toulouse criteria to the quantum realm.

Conclusions:

  • The study establishes a unified framework for analyzing frustration in quantum systems.
  • The framework distinguishes between geometric and purely quantum contributions to frustration.
  • The findings provide a new perspective on quantum spin systems and their properties.