Paulo T Araujo

Mahmud Ashraf Shamim, Moshiur Rahman, Mohamed Hibat-Allah et al.

Despite extensive study, the phase structure of the wavefunctions in frustrated Heisenberg antiferromagnets (HAF) is not yet systematically characterized. In this work, we represent the Hilbert space of an HAF as a weighted graph, which we term the Hilbert graph (HG), whose vertices are spin configurations and whose edges are generated by off-diagonal spin-flip terms of the Heisenberg Hamiltonian, with weights set by products of wavefunction amplitudes. Holding the amplitudes fixed and restricting phases to $\mathbb{Z}_2$ values, the phase-dependent variational energy can be recast as a classical Ising antiferromagnet on the HG, so that phase reconstruction of the ground state reduces to a weighted Max-Cut instance. This shows that phase reconstruction HAF is worst-case NP-hard and provides a direct link between wavefunction sign structure and combinatorial optimization.

Mahmud Ashraf Shamim, Eric A F Reinhardt, Talal Ahmed Chowdhury et al.

Neural Quantum States (NQS) are a class of variational wave functions parametrized by neural networks (NNs) to study quantum many-body systems. In this work, we propose \texttt{SineKAN}, a NQS \textit{ansatz} based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that \texttt{SineKAN} wavefunction with learnable sinusoidal activation functions can capture the ground state energies, fidelities and various correlation functions of the one dimensional Transverse-Field Ising model, Anisotropic Heisenberg model, and Antiferromagnetic $J_{1}-J_{2}$ model with different chain lengths. In our study of the $J_1-J_2$ model with $L=100$ sites, we find that the \texttt{SineKAN} model outperforms several previously explored neural quantum state \textit{ansätze}, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Multi-layer Perceptrons (MLP) \textit{a.k.a.} Feed Forward Neural Networks, when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm. We find that \texttt{SineKAN} models can be trained to high precisions and accuracies with minimal computational costs.