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Communications in Theoretical Physics

Probing Berezinskii–Kosterlitz–Thouless Phase Transition of Spin-Half XXZ Chain by Quantum Fisher Information*

Qiang Zheng, Yao Yao, Xun‐Wei Xu

Published Mar 1, 2015• 14 citations
Publisher

Abstract

Abstract The Berezinskii–Kosterlitz–Thouless phase transition of spin-1/2 XXZ chain is reinvestigated by the quantum Fisher information. Quantum Fisher informations of the whole N sites and the partial N/3 sites display remarkably similar behaviors near the critical point. The critical exponent of quantum Fisher information is obtained as β = 0.47, which is consistent with the results obtained by the concurrence and quantum discord.

DOI
10.1088/0253-6102/63/3/279

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arXiv:cond-mat/9809138•Journal of Physics A Mathematical and General•Jan 1, 1999•32 citations
Abstract The Berezinskii–Kosterlitz–Thouless phase transition of spin-1/2 XXZ chain is reinvestigated by the quantum Fisher information. Quantum Fisher informations of the whole N sites and the partial N/3 sites display remarkably similar behaviors near the critical point. The critical exponent of quantum Fisher information is obtained as β = 0.47, which is consistent with the results obtained by the concurrence and quantum discord.
Combining the ideas of quantum Fisher information and quantum renormalization group method, the Berezinskii-Kosterlitz-Thouless quantum phase transition of spin- 1/2 XXZ chain is investigated. Quantum Fisher informations of the whole N sites and the partial N/3 sites are studied. They display very similar behaviors, even though their mathematical formulas are very different from each other. The universally critical exponent of quantum Fisher information is obtained as beta=0.47, which is consistent with the results obtained by the renormalized concurrence or discord. We also discuss the relationship between quantum Fisher information and entanglement
Abstract Quantum fluctuations can give rise to a singular quantum critical point (QCP) in the ground state, whose influence extends to finite temperatures, forming a quantum critical regime (QCR). Recently, it has been shown that in the quantum Ising model, the symmetry-breaking, longitudinal field can induce a quantum supercritical regime (QSR) emanating from the QCP, which hosts a universally enhanced quantum supercritical magnetocaloric effect (Lv et al 2025 Nat. Commun. 16 10646). In this paper, we show that the QSR also emerges in the spin-1/2 XXZ model, in both the forms of Ising and Berezinskii–Kosterlitz–Thouless (BKT) supercriticality. Using ground-state and finite-temperature tensor-network methods, we investigate quantum supercritical phenomena near a BKT QCP. We reveal a quantum supercritical crossover scaling T ∝ h 2 / 3 and a Grüneisen ratio scaling Γ h ∝ T − 3 / 2 for the BKT QCP, which differ from the corresponding Ising supercritical scalings. Nevertheless, we find that the scaling function ϕ Γ ( x ) of the singular Grüneisen ratio for both BKT and Ising cases can be approximately described by the same expression ϕ Γ ( x ) ≈ x / ( 1 + x 2 ) . Our work extends the study of quantum supercritical phenomena from the Ising to the XXZ Heisenberg model, thereby revealing the presence of BKT quantum supercriticality and broadening the scope of quantum supercritical physics.
Quantum fluctuations can give rise to a singular quantum critical point (QCP) in the ground state, whose influence extends to finite temperatures, forming a quantum critical regime (QCR). Recently, it has been shown that in the quantum Ising model, the symmetry-breaking, longitudinal field can induce a quantum supercritical regime (QSR) emanating from the QCP, which hosts a universally enhanced quantum supercritical magnetocaloric effect (MCE). In this paper, we show that the QSR also emerges in the spin-1/2 XXZ model, in both the form of Ising and Berezinskii-Kosterlitz-Thouless (BKT) supercriticality. Using ground-state and finite-temperature tensor-network methods, we investigate quantum supercritical phenomena near a BKT QCP. We reveal a quantum supercritical crossover scaling T∝h2/3T \propto h^{2/3}T∝h2/3 and a Grüneisen ratio scaling Γh∝T−3/2Γ_h \propto T^{-3/2}Γh​∝T−3/2 for the BKT QCP, which differ from the corresponding Ising supercritical scalings. Nevertheless, we find that the scaling function ϕΓ(x)ϕ_Γ(x)ϕΓ​(x) of the singular Grüneisen ratio for both BKT and Ising cases can be approximately described by the same expression ϕΓ(x)≈x/(1+x2)ϕ_Γ(x) \approx x/(1+x^2)ϕΓ​(x)≈x/(1+x2). Our work extends the study of quantum supercritical phenomena from the Ising to the XXZ Heisenberg model, thereby revealing the presence of BKT quantum supercriticality and broadening the scope of quantum supercritical physics.
We study the plateau of the magnetization curve at M = M s /3 ( M s is the saturation magnetization) of the S = ½ trimerized XXZ spin chain. By examining the level crossing of low-lying excitations obtained from the numerical diagonalization, we precisely determine the phase boundary between the plateau state and the no-plateau state on the - t plane, where denotes the XXZ anisotropy and t the magnitude of the trimerization. This quantum phase transition is of the Berezinskii-Kosterlitz-Thouless type.