Disorder-driven loss of crystalline coherence in two-dimensional electron solids: Quantum Hartree-Fock and classical molecular dynamics

Sankar Das Sarma; Haining Pan

Home/Archive/arXiv

arXiv · 2610.06371

Disorder-driven loss of crystalline coherence in two-dimensional electron solids: Quantum Hartree-Fock and classical molecular dynamics

Sankar Das Sarma·Haining Pan

View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the effects of quenched disorder on two-dimensional electron solids using Hartree-Fock theory and classical molecular dynamics. Increasing disorder weakens crystalline correlations, broadens the structure factor, and reduces the measured coherence length toward the pristine lattice spacing. This evolution is consistent with the Imry-Ma and Larkin picture: random pinning disrupts translational order on sufficiently long scales, and stronger disorder reduces the distance over which crystalline organization survives. Classical simulations further show that stronger pinning raises the temperature for particle rearrangement even after crystalline order has disappeared. Disorder thus suppresses structural coherence while stabilizing an amorphous solid against thermal rearrangement.

Explore related subjects

cond-mat.dis-nn cond-mat.mes-hall cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Sankar Das Sarma, Haining Pan. 2026-10-05. Disorder-driven loss of crystalline coherence in two-dimensional electron solids: Quantum Hartree-Fock and classical molecular dynamics. https://arxiv.org/abs/2610.06371

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reentrance and temperature chaos in the $p$-spin Ising spin glass

Reentrant transitions and temperature chaos are two unusual properties of spin glasses. We recently established a general logical relation between these two phenomena [Phys. Rev. E \textbf{112}, 044140 (2025)]. In the present paper, we provide an explicit example of this logical relation in the fully connected Ising $p$-spin glass with a ferromagnetic bias. By expanding the free energy around the triple point, we show analytically that the ferromagnetic--spin glass boundary is reentrant in the vicinity of the triple point throughout the examined range of finite $p>2$. It then follows from the above logical relation that there exists at least one pair of distinct temperatures in the spin glass phase for which the overlap of spin configurations vanishes. This is a necessary condition for temperature chaos, but it would be quite unusual for the overlap to vanish only for selected temperature pairs but not for others within a single spin glass phase. These results therefore strongly suggest the existence of temperature chaos in the sense that the overlaps of spin configurations vanish for all temperature pairs throughout the spin glass phase. Independent evidence for this behavior is provided by a two-temperature replica calculation.

cond-mat.dis-nn↗

arXiv2026

Anderson localization in periodic elastic systems with random perturbations

This paper investigates Anderson localization in subwavelength elastic periodic systems with random perturbations. For the unperturbed system, we use layer potential techniques to reformulate the eigenvalue problem as boundary integral equations, and derive asymptotic formulas for the subwavelength eigenvalues. For perturbed systems, we apply the Floquet transform to obtain a periodic formulation and derive equations determining the resonant frequencies under general perturbations. Numerical experiments for perturbed periodic monomers and dimers agree with the theoretical predictions. We further demonstrate Anderson localization by increasing the strength and number of random perturbations. These results provide a mathematical foundation for understanding subwavelength localization in elastic metamaterials.

cond-mat.dis-nn↗

arXiv2026

Asymptotic Analysis of Empirical Risk Minimization on Entry-wise i.i.d. Heavy-Tailed Data

Many real-world datasets exhibit unusually large values far more frequently than predicted by Gaussian models. Heavy-tailed distributions capture this behavior, yet evaluating learning performance under them remains challenging because rare, large feature entries retain non-vanishing effects even in high dimensions. Even in the canonical setting of empirical risk minimization for linear regression with entry-wise i.i.d. symmetric $α$-stable data, a precise asymptotic characterization of prediction has been lacking. In this work, we introduce a functional order parameter that describes the random effective problem associated with each coefficient. Using the replica method, we fully characterize the generalization error in the proportional high-dimensional limit where the sample size and feature dimension diverge at a fixed ratio. Additionally, this analysis establishes a heavy-tail universality law, scaling laws relating typical errors to prediction reliability, and the Bayes-optimal prediction error. In addition to characterizing the effects of extreme entries on the learning process, our method applies broadly to other systems with persistent local heterogeneity.

cond-mat.dis-nn↗