arXiv subjects

Awwab A. Azam

Publications and source records attributed to Awwab A. Azam.

3 recordsLinked to original sources

arXiv2026

Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulators

We develop a representability-aware and interpolable neural network (NN) framework for predicting two-particle reduced density matrices (2-RDMs). The NN incorporates a subset of representability conditions through its architecture and loss function, and can operate on different momentum meshes, enabling evaluating the representability conditions across multiple meshes, which we call interpolated representability condition. The framework can be used either to predict 2-RDMs on large momentum meshes by interpolating exact results from small meshes, or as a variational 2-RDM ansatz optimized by energy minimization on arbitrary meshes. We apply this approach to the fractional Chern insulator in the one-band projected model of twisted bilayer MoTe$_2$ at twist angle $3.89^\circ$ and hole filling $2/3$. Trained on exact-diagonalization (ED) 2-RDMs from meshes with $12$ or $18$ momentum points using six different NN architectures, the best NN is the residual multilayer perceptron, which predicts the $6\times6$ 2-RDM with $97.07\%-98.18\%$ accuracy relative to the ED 2-RDM but predicts an energy $77.353$ meV above ED ground-state energy. We then variationally optimize the NN on several meshes including $6\times6$, predicting a $6\times 6$ energy of just $0.104$ meV below ED while maintaining $98.94\%-98.96\%$ accuracy. Compared with the conventional boundary-point semidefinite programming, which gives an energy $5.560$ meV below ED with $96.40\%-98.94\%$ accuracy, the NN achieves a more accurate energy and similar accuracy while using only less than 1/20 as many parameters. Eventually, we add a symmetric mesh of $48$ momentum points to the variational optimization of the NN, and provide a prediction of the many-body ground-state energy and the many-body quantum metric on that mesh.

cond-mat.str-el↗

arXiv2026

Wilson-Loop-Ideal Bands and General Idealization

Quantum geometry is universally bounded from below by Wilson-loop windings. In this work, we define an isolated set of bands to be Wilson-loop-ideal, if their quantum metric saturates the Wilson-loop lower bound. The definition naturally incorporates the known Chern-ideal and Euler-ideal bands, and allows us to define other types of ideal bands, such as Kane-Mele $Z_2$-ideal and inversion-fragile-ideal bands. In particular, we find that in the case of zero total Chern number, an isolated WL-ideal set of two bands with non-singular nonabelian Berry curvature and nontrivial normal Wilson-loop winding always admits a Chern-ideal gauge, without the need of a global good quantum number (such as spin). This enables the direct construction of new topologically ordered states, such as fractional topological insulator wavefunctions. We further propose a general framework of constructing monotonic flows that achieve Wilson-loop-ideal states starting from non-ideal bands through band mixing, where Wilson-loop-ideal states are not energy eigenstates but have smooth projectors similar to isolated bands. We apply the constructed flows to the realistic model of $3.89^\circ$ twisted bilayer MoTe$_2$, a moiré Rashba model and another moiré time-reversal-breaking models, and numerically find Chern-ideal, $Z_2$-ideal and inversion-fragile states, respectively, with relative error in the integrated quantum metric below $5\times 10^{-3}$. Our exact-diagonalization calculations on the numerically ideal states demonstrate the potential of our general definition of Wilson-loop-ideal bands and general procedure of constructing Wilson-loop-ideal states for future study of novel correlated physics.

cond-mat.mes-hall↗

arXiv2026

Reduced Density Matrices Through Machine Learning

$n$-particle reduced density matrices ($n$-RDMs) play a central role in understanding correlated phases of matter, but their calculation is often computationally inefficient for strongly-correlated states at large system sizes. In this work, we use neural network (NN) architectures to accelerate and even predict $n$-RDMs for large systems. Our underlying intuition is that, for gapped states, $n$-RDMs are often smooth functions over the Brillouin zone (BZ) and are therefore interpolable, allowing NNs trained on small-size systems to predict large-size ones. Building on this, we devise two NNs: (i) a self-attention NN that maps random RDMs to physical ones, and (ii) a Sinusoidal Representation Network (SIREN) that directly maps momentum-space coordinates to RDM values. We test the NNs on RDMs in three 2D models: the pair-pair correlation functions of the Richardson model of superconductivity, the translationally-invariant Hartree-Fock (HF) 1-RDM in a four-band repulsive model, and the translation-breaking HF 1-RDM in the half-filled Hubbard model. We find that a SIREN trained on a $6\times 6$ momentum mesh and a SIREN trained on $4$ tilted meshes (each of which has $12$ momentum points) can predict the $18\times 18$ pair-pair correlation function with a relative accuracy of $94.29\%$ and $93.77\%$, respectively. NNs trained on $6\times 6$ and $8\times 8$ meshes provide high-quality initial guesses for $50\times 50$ translation-invariant HF and $30\times 30$ fully translation-breaking-allowed HF, reducing the required number of iterations by up to $91.63\%$ and $92.78\%$, respectively, compared to random initializations. Our results illustrate the potential of NN-based methods for interpolable $n$-RDMs, which might open a new avenue for future research on strongly correlated phases.

cond-mat.str-el↗