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Non-quantized Zak phases, PT/APT symmetry transitions, and doubly degenerate exceptional points in a non-Hermitian spin-orbit coupled SSH model |
| Jun-Xing Huo(霍俊行)1, Jian Li(李健)1,2,3,†, Qing-Xu Li(李清旭)1,2,3, and Jia-Ji Zhu(朱家骥)1,2,3,‡ |
1 School of Science and Laboratory of Quantum Information Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
2 Institute for Advanced Sciences, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;
3 Southwest Center for Theoretical Physics, Chongqing University, Chongqing 401331, China |
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Abstract We theoretically investigate a one-dimensional Su-Schrieffer-Heeger (SSH) model with spin-orbit coupling (SOC) and sublattice-dependent gain and loss. As the gain and loss increase, the system transitions from a parity-time (${\rm PT}$) symmetric phase to a parity-time and anti-parity-time (${\rm PT\&APT}$) symmetry-breaking phase, and finally to an anti-parity-time (${\rm APT}$) symmetric phase. Notably, when the intracell and intercell hopping, intracell and intercell SOC parameters are all equal to half the gain-loss parameter, the model exhibits a doubly degenerate exceptional point (EP). When the SOC is equal for intracell and intercell interactions, a stronger hopping mechanism within cells compared to that between cells results in an increase in SOC that transitions the Zak phase from zero to a non-quantized value, eventually arriving at one. In contrast, a reduction in the strength of intracell hopping leads the Zak phase to transition from two to a non-quantized value, eventually arriving at one. If the intracell and intercell SOC are not aligned, altering these couplings leads to a shift in the Zak phase from two to a non-quantized level, then to one, re-entering the non-quantized region, and eventually arriving at zero. We suggest a practical experimental setup for our model that can be implemented using electrical circuits.
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Received: 13 February 2025
Revised: 19 March 2025
Accepted manuscript online: 02 April 2025
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PACS:
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03.65.Yz
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(Decoherence; open systems; quantum statistical methods)
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71.70.Ej
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(Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect)
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11.30.Er
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(Charge conjugation, parity, time reversal, and other discrete symmetries)
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73.43.Nq
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(Quantum phase transitions)
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| Fund: Project supported by the Natural Science Foundation of Chongqing, China (Grant No. CSTB2024NSCQ-MSX0736), Science and Technology Innovation Key R&D Program of Chongqing (Grant No. CSTB2024TIAD-STX0035), and the Research Foundation of Institute for Advanced Sciences of CQUPT (Grant No. E011A2022328). |
Corresponding Authors:
Jian Li, Jia-Ji Zhu
E-mail: jianli@cqupt.edu.cn;zhujj@cqupt.edu.cn
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Cite this article:
Jun-Xing Huo(霍俊行), Jian Li(李健), Qing-Xu Li(李清旭), and Jia-Ji Zhu(朱家骥) Non-quantized Zak phases, PT/APT symmetry transitions, and doubly degenerate exceptional points in a non-Hermitian spin-orbit coupled SSH model 2025 Chin. Phys. B 34 070301
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