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arXiv:1204.2627

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

Published Apr 12, 2012• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1204.2627

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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 study the geometric phase of the ground state in a one-dimensional transverse XY spin chain in the vicinity of a quantum multi-critical point. We approach the multi-critical point along different paths and estimate the geometric phase by applying a rotation in all spins about the z axis by an angle η. Although the geometric phase itself vanishes at the multi-critical point, the derivative with respect to the anisotropy parameter of the model shows peaks at different points on the ferromagnetic side close to it where the energy gap is a local minimum; we call these points 'quasi-critical'. The value of the derivative at any quasi-critical point scales with the system size in a power-law fashion with the exponent varying continuously with the parameter α that defines a path, up to a critical value α = α c = 2. For α > α c , or on the paramagnetic side, no such peak is observed. Numerically obtained results are in perfect agreement with analytical predictions.
We study the disentanglement evolution of two spin qubits which interact with a general XYXYXY spin-chain environment. The dynamical process of the disentanglement is numerically and analytically investigated in the vicinity of a quantum phase transition (QPT) of the spin chain in both weak and strong coupling cases. We find that the disentanglement of the two spin qubits may be greatly enhanced by the quantum critical behavior of the environmental spin chain. We give a detailed analysis to facilitate the understanding of the QPT-enhanced decaying behavior of the coherence factor. Furthermore, the scaling behavior in the disentanglement dynamics is also revealed and analyzed.
A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that corresponds to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. It is demonstrated that the resulting phase is resilient against the main sources of errors. A physical realization with ultracold atoms in optical lattices is presented.
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