Liuyun Dao | Searcharxiv

arXiv2026

Deterministic Loop Stochastic Series Expansion Algorithm for Quantum Spin Models in Magnetic Fields

The stochastic series expansion (SSE) algorithm is one of the most powerful quantum Monte Carlo methods and has been extensively applied to the study of quantum many body systems. Its efficiency is particularly enhanced with a deterministic loop update scheme in the study of the S=1/2 quantum spin systems that preserve SU(2) spin rotational symmetry. Once the symmetry is broken, such as by an external field, a directed loop method is typically required, resulting in a significant reduction in efficiency. Inspired by the SSE approach developed for the quantum Ising model, we introduce a deterministic loop SSE method that is particularly suited for antiferromagnetic systems under a staggered magnetic field. This method enables separate investigations of longitudinal and transverse modes in magnetically ordered phases arising from spontaneous symmetry breaking. We benchmark the performance of our algorithm against the standard directed loop approach applied to the antiferromagnetic Heisenberg chain and demonstrate that our method substantially reduces CPU time per Monte Carlo step, thereby can outperform the directed loop algorithm in efficiency.

cond-mat.str-el↗

arXiv2025

Multiscale Excitations in the Diluted Two-dimensional S = 1/2 Heisenberg Antiferromagnet

We study the excitation spectrum of the $S=1/2$ Heisenberg model on the randomly diluted square lattice by analytic continuation of QMC data. At dilution fractions $p=1/16$ and $p=1/8$, the dynamic structure factor $S({\bf q},ω)$ exhibits a damped magnon peak with anomalous dispersion near ${\bf q}=(0,0)$ and $(π,π)$, a non-dispersive low-energy localization peak, and a second peak between these two features. A magnon with anomalous dispersion, close to our result, was predicted in spin wave and $T$-matrix theory [A. Chernyshev et al., PRB {\bf 65}, 104407 (2002)], above the localization energy. However, no intermediate mode was predicted. Analyzing spectral functions in real space for individual vacancy realizations by energy tomography, we find that these excitations are concentrated on a small subset of the spins adjacent to vacancies. We argue that the low-energy excitations are those of a sparse random network of effective moments at a fraction of the vacancies. There is a shift in magnon spectral weight distribution, from the spins away from vacancies at high energy to those adjacent to vacancies at lower energy. We also analyze the Anderson quantum rotor excitation at $ω\propto N^{-1}$ (with $N=L^2$ the system size), which in the clean system is visible in $S({\bf q},ω)$ only at ${\bf q}=(π,π)$ but spreads through the Brillouin zone when $p>0$. Weight close to ${\bf q}=(0,0)$ and $(π,π)$ is explained by local sublattice imbalance within a dimer-monomer model but there is also structure arising from correlated singlet fluctuations, which we demonstrate by enhancing said fluctuations with four-spin couplings. All spectral features found here should be observable by elastic neutron scattering experiments on layered quantum antiferromagnets doped with nonmagnetic impurities.

cond-mat.str-el↗