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arXiv:2603.24311

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

Kumar Ghosh

cond-mat.str-elcond-mat.dis-nncond-mat.mtrl-sciquant-phSubmitted Mar 25, 2026• Announced Mar 26, 2026• 0 citations
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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 $α\in\{1.0,\,0.7,\,0.5,\,0.3\}$, where the analytically exact classical threshold is ${g_c^{\mathrm{class}}}(α)=2α/3$. The suppression ratio $r(α)$ exhibits a sharp two-regime structure: the three quasi-1D geometries ($α\leq0.7$) are mutually consistent with a universal plateau $\bar{r}=0.450$ ($χ^2/\mathrm{dof}=1.10$, $p=0.33$), 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 $α^*\approx0.7$. Inner Binder cumulant pairs, which converge fastest to the thermodynamic limit, resolve $r(1.0)\approx0.412$ and a step $Δr=0.038\pm0.015$ from the quasi-1D plateau. A four-point linear fit $r(α)=0.494-0.063\,α$ summarises both regimes; its $α\to0$ 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 $α\in[α^*,1]$. Two sequential blind predictions, confirmed at $0.2σ$ and $0.7σ$ 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.

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13 pages 6 figures

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We study the frustrated Ising model on the two-dimensional L×LL \times LL×L square lattice with ferromagnetic (FM) nearest-neighbor and antiferromagnetic diagonal-neighbor interactions using the D-wave quantum annealing machine (D-QAM) with 5000+ qubits composed on structure of the Pegasus graph. As the former Monte Carlo and mean field results, we find the FM to stripe order phase transition, through observations of the magnetization MMM, energy, magnetic susceptibility and structure factor. We also analyze probability which occurs any MMM at a given interaction for many quantum annealing shots to estimate the shape of objective function fff. The only one value of MMM with specific phase is observed in the regions far from phase transition for many quantum annealing shots, while several values of MMM with different possibilities are appeared in the regimes of phase transition. We guess that fff in the regimes of phase transition retains the multi-modal structure with several local minimums, due to the strong degeneracies caused by frustrations. Finally, we discuss fail of the quantum annealing simulations, through analysis of the number of the chains, defined as the same variable with NNN-qubits, as a function of LLL.
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Abstract Motivated by recent progress on the experimental realization of proximate deconfined quantum critical point in a frustrated quantum magnet, we study the low-energy spin dynamics of a related checkerboard J-Q model by using quantum Monte Carlo simulations. The ground state of this model undergoes a weakly first-order quantum phase transition with an emergent O(4) symmetry between an antiferromagnetic state and a plaquette valence bond solid. The calculated spin lattice relaxation rate of nuclear magnetic resonance, 1 / T 1 , exhibits distinct low-temperature behaviors depending on the ground states. With decreasing the temperature, 1 / T 1 rises up on the antiferromagnetic side, characterizing a crossover to the renormalized classical regime, whereas 1 / T 1 drops exponentially on the side of valence bond solid, reflecting the gap opening in the plaquette ordered phase. The extracted spin gap scales with the distance to the transition point as a power-law with an exponent φ ≈ 0.3, consistent with the scaling ansatz ϕ = ν z with ν ≈ 0.3 and z = 1. Near the quantum phase transition, the temperature dependent 1 / T 1 shows a broad crossover regime where a universal scaling 1 / T 1 ∼ T η with η ≈ 0.6 is found. Our results suggest a quantum scaling regime associated with the emergent enhanced symmetry near this first-order quantum phase transition.
Abstract Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv: 2006.08921v2 ; 2020 2006.15087v1 ). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager’s equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions s i , j x s k , l x + s i , j y s k , l y can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.
The Ising model with nearest-neighbor interactions on a two-dimensional (2D) square lattice is one of the simplest models for studying ferro-magnetic to para-magnetic transitions. Extensive results are available in the literature for this model, which has become a paradigm for the study of magnetic phase transitions in materials, both theoretically and numerically. After a brief review of the main results obtained with a classical computer, we show how to implement on the D- Wave quantum annealer a more complex Ising model with the addition of competing antiferromagnetic interactions between the diagonal next-to-nearest neighbors with two coupling constants J1 and J2. The dynamics of this system, owing to frustration, are richer than those of the simple Ising model and exhibit a third striped (or antiferromagnetic) phase in addition to the ferro- and para-magnetic phases. In this work, we observed all three phases on the D-Wave hardware, studied the behavior of the solution with different annealing parameters, such as the chain strength and annealing time, and showed how to identify the phase transition by varying the ratio between the ferromagnetic and antiferromagnetic couplings. The same system is studied on a classical computer, with the possibility of taking into account the temperature (fixed on D-Wave) as a free parameter and to explore the full phase diagram: some comparative conclusions with D-Wave are drawn.
We outline the recent results on the ground state for a class of one- and two-dimensional frustrated quantum spin models with competing ferro(F)- and antiferromagnetic (AF) interactions. Frustrated spin systems are known to have many interesting properties due to large quantum fluctuations. As a result of these fluctuations usual mean-field approach gives quite crude (if not false) description of these systems. Therefore, exactly solvable models are very instructive at investigations of such systems. The exact ground state wave function of proposed models has a structure of the valence-bond state (VBS) type. One of the 1D model describes the transition line between the F and AF phase. The exact singlet ground state on this line has a double-spiral ordering. Using different approximation methods we study the magnetization curve in the AF phase. The second considered set of the 1D and 2D models has an exact non-degenerate ground state with exponentially decaying spin correlations. We also proposed the 1D and 2D electronic models with exact ground state represented in terms of singlet bond functions which are the generalization of the RVB functions including ionic states.