Exact analytic approaches to the two-dimensional t-J model at low electron density

C. Stephen Hellberg, Efstratios Manousakis

Published Dec 31, 1996• 0 citations

Abstract

The phase diagram of the two-dimensional t-J model in the limit of infinitesimal electron density is determined exactly with analytic approaches. Numerical work is only required to show other potential ground states are never stabilized. Significant differences with previous work on the model are found. The ground state exhibits pairing for all interaction strengths insufficient to cause phase separation. The pairing is p-wave for small interaction strengths, d{sub x{sup 2}{minus}y{sup 2}} for intermediate J/t, and s-wave for larger J/t.

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Exact analytic approaches to the two-dimensional t-J model at low electron density

C. Stephen Hellberg, Efstratios Manousakis

Published Dec 31, 1996• 0 citations

OpenAlex

Abstract

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arXiv:cond-mat/9911071Physical review. B, Condensed matterMay 1, 200046 citations

J

, consists of three phases, viz. a gas of electrons for $0\ensuremath{\leqslant}J<2t$, a gas of pairs for $2t\ensuremath{\leqslant}J<3.29t$, and a fully phase-separated state for

J>3.29t

. Further, we rigorously prove that a gas of electrons start forming pairs at

J=2t

and the value is the same for any bipartite lattice in any dimension. We have elaborately explored the possibilities of formation of bigger clusters, i.e., bound states of three, four, and six electrons by performing exact diagonalization and perturbative analysis and ruled out formation of such clusters in the phase diagram.

{\mathit{J}}_{\mathrm{PS}}

(N) is examined by calculating the free energy as a function of the electron concentration. We find that

{\mathit{J}}_{\mathrm{PS}}

(N) increases with the lattice size N. An extrapolation of our finite-size results to the thermodynamic limit gives

{\mathit{J}}_{\mathrm{PS}}

(\ensuremath{\infty})/t=4.1 (\ifmmode\pm\else\textpm\fi{}0.1).

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.