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Multiscale excitations in the diluted two-dimensional S=1/2 Heisenberg antiferromagnet

Liuyun Dao1, Hui Shao1,2,*, and Anders W. Sandvik3,4,†

  • 1Center for Advanced Quantum Studies, School of Physics and Astronomy, Beijing Normal University, Beijing 100875, People's Republic of China
  • 2Key Laboratory of Multiscale Spin Physics, Ministry of Education, Beijing 100875, People's Republic of China
  • 3Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
  • 4Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

  • *Contact author: huishao@bnu.edu.cn
  • †Contact author: sandvik@bu.edu
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Phys. Rev. Research 7, 023283 – Published 20 June, 2025

DOI: https://doi.org/10.1103/h4dh-bjmq

Abstract

We study the excitation spectrum of the S=1/2 Heisenberg model on the randomly diluted square lattice by stochastic analytic continuation of imaginary-time correlations obtained by quantum Monte Carlo simulations in the low-temperature limit. Focusing on relatively low dilution fractions, p=1/16 and p=1/8, the dynamic structure factor S(q,ω) exhibits a strongly damped magnon peak with anomalous dispersion near q=(0,0) and (π,π), a nondispersive low-energy peak from localized excitations, and a second peak within the continuum connecting these two features. A magnon with anomalous logarithmic dispersion, close to our result, was predicted in spin wave and T-matrix theory [Chernyshev et al., Phys. Rev. B 65, 104407 (2002)], with the quasiparticle description breaking down at the low 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 subset of the spins adjacent to vacancies, with fewer spins involved as the energy is lowered. We argue that the low-energy excitations are those of a sparse random network of effective moments at a fraction of the vacancies, leading to a damped diffusive-like behavior with localization at the lowest energies (the localized mode). In the case of the magnon, there is a shift in the real-space 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∝N−1 (with N=L2 the system size), which in the clean system is visible in S(q,ω) only at q=(π,π) but spreads through the entire Brillouin zone due to the lack of translational invariance when p>0. Beyond weight close to q=(0,0) and (π,π), which we explain by local sublattice imbalance within a classical dimer-monomer model, there is also intricate structure arising from correlated singlet fluctuations, which we demonstrate by enhancing said fluctuations with four-spin couplings in the Hamiltonian. The features in momentum space reflect spatially nonuniform breaking of the spin rotation symmetry and should be experimentally observable with elastic neutron scattering on layered quantum antiferromagnets doped with nonmagnetic impurities. All the ω>0 excitations should be observable by inelastic neutron scattering. Technically, our work demonstrates that surprisingly complex spectral information can be obtained from quantum Monte Carlo data, despite the “ill-posed” numerical analytic continuation problem.

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Phys. Rev. Research 7, 023283– Published 20 June, 2025
  • Received 12 August 2024
  • Accepted 21 May 2025
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