Elementary excitations in undoped layered cuprates

TL;DR

The paper addresses spin dynamics in the square-lattice spin-1/2 Heisenberg model with ring exchange relevant to parent cuprates, proposing bond-operator theory (BOT) to capture both magnons and spin-0 bound states. By extending the unit cell to a plaquette and using a $1/n$ diagrammatic expansion, BOT yields quantitative spectra for magnons and three spin-0 quasiparticles, notably the singlon and amplitude (Higgs) modes, whose signatures explain Raman, RIXS, and infrared anomalies. The study provides detailed comparisons with La$_{2}$CuO$_{4}$ and Sr$_{2}$CuO$_{2}$Cl$_{2}$, reproducing magnon dispersions and identifying the origin of key spectroscopic features across multiple probes, while highlighting a quantum phase transition near $R\sim J$. The results establish BOT as a powerful, unified framework for multimagnon dynamics in cuprates and connect microscopic exchange parameters to diverse experimental observables.

Abstract

Using the recently proposed bond-operator technique (BOT), we discuss spin dynamics of the Heisenberg spin-$\frac12$ antiferromagnet with the ring exchange and small interactions between the second- and the third-neighbor spins on the square lattice at $T=0$. This model was suggested before for description of parent compounds of high-temperature superconducting layered cuprates. BOT describes accurately short-range spin correlations in quantum systems and provides a quantitative description of elementary excitations which appear in other approaches as bound states of conventional low-energy quasiparticles. We demonstrate that besides well-known magnons (spin-1 excitations) there are three well-defined spin-0 quasiparticles in the considered model whose energies lie near the magnon spectrum. Two of them, the amplitude (Higgs) mode and the quasiparticle which we named singlon, produce pronounced anomalies observed experimentally in the Raman scattering, resonant inelastic x-ray scattering, and infrared optical absorption. We find sets of the model parameters which describe quantitatively experimental data obtained in $\rm La_2CuO_4$ and $\rm Sr_2CuO_2Cl_2$.

Figures (11)

• Figure 1: Diagrams giving corrections of the first-order in $1/n$ to (a) the ground state energy and the staggered magnetization, and (b), (c) to self-energy parts.
• Figure 2: Diagrams for dynamical spin correlators \ref{['dsf']} and \ref{['dsfpp']} to be taken into account in the first order in $1/n$.
• Figure 3: The crystal and the magnetic Brillouin zones (BZs) are presented (the largest and the middle squares, respectively) for the simple square lattice. The distance between nearest lattice sites is set to be equal to unity. The smallest (red) square and the yellow area are the first and the second BZs, correspondingly, in the case of four sites in the unit cell.
• Figure 4: Evolution of spectra $\epsilon_{\bf k}$ of lower energy quasiparticles in model \ref{['ham']} upon varying $R$ at $J'=J"=R/20$ found using the BOT in the first order in $1/n$. The singlon, the amplitude (Higgs), and the S0 modes are well-defined spin-0 quasiparticles whose damping $\gamma_{\bf k}$ are presented with dashed lines of corresponding colors. Also shown in panel a) are magnon spectra obtained by the series expansion around the Ising limit series, within the spin-wave theory (SWT) in the second igarigar2 and in the third syromyat orders in $1/S$, and neutron scattering experiment in CFTD chris1piazza. Borders of the first BZ with four spins in the unit cell are shown by red vertical lines (see Fig. \ref{['bz']}). Breaks on these lines of spectra of magnons and the Higgs mode are discussed in the text.
• Figure 5: Magnon energies at ${\bf k}=(\pi,0)$ and ${\bf k}=(\pi/2,\pi/2)$ at different values of $R$ and $J'=J"=R/20$ (see Eqs. \ref{['jp']} and \ref{['r']}) found using the BOT (present study), the linear spin-wave theory(LSWT), and exact diagonalization (ED) of finite clusters containing $N\le32$ sites with the subsequent linear in $1/N$ extrapolation to thermodynamic limit (Ref. ringnum1). The accuracy of ED results at ${\bf k}=(\pi/2,\pi/2)$ is not estimated because data for only $N=16$ and $N=32$ are available for this momentum. ringnum1 The accuracy of ED results degrades quickly upon approaching the quantum critical point at $R\sim1$ as it is seen from the data for ${\bf k}=(\pi,0)$. Numerical results obtained at $R=0$ using series expansion around the Ising limit series are also shown (series).