How a complex Zeeman field drives quantum phase transitions in the Ising model: From the perspective of geometric phase and symmetry
Abstract
Inspired by the realizations of imaginary magnetic field in a non-Hermitian atomic systems by laser assisted spin-selective dissipations (Lapp et al., 2019; Li et al., 2019), we investigate the quantum phase transitions of Ising model driven by the constant and staggered complex Zeeman field and find that the quantum phase transition is due to the competition of antiferromagnetic phase and ferromagnetic phase. With the Jordan–Wigner transformation, the model is transformed to a lattice model. By discussing the geometric phase and symmetry of the equivalent model, we can understand the Lee–Yang zeros in a new perspective. The studies indicate the complex parameter significantly changes the topological structure of the complex energy spectrum and the parity–time PT symmetry of the Hamiltonian. Due to the chiral symmetry of the model, the chiral indices are used as topological numbers to distinguish different topological phases. We find the quantum phase transition occurs when the coupling |J| is equal to complex Zeeman field |h| whether in the constant or staggered case.
- Publication:
-
Optik
- Pub Date:
- December 2021
- DOI:
- 10.1016/j.ijleo.2021.168031
- Bibcode:
- 2021Optik.24868031W
- Keywords:
-
- Ising model;
- Imaginary magnetic field;
- Non-Hermitian;
- Quantum phase transition