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

TL;DR

This study explores the effects of long-range antiferromagnetic interactions on pairing, spin-charge separation, and quasiparticle formation in a 1D $t$-$J$ model, revealing complex phase behavior and coherent quasiparticles.

Contribution

It provides a comprehensive numerical analysis of the 1D $t$-$J$ model with long-range interactions, showing how these interactions influence phase separation, quasiparticle formation, and spectral features.

Findings

Long-range AFM order can be realized at half-filling.

Phase segregation occurs between AFM insulator and metallic phases.

Coherent quasiparticle bands emerge with finite doping.

Abstract

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 N\'eel 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 quasi-particles in a range of parameters and densities. We numerically calculate the photoemission spectrum of the model, showing the appearance of a coherent quasi-particle 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 quasi-particles 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.