Geometric phase of a central spin coupled to an antiferromagnetic environment

Abstract

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.

Geometric phase and phase diagram for a non-Hermitian quantumXYmodel

“…In the realm of traditional quantum mechanics, the geometric phase has been introduced to analyze the quantum phase transitions of the XY model [15][16][17] and much effort has been devoted to various Hermitian many-body systems [18][19][20][21][22][23][24][25][26].…”

Linear Entropy of a Driven Central Spin Interacting with an Antiferromagnetic Environment

“…The system, which is considered here, represents a central spin interacting with an antiferromagnetic spin environment [13] [14]. The central spin and the antiferromagnetic spin environment are made of spin-1/2 atoms and the frequency c ω of the magnetic field is tuned to be resonant with the central spin to detect the central spin and control its states.…”

“…Ω = recognizing in which situations entanglement can be performed, we compute the atomic inversion in Figure 1(b), using the same parameters. In view of the atomic inversion general behavior, and the results presented in [13], it naturally arises the following question: is there any long-lived entanglement or completely disentanglement that allows to access information about the energy level structure of the system, for long time limit? In Figure 1(b), we show that the use of long time interaction does not guarantee the successful retrieval of completely collapse of the atomic inversion and the revival reappears with different amplitude.…”

“…Also, different aspects of the decoherence and spin bath environment interaction have been considered [12]- [17], e.g. the importance of level statistics for the decoherence of a central spin due to a spin environment [12], geometric phase of a central spin interacting with an antiferromagnetic environment [13], influence of an external magnetic field on the decoherence of a central spin coupled to an antiferromagnetic environment [17] etc. It is thus particularly interesting to investigate how the dynamics of the entanglement of a driven central spin interacting with an antiferromagnetic spin bath is affected.…”

Conventional quantum phase transition driven by a complex parameter in a non-HermitianPT−symmetricIsing model

“…In the realm of traditional quantum mechanics, geometric phase has been introduced to analyze the quantum phase transitions of the XY model [19][20][21], and much effort has been devoted to various Hermitian manybody systems [22][23][24][25][26][27][28][29][30]. A natural question is whether or not the geometric phase of the ground state in the present model can be utilized to characterize the quantum phase boundary.…”