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Stability of the quantum Sherrington-Kirkpatrick spin glass model
1University of California Santa Cruz, California 95064, USA.
Physical Review. E
|January 20, 2018
Summary
This study numerically solves the quantum Sherrington-Kirkpatrick (SK) model. It reveals replica symmetry breaking occurs at T=0, identifying a new quantum de Almeida-Thouless (QuAT) line, potentially impacting quantum annealers.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Statistical Mechanics
Background:
- The quantum Sherrington-Kirkpatrick (SK) model describes infinite-range Ising spin glasses in a transverse field.
- Understanding phase transitions and replica symmetry breaking is crucial in spin glass theory.
Purpose of the Study:
- To numerically solve the quantum SK model by mapping it to an effective one-dimensional model.
- To investigate the stability of the replica symmetric solution and identify phase transition lines.
Main Methods:
- Numerical solution of the effective one-dimensional model in the thermodynamic limit.
- Analysis of replica symmetry breaking in the quantum SK model.
Main Results:
- The replica symmetric solution remains unstable down to zero temperature.
- A quantum de Almeida-Thouless (QuAT) line exists in the transverse field-longitudinal field plane at T=0.
- The de Almeida-Thouless (AT) line persists in the longitudinal field-temperature plane.
Conclusions:
- The findings challenge previous claims about replica symmetry stability in the quantum SK model.
- The identified QuAT line may influence quantum annealer performance for biased spin glass problems.
- Further research is needed to determine if the QuAT line exists in short-range interaction models.
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