K -edge and L3 -edge RIXS study of columnar and staggered quantum dimer phases of the square lattice Heisenberg model

We compute the K- and L3-edge resonant inelastic x-ray-scattering (RIXS) spectrum of the columnar and the staggered quantum dimer states accessible to the square lattice Heisenberg magnet. Utilizing a bond-operator representation mean-field theory we investigate the RIXS features of the one- and two-triplon excitation spectrum supported by the quantum dimer model in the background of condensed singlet excitation. We find that the two-triplon excitation boundary lies within an energy range of 2.7J2(1.7J2) to 9J2(7.5J2) for the columnar (staggered) phase, where J2 is the interbond coupling strength. We estimated the two-triplon gap to be 2.7J2 (1.7J2) for the columnar (staggered) dimer phase. The highest intensity of the K-edge RIXS spectrum is localized approximately around the (π/2,π/2) point for both the columnar and the staggered phases. At the L3 edge we study the one- and two-triplon signal considering experimental scattering geometry, polarization restriction, and experimental resolution effects. Our calculations find a contribution to the two-triplon RIXS signal that originates from the local hard-core dimer constraint. This leads to a finite nonzero signal at the (0,0) momentum transfer which can offer an explanation for the existing ladder RIXS experiments and also predicts a nonzero signal for the two-dimensional quantum dimer system. We find that the L3-edge RIXS response of the one- and two-triplon signal could exist in antiphase rung modulation for zero and π as found in inelastic neutron scattering. Since the disordered phase has the potential to harbor a variety of quantum paramagnetic states, our RIXS calculations provide useful signatures to identify the true nature of the ordering pattern.