Abstract. We study the ‘asymmetric ’ Hubbard model, where hoppings of electrons depend on their spin. For strong interactions and sufficiently asymmetric hoppings, it is proved that the ground state displays phase separation away from half-filling. This extends a recent result obtained with Freericks and Lieb for the Falicov-Kimball model. It is based on estimates for the sum of lowest eigenvalues of the discrete Laplacian in arbitrary domains.

Sep 13, 201314 citations

Journal of Statistical Physics

Stability of Ground States of 2d Strongly Asymmetric Correlated-Hopping Hubbard Model

Jacek Wojtkiewicz

Published Sep 1, 2003• 3 citations

Publisher

DOI: 10.1023/a:1024667609435

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n

and the magnitude of the asymmetry

{t}_{f}∕{t}_{d}

between the hopping integrals of

f

and

d

electrons two different scenarios in formation of ground states are observed. At low electron fillings $(n\ensuremath{\leqslant}1∕3)$ the ground states are always phase segregated in the limit of strong asymmetry

({t}_{d}⪢{t}_{f})

. With decreasing asymmetry the system undergoes a transition to the phase-separated state and then to the homogeneous state. For electron fillings

n>1∕3

and weak Coulomb interactions the ground state is homogeneous for all values of asymmetry, while for intermediate and strong interactions the system exhibits the same sequence of phase transitions as for

n

small. Moreover, it is shown that the segregated phase is significantly stabilized with increasing electron filling, while the separated phases disappear gradually from the ground-state phase diagrams.