Breakdown of quasiparticle picture in the low-density limit of the 1D Hubbard model

Sebastian Eggert, Stefan Soeffing, Imke Schneider

James F. Annett, William H. Beere

Shaojin Qin, Tiezheng Qian, Lu Yu +1 more

Using the finite-size scaling of results obtained by exact diagonalization, we study the low-density limit of the one-dimensional Hubbard model. Calculating the quasiparticle weight, we demonstrate that for a given particle number N and system size L, there always exists a crossover point ${\mathit{U}}_{\mathit{c}}$ separating the Fermi-liquid (U${\mathit{U}}_{\mathit{c}}$) and non-Fermi-liquid (U>${\mathit{U}}_{\mathit{c}}$) regimes (U is the Hubbard repulsion). We find that for a fixed N, ${\mathit{U}}_{\mathit{c}}$ is inversely proportional to L, keeping ${\mathit{U}}_{\mathit{c}}$L/t constant (with t as the hopping integral), as L is large enough. It follows that in the low-density (in fact vanishing density) limit L\ensuremath{\rightarrow}\ensuremath{\infty}, ${\mathit{U}}_{\mathit{c}}$\ensuremath{\rightarrow}0, so the system is always in the non-Fermi-liquid regime as long as U>0. We show that our numerical results are consistent with the Bethe-ansatz solution.

Sandro Sorella, Alberto Parola

Starting from the known Lieb and Wu solution of the one-dimension-Hubbard model in the U to infinity limit, the authors show how the spin-charge decoupling of the elementary excitations is responsible for several peculiar features in one-particle properties, such as momentum distribution, quasiparticle weight and the Green function. In particular they analyse in detail the structure of the one-hole Green function at half-filling, which has not been previously calculated by field theory methods due to the breakdown of conformal invariance. A rich structure is found with branch cut singularities at omega =+or-2 sin k but no simple poles. The non-trivial dependence on the momentum of the hole allows for hole propagation although the analytic structure of G(k, omega ) is quite different from that usually characterizing band insulators. These results provide a precise characterization of one-dimensional Mott insulators. The relationship between the branch cuts of the Green function and the finite-size scaling of the quasiparticle weight is also discussed together with its implications for the analysis of numerical data.

Osamu Narikiyo, Yasumasa Hasegawa, Hidetoshi Fukuyama

Yuekun Niu, Yu 煜 Ni 倪, Jiaming Wang +3 more

The orbital-selective Mott phase (OSMP) is commonly described as a coexistence of localized and itinerant electrons within effectively decoupled orbitals, but emerging evidence for quasiparticle breakdown points to physics beyond this picture, whose microscopic origin remains unknown. Using dynamical mean-field theory for the two-band Hubbard model, we show that the spin-flip and Ising-type components of Hund's coupling generate local spin excitations (LSEs). These LSEs couple electrons between different orbitals, renormalize quasiparticle lifetimes and binding energies, and thereby destroy well-defined quasiparticles in the OSMP. Removing these two components of Hund's coupling restores coherent quasiparticle behavior and fully decouples the charge dynamics of the two bands. Our results therefore identify electronic coupling to LSEs as the fundamental mechanism driving quasiparticle breakdown within the OSMP.