Breakdown of the Luttinger sum - rule at the Mott - Hubbard transition in the one - dimensional t 1 − t 2 Hubbard model .

– We investigate the momentum distribution function near the Mott-Hubbard transition in the one-dimensional t1 − t2 Hubbard model (the zig-zag Hubbard chain), with the density-matrix renormalization-group technique. We show that for strong interactions the Mott-Hubbard transition occurs between the metallic-phase and an insulating dimerized phase with incommensurate spin excitations, suggesting a decoupling of magnetic and charge excitations not present in weak coupling. We illustrate the signatures for the Mott-Hubbard transition and the commensurate-incommensurate transition in the insulating spin-gaped state in their respective ground-state momentum distribution functions. Introduction Many aspects of the low-energy physics of an electronic system are influenced by the shape of its Fermi surface and the occupation of nearby states. Finite temperature, disorder or strong correlations may change the Fermi-surface geometry and or topology and induce magnetic and other instabilities. The investigation of the interplay of magnetic interactions, in particular the existence of incommensurate phases, with charge excitations emerges as one of the central issues in the physics of low-dimensional electronic systems [1–7]. The nature and mechanism of the Mott-Hubbard transition, as one of its most striking manifestations, has been subject to intense investigation for many years. It is therefore important to study the renormalization of individual Fermi-surface sections under the influence of electron-electron correlations in competition with frustrating interactions. Recent investigations suggested a spontaneous, interaction induced deformation of the Fermi surface of the 2D (extended) Hubbard model close to half filling, indicating in part a violation of the Luttinger sum-rule [8–10]. The possibility of a relevant Fermi-surface renormalization near the Mott-Hubbard (MH) transition in one-dimensional generalized Hubbard models has been raised on the basis of a DMRG-study [11], drawing on arguments from results obtained for the Fermi-surface flow by RG [12,13]. In this letter we examine this Mott-Hubbard transition in one of the prototypical frustrated one-dimensional models: the half-filled zig-zag Hubbard ladder. For appropriate choices of the