Excited-state quantum phase transitions in the two-spin elliptic Gaudin model

Area of Science:

• Quantum mechanics
• Statistical physics
• Condensed matter theory

Background:

• The two-spin elliptic Gaudin model is a complex quantum system with applications in various physical phenomena.
• Understanding its integrability and phase transitions is crucial for advancing quantum many-body physics.

Purpose of the Study:

• To analyze the integrability of the two-spin elliptic Gaudin model across arbitrary Hamiltonian parameters.
• To investigate the presence and nature of quantum phase transitions in the model's spectral bands.
• To explore the symmetry-breaking aspects associated with these excited-state quantum phase transitions.

Main Methods:

• Utilizing a semiclassical approximation for the limit of large spin coupled to a small one, reducing degrees of freedom.
• Deriving analytical expressions for critical energies within the semiclassical framework.
• Performing exact diagonalizations on large systems to corroborate theoretical predictions.

Main Results:

• The model's spectrum is divided into non-overlapping bands under specific conditions.
• Excited-state quantum phase transitions are identified within these bands, even without quantum phase transitions at band heads.
• These transitions involve the breaking of parity symmetry in one region and time-reversal symmetry in another.

Conclusions:

• The study provides a comprehensive analysis of the integrability and quantum phase transitions in the two-spin elliptic Gaudin model.
• Semiclassical and exact diagonalization methods confirm the existence of excited-state quantum phase transitions and associated symmetry breaking.
• The findings offer insights into the complex behavior of quantum many-body systems and their phase diagrams.