Fate of pairing and spin-charge separation in the presence of long-range antiferromagnetism

We present a numerical study of competing orders in the 1D t-J model with long-range RKKY-like staggered spin interactions. By circumventing the constraints imposed by Mermin-Wagner's theorem, this Hamiltonian can realize long-range Neel order at half filling. We determine the full phase diagram as a function of the exchange and particle density using the density matrix renormalization group (DMRG) method. We show that pairing is disfavored and the AFM insulator and metallic phases are separated by a broad regime with phase segregation, before spin-charge separation re-emerges at low densities. Upon doping, interactions induce a confining potential that binds holons and spinons into full fledged fermionic quasiparticles in a range of parameters and densities. We numerically calculate the photoemission spectrum of the model, showing the appearance of a coherent quasiparticle band splitting away from the holon-spinon continuum with a width determined by J that survives at finite doping. Comparison with analytical results using the self-consistent Born approximation (SCBA) and by solving the spinon-holon problem offer insight into the internal structure of the quasiparticles and help us explain the different features in the spectrum. We discuss how this simple toy model can teach us about the phenomenology of its higher-dimensional counterpart.

Automated summary

This study presents a numerical investigation of competing orders in the 1D t-J model with long-range RKKY-like staggered spin interactions. By circumventing the constraints of Mermin-Wagner's theorem, this model can exhibit long-range Neel order at half filling. The full phase diagram as a function of exchange and particle density is determined using the density matrix renormalization group (DMRG) method. It is found that pairing is discouraged, and the AFM insulator and metallic phases are separated by a broad phase segregation region. The effects of phase separation re-emerge at low densities. Upon doping, interactions induce a confining potential that binds holons and spinons into fermionic quasiparticles. The photoemission spectrum of the model is numerically calculated, revealing the appearance of a coherent quasiparticle band with a width determined by J that survives at finite doping. Comparison with analytical results and the spinon-holon problem provide insights into the internal structure of the quasiparticles and explain the different features in the spectrum. The study also discusses the implications of this simple toy model for the phenomenology of higher-dimensional counterparts.