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Modern Physics Letters B

Probing quantum critical points by Fisher information at finite temperature

Qian Wang, Wen-ge Wang

Published Apr 6, 2017• 6 citations
Publisher

Abstract

We study the quantum Fisher information (QFI) of a one-dimensional anisotropic XY chain in a transverse field with three-spin interaction. It is shown that the QFI, computed at a finite temperature, can be used to estimate the critical point (CP) of the quantum phase transition (QPT) at zero temperature. The accuracy of the obtained result depends on both the anisotropy parameter of the chain and the local observable used in the computation of QFI.

DOI
10.1142/s021798491750107x

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We study the quantum Fisher information (QFI) of a one-dimensional anisotropic XY chain in a transverse field with three-spin interaction. It is shown that the QFI, computed at a finite temperature, can be used to estimate the critical point (CP) of the quantum phase transition (QPT) at zero temperature. The accuracy of the obtained result depends on both the anisotropy parameter of the chain and the local observable used in the computation of QFI.
We study the relationship between the quantum Fisher information (QFI) of spin pairs and the topological quantum phase transitions (TQPTs) of the extended XY model driven by the anisotropies of the nearest-neighbor and the next-nearest-neighbor spins, the transverse magnetic field, and the three-spin interaction. We find that the first derivative of QFI can correctly characterize the TQPTs at absolute zero temperature. Meanwhile, the impacts of the thermal fluctuations and the site distance of spin pairs on the critical behaviors of the QFI are studied. It is found that the first derivative of QFI for the nearest neighbor or the long-distance spin pairs can only correctly characterize the critical points of the TQPTs at sufficiently low temperature. Remarkably, when the anisotropy of the nearest-neighbor and the next-nearest-neighbor spins are the driven parameters and the site distance R=5R=5R=5, the QFI itself can characterize the TQPTs at absolute zero temperature.
The quantum Fisher information is of considerable interest not only for quantum metrology but also because it is a useful entanglement measure for finite temperature mixed states. In particular, it estimates the degree to which multipartite entanglement is present. Recent results have related the quantum Fisher information to experimentally measurable probes. While in principle possible, a direct evaluation of the quantum Fisher information at finite temperatures is technically challenging and here we show that a simple estimate can be obtained for materials where the single-mode approximation is valid. We focus on the S=1S=1S=1 antiferromagnetic Heisenberg model with uniaxial anisotropy. Quantum Monte Carlo techniques are used to determine low-temperature correlations from which the quantum Fisher information can be estimated within the single-mode approximation. The quantum Fisher information is compared to the quantum variance for the staggered magnetization operators in the transverse direction and inequalities between the quantum Fisher information, the quantum variance, and the full variance are discussed. Both the quantum and full variance as well as the quantum Fisher information are examined at finite temperatures above the isotropic point and at the quantum critical point for the Haldane-N\'eel transition. A finite size scaling study of the quantum Fisher information is performed at the quantum critical point and used to confirm the Ising nature of the Haldane-N\'eel transition.
In this work, we study temperature sensing with finite-sized strongly correlated systems exhibiting quantum phase transitions. We use the quantum Fisher information (QFI) approach to quantify the sensitivity in the temperature estimation, and apply a finite-size scaling framework to link this sensitivity to critical exponents of the system around critical points. We numerically calculate the QFI around the critical points for two experimentally-realizable systems: the spin-1 Bose-Einstein condensate and the spin-chain Heisenberg XX model in the presence of an external magnetic field. Our results confirm finite-size scaling properties of the QFI. Furthermore, we discuss experimentally-accessible observables that (nearly) saturate the QFI at the critical points for these two systems.
In this work we evaluate quantum Fisher information (QFI) of a two-qubit reduced state in the Ising-XXZ diamond structure at finite temperatures, which is applied to demonstrate quantum criticality and quantum phase transition in this model. Here we adopt the average QFI with respect to the local orthonormal observable bases [Phys. Rev. A. 88, 014,301 (2013)]. The results show that QFI around quantum critical points decreases or increases steeper when the system temperature is relatively lower. Meanwhile the singularity of QFI’ first-derivatives is becoming more and more obvious as the temperature is approaching zero. By the finite-temperature QFI and its scaling relation with temperature, quantum phase transitions can be well detected from the entangled state in ferrimagnetic phase to an unentangled state in ferrimagnetic phase or to an unentangled state in ferromagnetic phase. Moreover it is further found that the two kinds of phase transitions can be distinguished by the different scaling behaviors. It has been proved that QFI has enough capability to characterize quantum phase transition at finite temperature.
We consider a process of parameter estimation in a spin-jjj system surrounded by a quantum-critical spin chain. Quantum Fisher information lies at the heart of the estimation task. We employ Ising spin chain in a transverse field as the environment which exhibits a quantum phase transition. Fisher information decays with time almost monotonously when the environment reaches the critical point. By choosing a fixed time or taking the time average, one can see the quantum Fisher information presents a sudden drop at the critical point. Different initial states of the environment are considered. The phenomenon that the quantum Fisher information, namely, the precision of estimation, changes dramatically can be used to detect the quantum criticality of the environment. We also introduce a general method to obtain the maximal Fisher information for a given state.