Numerical Calculations of the B1g Raman Spectrum of the Two-Dimensional Heisenberg Model

Abstract

The B1g Raman spectrum of the two-dimensional S=1/2 Heisenberg model is discussed within Loudon-Fleury theory at both zero and finite temperature. The exact T=0 spectrum for lattices with up to 6*6 sites is computed using Lanczos exact diagonalization. A quantum Monte Carlo (QMC) method is used to calculate the corresponding imaginary-time correlation function and its first two derivatives for lattices with up to 16*16 spins. The imaginary-time data is continued to real frequency using the maximum-entropy method, as well as a fit based on spinwave theory. The numerical results are compared with spinwave calculations for finite lattices. There is a surprisingly large change in the exact spectrum going from 4*4 to 6*6 sites. In the former case there is a single dominant two-magnon peak at frequency w/J appr. 3.0, whereas in the latter case there are two approximately equal-sized peaks at w/J appr. 2.7 and 3.9. This is in good qualitative agreement with the spinwave calculations including two-magnon processes on the same lattices. Both the Lanczos and the QMC results indicate that the actual infinite-size two-magnon profile is broader than the narrow peak obtained in spinwave theory, but the positions of the maxima agree to within a few percent. The higher-order contributions present in the numerical results are merged with the two-magnon profile and extend up to frequencies w/J appr. 7. The first three frequency cumulants of the spectrum are in excellent agreement with results previously obtained from a series expansion around the Ising limit. Typical experimental B1g$ spectra for La2CuO4 are only slightly broader than what we obtain here. The exchange constant extracted from the peak position is J appr. 1400K, in good agreement with values obtained from neutron scattering and NMR experiments.

15 pages, Revtex, 13 PostScript figures

References in corpus (1)

• Superexchange coupling and spin susceptibility spectral weight in undoped monolayer cuprates

Cited by in corpus (31)

• Inelastic Light Scattering From Correlated Electrons
• Fermionic response from fractionalization in an insulating two-dimensional magnet
• High-energy magnon dispersion and multi-magnon continuum in the two-dimensional Heisenberg antiferromagnet
• Asymmetry of the electronic states in hole- and electron-doped cuprates: Exact diagonalization study of the t-t'-t''-J model
• Progress on stochastic analytic continuation of quantum Monte Carlo data
• Mid-infrared absorption in YBa2Cu3O6: Failure of spin-wave theory in undoped cuprates?
• Magnetic nature of the 500 meV peak in $\mathrm{L}{\mathrm{a}}_{2-\mathrm{x}}\mathrm{S}{\mathrm{r}}_{\mathrm{x}}\mathrm{Cu}{\mathrm{O}}_4$ observed with resonant inelastic x-ray scattering at the Cu $K$-edge
• Spin dynamics of Sr_14Cu_24O_41 two-leg ladder studied by Raman spectroscopy
• Two-magnon excitations in resonant inelastic x-ray scattering from quantum Heisenberg antiferromagnets
• Electronic Raman scattering in correlated materials: exact treatment of nonresonant, mixed, and resonant scattering with dynamical mean field theory
• Theory of inelastic light scattering in spin-1 systems: resonant regimes and detection of quadrupolar order
• Resonant Two-Magnon Raman Scattering and Photoexcited States in Two-Dimensional Mott Insulators
• Theoretical analysis of magnetic Raman scattering in La2CuO4: two-magnon intensity with the inclusion of ring exchange
• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Raman Response of Magnetic Excitations in Cuprate Ladders and Planes
• Momentum dependent light scattering in insulating cuprates
• Symmetry and light coupling to phononic and collective magnetic excitations in SrCu_2(BO_3)_2
• Raman scattering for triangular lattices spin-1/2 Heisenberg antiferromagnets
• Supermagnonic propagation in two-dimensional antiferromagnets
• Two-magnon Raman scattering in insulating cuprates: Modifications of the effective Raman operator
• Magnetic Raman Scattering of Insulating Cuprates
• Electron-phonon coupling in undoped cuprate $YB{a}_{2}C{u}_3{O}_6$ estimated from Raman and optical conductivity spectra
• Estimates of the dynamic structure factor for the finite temperature electron liquid via analytic continuation of path integral Monte Carlo data
• Cavity-Enhanced Optical Manipulation of Antiferromagnetic Magnon-Pairs
• Optical observation of quasiperiodic Heisenberg antiferromagnets in two dimensions
• Magnetic and Charge Correlations in La{2-x-y}Nd_ySr_xCuO_4: Raman Scattering Study
• Two-magnon excitations in resonant inelastic x-ray scattering studied by spin-density-wave formalism
• Polarized Raman Response of Two-Dimensional Quasiperiodic Antiferromagnets: Configuration-Interaction versus Green's Function Approaches
• Time-dependent Schwinger boson mean-field theory of supermagnonic propagation in 2D antiferromagnets
• Spin wave approach to the two-magnon Raman scattering in an J1x-J1y-J2-Jc antiferromagnetic Heisenberg model
• Elementary excitations in undoped layered cuprates