Berezinskii-Kosterlitz-Thouless Quantum Supercriticality in XXZ Heisenberg Spin Chain

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 $T \propto h^{2/3}$ and a Gr\"uneisen ratio scaling $\Gamma_h \propto T^{-3/2}$ for the BKT QCP, which differ from the corresponding Ising supercritical scalings. Nevertheless, we find that the scaling function $\phi_{\Gamma}(x)$ of the singular Gr\"uneisen ratio for both BKT and Ising cases can be approximately described by the same expression $\phi_{\Gamma}(x) \approx x/(1+x^2)$. 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.