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Probing quantum frustrated systems via factorization of the ground state
Salvatore M Giampaolo1, Gerardo Adesso, Fabrizio Illuminati
1Dipartimento di Matematica e Informatica, Università degli Studi di Salerno, CNR-SPIN, CNISM, Unità di Salerno, and INFN, Sezione di Napoli-Gruppo Collegato di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy.
Physical Review Letters
|September 28, 2010
Summary
Frustrated quantum systems exhibit order when ground states are fully factorized. Ground-state separability quantifies frustration, indicating systems unable to achieve classical-like solutions.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter physics
Background:
- Frustrated quantum systems present challenges in understanding their ordered states.
- Classical-like solutions are often unattainable in strongly frustrated systems.
- Ground-state properties are crucial for characterizing quantum system behavior.
Purpose of the Study:
- To rigorously establish the link between definite orders in frustrated quantum systems and fully factorized ground states.
- To introduce ground-state separability as a quantitative measure of frustration.
- To determine the critical frustration and factorized ground states for various spin models.
Main Methods:
- Analysis of nonexactly solvable spin models with varying interaction ranges.
- Rigorous mathematical treatment relating order to ground-state factorization.
- Investigation of disentangling transitions in weakly frustrated systems.
Main Results:
- A direct correlation is found between definite order and fully factorized ground states below a critical frustration threshold.
- Ground-state separability is identified as a natural measure of frustration.
- The critical frustration and factorized ground states are explicitly determined for diverse spin models.
- Disentangling transitions in weak frustration regimes are identified.
Conclusions:
- Ground-state separability effectively measures frustration in quantum systems.
- Strongly frustrated systems inherently lack classical-like solutions.
- The findings have implications for understanding stochastic gene expression and the stability of modulated structures.
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