Geometric phase and quantum phase transition: Two-band model

2008/08/01 by H. T. Cui, Jie Yi · 12 citations
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Connection (principal bundle) #Geometric modeling #Geometric phase #Geometry #Ground state #Mathematics #Operator (biology) #Phase (matter) #Phase transition #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Statistical physics #Topological Materials and Phenomena #quant-ph

paper · pdf · doi:10.1103/physreva.78.022101

published in Physical Review A 78(2) (American Physical Society) · 7.5 pages and comments are welcome

openalex publication_date 2008/08/01 · arxiv created 2008/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation value. In contrast to the previous numerical examinations, our discussion presents an exact calculation for the determination of the geometric phase. Through two representative examples, our calculation shows the intimate connection between the geometric phase and phase transition: different behaviors of the geometric phase can be identified in this paper, which are directly related to the energy gap above the ground state.

Citations

• Solitons in conducting polymers
• Topological classification of gapped spin chains: Quantized Berry phase as a local order parameter
• Lattice twist operators and vertex operators in sine-Gordon theory in one dimension
• Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
• Quantum Critical Scaling of the Geometric Tensors
• Quantal phase factors accompanying adiabatic changes
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Two soluble models of an antiferromagnetic chain
• Entanglement in many-body systems

Cited by

• Dynamics of the geometric phase in the adiabatic limit of a quench induced quantum phase transition
• Accurate Formula for the Macroscopic Polarization of Strongly Correlated Materials