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Long-range quantum Ising spin glasses at t=0: gapless collective excitations and universality
1The Abdus Salam ICTP-Strada Costiera 11, 34151, Trieste, Italy.
Physical Review Letters
|December 11, 2012
Summary
The quantum glass phase of the Sherrington-Kirkpatrick model is critical, showing collective excitations. These excitations behave like weakly coupled oscillators, with low-frequency spectra independent of transverse field strength.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Quantum Mechanics
Background:
- The Sherrington-Kirkpatrick (SK) model is a fundamental model in statistical mechanics for spin glasses.
- Understanding the quantum glass phase and its critical properties is crucial for disordered systems.
Purpose of the Study:
- To solve the SK model in a transverse field deep in its quantum glass phase at zero temperature.
- To characterize the nature of the glass phase and its excitations.
Main Methods:
- Analytical solution of the SK model in a transverse field.
- Zero-temperature analysis.
- Effective potential approach.
Main Results:
- The quantum glass phase is shown to be critical everywhere.
- Collective excitations with a gapless Ohmic spectral function are identified.
- These excitations are interpreted as disordered, weakly coupled, underdamped oscillators.
- The low-frequency spectrum is found to be independent of the transverse field strength for small fields.
Conclusions:
- The quantum glass phase exhibits universal critical behavior characterized by gapless collective excitations.
- The spectral function provides insights into the microscopic behavior of disordered quantum systems.
- The independence of the low-frequency spectrum from transverse field fluctuations suggests robust critical properties.
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