arXiv subjects

Tzen Ong

Publications and source records attributed to Tzen Ong.

4 recordsLinked to original sources

arXiv2026

Scaling universal Fermi network toward ground states: A diffusion-Monte-Carlo assessment

In this work, we show that Fermi Sets---a provably universal neural network architecture for fermionic wavefunctions---can be systematically scaled up to find interacting ground states through energy minimization in a variational Monte Carlo framework. By further performing fixed-phase diffusion Monte Carlo (DMC) on the optimized neural network wavefunction, we demonstrate that as the network size increases, the variational energy systematically decreases while the energy improvement from DMC collapses monotonically to zero, indicating convergence to the ground state. We illustrate the scaling of Fermi Sets accompanied by the DMC assessment for interacting electrons in jellium and in a quantum dot under high magnetic fields.

cond-mat.str-el↗

arXiv2025

Quantum Algorithm for Low-Energy Effective Hamiltonians and Subspace Eigenvalue Problem

Subspace eigenvalue problems arise ubiquitously in quantum chemistry and condensed-matter physics, where the relevant object is often a low-energy manifold rather than a single ground-state wavefunction. In this work, we propose a fault-tolerant quantum algorithm for this subspace-level task based on the Feshbach effective-Hamiltonian formalism. Given block-encoding access to the full Hamiltonian and a chosen $d$-dimensional reference subspace, the algorithm estimates eigenvalues of states with nonzero overlap with the reference subspace through a local secant fixed-point search. It then implements the associated wave operator and prepares an orthonormal basis whose span approximates the target invariant subspace. The construction combines projected block encodings with quantum singular value transformation (QSVT), which approximates the complementary-space resolvent and thereby provides both the self-energy used for eigenvalue estimation and the wave operator used for eigenstate reconstruction. For target accuracy $\varepsilon$, a single evaluation of the effective Hamiltonian has query complexity $\widetilde{O}(d^3/(g^2\varepsilon))$, up to block-encoding normalization factors, where $g$ is the distance between the target eigenvalue and the nearest pole of the effective Hamiltonian. Under the stated local regularity conditions, the secant search requires only $O(\log\log(1/\varepsilon))$ effective-Hamiltonian evaluations to reach the working precision. Classical numerical emulations for an open $4\times2$ Fermi--Hubbard cluster, all-electron LiH bond stretching, and $[\mathrm{Ru(bpy)}_{3}]^{2+}$ demonstrate the resolution and reconstruction of low-energy states and manifolds across spin-sector crossings, near-degeneracies, and dense excited-state spectra.

quant-ph↗

arXiv2025

Attention is all you need to solve chiral superconductivity

Recent advances on neural quantum states have shown that correlations between quantum particles can be efficiently captured by attention -- a foundation of modern neural architectures that enables neural networks to learn the relation between objects. In this work, we show that a general-purpose self-attention Fermi neural network is able to find chiral $p_x \pm ip_y$ superconductivity in an attractive Fermi gas by energy minimization, without prior knowledge or bias towards pairing. The superconducting state is identified from the optimized wavefunction by measuring various physical observables. We develop a symmetry projection method that reveals the ground state angular momentum and time-reversal symmetry breaking, and a computation of the full two-body reduced density matrix spectrum that reveals the off-diagonal long-range order due to the dominant chiral $p$-wave pairing channel. Our work paves the way for AI-driven discovery of unconventional and topological superconductivity in strongly correlated quantum materials.

cond-mat.supr-con↗

arXiv2023

Feature Spectrum Topology

Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological phases. However, symmetry-based topological characterizations rely heavily on symmetry analysis and are incapable of detecting the topological phases in systems where the symmetry is broken, thus missing a large portion of interesting topological physics. Here, we propose a new approach to understanding the topological nature of quantum materials, which we call feature spectrum topology. In this framework, the ground-state is separated into different partitions by the eigenspectrum of a feature, a particular chosen internal quantum degree of freedom, such as spin or pseudo-spin, and the topological properties are determined by analysis of these ground-state partitions. We show that bulk-boundary correspondence guarantees gapless spectral flows in either one of the energy or feature spectrum. Most importantly, such 'feature-energy duality' of gapless spectral flows serves as a fundamental manifestation of a topological phase, thereby paving a new way towards topological characterizations beyond symmetry considerations. Our development reveals the topological nature of a quantum ground state hidden outside symmetry-based characterizations, hence, providing a platform for a more refined search of unconventional topological materials.

cond-mat.mtrl-sci↗