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
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∝h2/3 and a Grüneisen ratio scaling
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) of the singular Grüneisen ratio for both BKT and Ising cases can be approximately described by the same expression
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.
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.
This study investigates quantum Fisher information (QFI) with respect to a class of nonlocal operators $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{O}$ in one-dimensional quantum chains. Based upon the triangular matrix-product-operator theory, we establish a universal scaling behavior of QFI with respect to $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{O}$ for general infinite matrix-product states (iMPSs): $\mathcal{F}\ensuremath{\sim}{\ensuremath{\varrho}}_{2}{N}^{2}+{\ensuremath{\varrho}}_{1}N+{\ensuremath{\varrho}}_{0}$, where the coefficients ${\ensuremath{\varrho}}_{i}$ can be efficiently identified by iMPS algorithms. Applied to a spin-1 Bilinear-Biquadratic model and an XXZ model, the scaling coefficients ${{\ensuremath{\varrho}}_{i}}$ distinguish various phases through distinct scaling behaviors: For instance, the topologically ordered Haldane phase exhibits characteristic quadratic scaling (${\ensuremath{\varrho}}_{2}\ensuremath{\ne}0$), while the trimer and dimer phases are featured with linear scaling (${\ensuremath{\varrho}}_{1}\ensuremath{\ne}0$). Notably, since the QFI scaling behavior undergoes fundamental changes between distinct phases, these coefficients provide signals at first-order, second-order, and Berezinskii-Kosterlitz-Thouless type quantum phase transitions in these models. Furthermore, finite bond-dimension (
D) scaling analysis reveals a dichotomy. For gapped phases, the coefficients converge rapidly as
D increases. Conversely, for critical systems, the coefficients exhibit
D-scaling effects that depend on the specific model. By bypassing finite-size fittings with limited
N, our approach accesses the thermodynamic-limit physics for QFI with respect to nonlocal operators, offering new avenues for characterizing exotic quantum phases in one-dimensional quantum systems.