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

TL;DR

This study uses a quantum annealer to explore quantum phase transitions in frustrated Ising models, revealing a universal suppression of ferromagnetic stability across different geometries and a clear crossover from quasi-1D to 2D behavior.

Contribution

First experimental measurement of quantum phase boundaries in frustrated Ising models across the quasi-1D to 2D crossover using quantum annealing.

Findings

Quantum fluctuations suppress approximately 55% of classical ferromagnetic stability.

Universal plateau in suppression ratio for quasi-1D geometries.

Validated crossover law with sequential blind predictions.

Abstract

Quantum magnets in the $M\mathrm{Nb_2O_6}$ 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 $L\leq27$ (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 ($\alpha\leq0.7$) 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 $\alpha^*\approx0.7$. Inner Binder cumulant pairs, which converge fastest to the thermodynamic limit, resolve $r(1.0)\approx0.412$ and a step $\Delta r=0.038\pm0.015$ from the quasi-1D plateau. A four-point linear fit $r(\alpha)=0.494-0.063\,\alpha$ summarises both regimes; its $\alpha\to0$ 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 $\alpha\in[\alpha^*,1]$. 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 ($f_{\rm uniq}=1.000$), and null valence-bond solid order.