Study of spin and charge dynamics in one-dimensional cuprates using resonant inelastic x-ray scattering

One-dimensional (1D) antiferromagnetic chains and ladders realized in strongly correlated materials have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and other emergent phenomena. In this thesis, we examine spin and charge dynamics of 1D antiferromagnets revealed by resonant inelastic x-ray scattering (RIXS) using numerical techniques, including exact diagonalization and density matrix renormalization group. One of the major findings of this thesis is the first direct observation of multi-spinon excitations at the oxygen K-edge of Sr2CuO3, a prototype 1D cuprate, establishing RIXS as a complementary probe to inelastic neutron scattering (INS) in search of quantum spin liquids. In another study on 1D doped antiferromagnets, the RIXS spectra are shown to be rich, containing distinct two- and four-spinon excitations, dispersive antiholon excitations, and combinations thereof, further establishing that RIXS can serve as a probe of spin-charge separation in these materials. Finally, a systematic theoretical investigation of the Cu L-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving and spin-conserving channels is presented. The spectra host many exotic excitations, in particular, singlet twotriplon bound state excitations. Furthermore, direct signatures of charge quasiparticle excitations are revealed by RIXS in the doped ladders. This dissertation helps establish RIXS as an important tool for revealing the signatures of spin and charge fractionalization, and other collective excitations in strongly correlated material