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Results in Physics

Quantum Fisher information at finite temperatures and the critical properties in Ising-Heisenberg diamond chain

Yao Ren, Z.J. Zhao, Xin Yang, G.H. Wang, Y.D. Leng, Guojun Gao, Xiaolin Liu

Published Apr 26, 2022• 7 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2022.105542

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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.
In this work we explore the quantum correlation quantified by trace distance discord as a measure to analyze the quantum critical behaviors in the Ising-XXZ diamond structure at finite temperatures. It is found that the first-order derivative of the trace distance discord exhibits a maximum around the critical point at finite temperatures. By analyzing the finite-temperature scaling behavior, we show that such a quantum correlation can detect exactly the quantum phase transitions from the entan-gled state in ferrimagnetic phase to an unentangled state in ferrimagnetic phase or to an unentangled state in ferromagnetic phase. The results also indicate that the above two kinds of transitions can be distinguished by the different finite-temperature scaling behaviors. Moreover, we find that the trace distance discord, in contrast to other typical quantum correlations (e.g., concurrence, quantum discord and Hellinger distance), may be more reliable to exactly spotlight the critical points of this model at finite temperatures under certain situations.
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.
We investigate a spin-1/2 Ising-XYZ diamond chain with Ising-like interaction between nodal and interstitial sites and Heisenberg-like interaction between interstitial sites, subjected to an external magnetic field applied along the zzz-direction. This model presents exact analytical solution and can be solved using the transfer matrix technique. Here, we study the entropy and quantum entanglement in the quasi-phase region, which can be quantified through concurrence. For the chosen parameters, the system presents three regions with different spin orientation at the finite temperature, which we call quasi-phase ferrimagnetic (qFIqFIqFI) and two types of quasi-phase ferromagnetic Ising and modulated ferromagnetic Heisenberg (qMF0qMF_0qMF0​) and (qMF2qMF_2qMF2​). We show that the quantum entanglement remains almost constant in qMF0qMF_0qMF0​ until considerable temperature values. In addition, we verify that the quantum entanglement is null in the pseudo-transition between the qFIqFIqFI e qMF0qMF_0qMF0​, but in the interface between qMF0qMF_0qMF0​ and qMF2qMF_2qMF2​ is entangled. We observe an abrupt increase in the entropy curves in the pseudo-critical temperature. We also observe when the temperature is lower than the pseudo-critical temperature the entropy remains almost constant at zero and the quantum entanglement in this same region remains almost constant.
We compute the quantum Fisher information (QFI) associated with two different local operators in the ground state of the Kitaev honeycomb model, and find divergent behavior in the second derivatives of these quantities with respect to the driving parameter at the quantum phase transition between the gapped and gapless phases for both fully antiferromagnetic and fully ferromagnetic exchange couplings, thus demonstrating that the second derivative a locally defined, experimentally accessible, QFI can detect topological quantum phase transitions. The QFI associated with a local magnetization operator behaves differently from that associated with a local bond operator depending on whether the critical point is approached from the gapped or gapless side. We show how the behavior of the second derivative of the QFI at the critical point can be understood in terms of the diverging length scales associated to the two and four point correlators of the Majorana degrees of freedom. We present critical exponents associated with the divergences of these length scales.
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.