Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0703049 · Physical Review A

Geometric phases induced in auxiliary qubits by many-body systems near their critical points

X. X. Yi, W. Wang

Published Mar 5, 2007• 36 citations
arXivHTMLPDF

Abstract

The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the qubit, respectively. As an example, we consider the $XY$ spin chain dephasingly coupled to a qubit. The geometric phase induced in the qubit is presented and discussed. The results show that the geometric phase might be used to signal the critical points of a many-body system, and it tends to zero as the parameters of the many-body system go away from the critical points.

DOI
10.1103/physreva.75.032103

Related papers

Geometric phase of a central spin coupled to an antiferromagnetic environment

Xiao-Zhong Yuan, Hsi‐Sheng Goan, Ka‐Di Zhu

Using the spin-wave approximation, we study the geometric phase (GP) of a central spin (signal qubit) coupled to an antiferromagnetic (AF) environment under the application of an external global magnetic field. The external magnetic field affects the GP of the qubit directly and also indirectly through its effect on the AF environment. We find that when the applied magnetic field is increased to the critical magnetic field point, the AF environment undergoes a spin-flop transition, a first-order phase transition, and at the same time the GP of the qubit changes abruptly to zero. This sensitive change of the GP of a signal qubit to the parameter change of a many-body environment near its critical point may serve as another efficient tool or witness to study the many-body phase transition. The influences of the AF environment temperature and crystal anisotropy field on the GP are also investigated.

arXiv:1003.1300•Physical Review A•Mar 12, 2010•11 citations

Detecting multi-spin interaction of an XY spin chain by geometric phase of a coupled qubit

Xiu-Xing Zhang, Ai-Ping, Zhang, Li Fu-Li

We investigate geometric phase (GP) of a qubit symmetrically coupled to a XY spin chain with three-spin interaction in a transverse magnetic field. An analytical expression for the GP is found in the weak coupling limit. It is shown that the GP displays a sharp peak or dip around the quantum phase transition (QPT) point of the spin chain. Without the three-spin interaction, the GP has a peak or dip around the critical point $λ=1$. If the three-spin interaction exists, the peak or dip position is obviously shifted away from the original position. This result reveals that the GP may be taken as an observable to detect both the existence and strength of multi-spin interaction in a spin chain.

arXiv:1204.2627•Apr 12, 2012•0 citations

Geometric phase of two-qubit system in dephasing environment

Xiaoya Cai, Hui Pan, Z. S. Wang

We investigated the geometric phase for interaction between superconducting two-qubit system in dephased environment. The Pancharatnam phase and the Berry phase are studied. Numerical results are discussed. By considering the differently initial conditions, we find that the time-dependent Pancharatnam phase keeps the initial entangling message. On the other hand, the transition of Pancharatnam phase is dependent of the phase change in the superconducting two-qubit coupling system. Our results may be helpful to implement the time-dependent geometric quantum computation.

International Journal of Modern Physics B•Nov 13, 2015•1 citation

Geometric phase in open systems: Beyond the Markov approximation and weak-coupling limit

X. X. Yi, D. M. Tong, L. C. Wang +2 more

Beyond the quantum Markov approximation and the weak-coupling limit, we present a general theory to calculate the geometric phase for open systems with and without conserved energy. As an example, the geometric phase for a two-level system coupling both dephasingly and dissipatively to its environment is calculated. Comparison with the results from quantum trajectory analysis is presented and discussed.

arXiv:quant-ph/0602181•Physical Review A•May 12, 2006•40 citations

Geometric phase in dephasing systems

X. X. Yi, L. C. Wang, Wei Wang

Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak-coupling limit, and it involves the phase information of the environment in general. In contrast with the geometric phase in dissipative systems, the geometric phase acquired by the system can be observed on a long time scale. We also show that with the system decohering to its pointer states, the geometric phase factor tends to a weighted sum over the phase factors pertaining to the pointer states.

arXiv:quant-ph/0501085•Physical Review A•Apr 22, 2005•36 citations

Induced modification of the geometric phase of a qubit coupled to an XY spin chain by Dzyaloshinsky—Moriya interaction

Aiping Zhang, Fuli Li

We consider a qubit symmetrically and transversely coupled to an XY spin chain with Dzyaloshinsky—Moriya (DM) interaction in the presence of a transverse magnetic field. An analytical expression for the geometric phase of the qubit is obtained in the weak coupling limit. We find that the modification of the geometrical phase induced by the spin chain environment is greatly enhanced by DM interaction in the weak coupling limit around the quantum phase transition point of the spin chain.

Chinese Physics B•Mar 1, 2013•5 citations
The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the qubit, respectively. As an example, we consider the XYXYXY spin chain dephasingly coupled to a qubit. The geometric phase induced in the qubit is presented and discussed. The results show that the geometric phase might be used to signal the critical points of a many-body system, and it tends to zero as the parameters of the many-body system go away from the critical points.
Using the spin-wave approximation, we study the geometric phase (GP) of a central spin (signal qubit) coupled to an antiferromagnetic (AF) environment under the application of an external global magnetic field. The external magnetic field affects the GP of the qubit directly and also indirectly through its effect on the AF environment. We find that when the applied magnetic field is increased to the critical magnetic field point, the AF environment undergoes a spin-flop transition, a first-order phase transition, and at the same time the GP of the qubit changes abruptly to zero. This sensitive change of the GP of a signal qubit to the parameter change of a many-body environment near its critical point may serve as another efficient tool or witness to study the many-body phase transition. The influences of the AF environment temperature and crystal anisotropy field on the GP are also investigated.
We investigate geometric phase (GP) of a qubit symmetrically coupled to a XY spin chain with three-spin interaction in a transverse magnetic field. An analytical expression for the GP is found in the weak coupling limit. It is shown that the GP displays a sharp peak or dip around the quantum phase transition (QPT) point of the spin chain. Without the three-spin interaction, the GP has a peak or dip around the critical point λ=1λ=1λ=1. If the three-spin interaction exists, the peak or dip position is obviously shifted away from the original position. This result reveals that the GP may be taken as an observable to detect both the existence and strength of multi-spin interaction in a spin chain.
We investigated the geometric phase for interaction between superconducting two-qubit system in dephased environment. The Pancharatnam phase and the Berry phase are studied. Numerical results are discussed. By considering the differently initial conditions, we find that the time-dependent Pancharatnam phase keeps the initial entangling message. On the other hand, the transition of Pancharatnam phase is dependent of the phase change in the superconducting two-qubit coupling system. Our results may be helpful to implement the time-dependent geometric quantum computation.
Beyond the quantum Markov approximation, we calculate the geometric phase of a two-level system driven by a quantized magnetic field subject to phase dephasing. The phase reduces to the standard geometric phase in the weak-coupling limit, and it involves the phase information of the environment in general. In contrast with the geometric phase in dissipative systems, the geometric phase acquired by the system can be observed on a long time scale. We also show that with the system decohering to its pointer states, the geometric phase factor tends to a weighted sum over the phase factors pertaining to the pointer states.