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arXiv:0901.4507 · Physical Review B

Nanoscale phase separation and superconductivity in the one-dimensional Hirsch model

Alberto Anfossi, C. Degli Esposti Boschi, Arianna Montorsi

Published Jun 9, 2009• 10 citations
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Abstract

We investigate numerically at various fillings the ground state of the one-dimensional Hubbard model with correlated hopping $x$ (Hirsch model). It is found that, for a large range of filling values $n$ around half filling, and for repulsive Coulomb interaction $u\ensuremath{\le}{u}_{c}(x,n)$, phase separation at a nanoscale (NPS phase) between two conducting phases at different densities occurs when $x\ensuremath{\gtrsim}2/3$. The NPS phase is accompanied by the opening of a spin gap and the system behaves as a Luther-Emery liquid with dominant superconducting correlations. Close to half filling, an anomalous peak emerges in the charge structure factor related to the density of doubly occupied sites, which determines the size of the droplets in the NPS phase. For $1/2\ensuremath{\lesssim}x\ensuremath{\lesssim}2/3$ a crossover to a homogeneous phase, still superconducting, takes place.

DOI
10.1103/physrevb.79.235117

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We investigate the transition to the insulating state in the one-dimensional Hubbard model with bond-charge interaction xxx (Hirsch model), at half-filling and T=0T=0T=0. By means of the density-matrix renormalization group algorithm the charge gap closure is examined by both standard finite-size scaling analysis and looking at singularities in the derivatives of single-site entanglement. The results of the two techniques show that a quantum phase transition takes place at a finite Coulomb interaction uc(x){u}_{\mathrm{c}}(x)uc​(x) for $x\ensuremath{\gtrsim}0.5$. The region 0<u<uc0<u<{u}_{\mathrm{c}}0<u<uc​ turns out to have a superconducting nature, at least for not too large x>xcx>{x}_{\mathrm{c}}x>xc​.
We determine the ground-state phase diagram of a Hubbard Hamiltonian with correlated hopping, which is asymmetric under particle–hole transform. By lowering the repulsive Coulomb interaction U at appropriate filling and interaction parameters, the ground state separates into hole and electron conducting phases: two different wavevectors characterize the system and charge–charge correlations become incommensurate. By further decreasing U another transition occurs at which the hole conducting region becomes insulating, and conventional phase separation takes place. Finally, for negative U the whole system eventually becomes a paired insulator. It is speculated that such behavior could be at the origin of the incommensurate superconducting phase recently discovered in the 1D Hirsch model. The exact phase boundaries are calculated in one dimension.
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