Universal Quantum Suppression in Frustrated Ising Magnets across the Quasi-1D to 2D Crossover via Quantum Annealing

Abstract

Quantum magnets in the $M\mathrm{N}{\mathrm{b}}_2{\mathrm{O}}_6$ and BaCo${}_2$V${}_2$O${}_8$ families realise frustrated transverse-field Ising models whose competing ferromagnetic and antiferromagnetic couplings generate a sign problem provably intractable for quantum Monte Carlo at any system size, leaving their quantum phase boundaries numerically Inaccessible. Using a D-Wave Advantage2 quantum annealer at $L\le 27$ (729 spins), we obtain the large-$L$ critical points for this model family, measuring quantum-driven transitions at $g_c^{\mathrm{QPU}}\in \{0.286,0.210,0.156,0.093\}$ for $\alpha \in \{1.0,0.7,0.5,0.3\}$, where the analytically exact classical threshold is $g_c^{\mathrm{class}}(\alpha )=2\alpha /3$. The suppression ratio $r(\alpha )$ exhibits a sharp two-regime structure: the three quasi-1D geometries ($\alpha \le 0.7$) are mutually consistent with a universal plateau $\bar{r}=0.450$ (${\chi }^2/\mathrm{dof}=1.10$, $p=0.33$), demonstrating that quantum fluctuations destroy approximately $55\%$ of the classical FM stability window independently of coupling anisotropy, while $r$ steps down to the 2D limit above the empirical crossover scale ${\alpha }^{\ast }\approx 0.7$. Inner Binder cumulant pairs, which converge fastest to the thermodynamic limit, resolve $r(1.0)\approx 0.412$ and a step $\Delta r=0.038\pm 0.015$ from the quasi-1D plateau. A four-point linear fit $r(\alpha )=0.494-0.063\alpha$ summarises both regimes; its $\alpha \to 0$ intercept recovers the exact 1D result of Pfeuty within 1.7 standard deviations, and its slope is a lower bound on the true crossover amplitude concentrated in $\alpha \in [{\alpha }^{\ast },1]$. Two sequential blind predictions, confirmed at $0.2\sigma$ and $0.7\sigma$ before each measurement, validate the crossover law. All four geometries show a direct ferromagnet-to-paramagnet transition, complete quantum ergodicity ($f_{\mathrm{uniq}}=1.000$), and null valence-bond solid order.

13 pages 6 figures