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Geometric phases and quantum phase transitions in open systems
Alexander I Nesterov1, S G Ovchinnikov
1Departamento de Física, CUCEI, Universidad de Guadalajara, Av. Revolución 1500, Guadalajara, Codigo Postal 44420, Jalisco, México. nesterov@cencar.udg.mx
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 4, 2008
Summary
This study links quantum phase transitions to geometric phases in open quantum systems. The first-order quantum phase transition in a dissipative Ising model is characterized by its geometric phase.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Non-Hermitian systems
Background:
- Open quantum systems exhibit complex dynamics influenced by dissipation.
- Non-Hermitian Hamiltonians are crucial for describing systems with gain or loss.
- Quantum phase transitions (QPTs) signify abrupt changes in a system's ground state properties.
Purpose of the Study:
- To establish a relationship between quantum phase transitions and complex geometric phases in open quantum systems.
- To investigate the geometric phase of the ground state in a specific dissipative model.
- To characterize the order of the quantum phase transition in the studied system.
Main Methods:
- Governing open quantum systems with a non-Hermitian effective Hamiltonian.
- Analyzing systems with accidental crossings of eigenvalues.
- Evaluating the geometric phase associated with the ground state.
- Utilizing the one-dimensional dissipative Ising model in a transverse magnetic field.
Main Results:
- A direct relationship is established between QPTs and complex geometric phases.
- The geometric phase for the ground state of the 1D dissipative Ising model is calculated.
- The quantum phase transition in this model is identified as a first-order transition.
Conclusions:
- Geometric phases offer a new perspective for understanding QPTs in open, non-Hermitian systems.
- The first-order nature of the QPT in the dissipative Ising model is confirmed through geometric phase analysis.
- This work provides a framework for exploring QPTs in dissipative quantum technologies.
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