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International Journal of Modern Physics B

MECHANISM OF STRIPES IN t–J MODEL

Tôru Sakai

Published Dec 20, 2000• 0 citations
Publisher

Abstract

We consider a possible mechanism of the charge stripe order due to the next-nearest neighbor exchange interaction J′ in the two-dimensional t–J model, based on the concept of the phase separation. We also calculate some hole correlation functions of the finite cluster of the model using the numerical diagonalization, to examine the realization of the mechanism.

DOI
10.1142/s0217979200003691

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We consider a possible mechanism of the charge stripe order due to the next-nearest neighbor exchange interaction J′ in the two-dimensional t–J model, based on the concept of the phase separation. We also calculate some hole correlation functions of the finite cluster of the model using the numerical diagonalization, to examine the realization of the mechanism.
We consider a possible mechanism of the charge stripes in the high- T c cuprates, based on some additional interactions in the two-dimensional t – J model; the next-nearest-neighbour and/or four-spin (ring) exchange interactions. The many-hole correlation functions obtained by numerical exact diagonalization of a finite-cluster t – J model including the correction terms indicate the realization of the mechanism and give some preliminary phase diagrams. A realistic combination of these additional terms is also studied.
In the spinless fermion model on a square lattice with infinite nearest-neighbor repulsion, holes doped into the half-filled ordered state form stripes which, at low doping, are stable against phase separation into an ordered state and a hole-rich metal. Here we consider transport of additional holes along these stripes. The motion of a single hole on a stripe is mapped to a one-dimensional problem, a variational wave function is constructed and the energy spectrum is calculated and compared to energies obtained by exact diagonalization.
We have examined the effects of extended hopping parameters in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model on the binding and spatial distribution of charge carriers. Previous studies have shown that a negative next-nearest-neighbor hopping in the physical parameter range serves to weaken striped behavior in the model. We show using exact diagonalization that a physically relevant set of parameters for the hole doped cuprates that includes next-next-nearest-neighbor hopping strengthens the binding of the holes and enhances stripe behavior in the underdoped regime.
The frustrated t-J model is investigated by using the exact-diagonalization (ED) method on an 8-site cluster. The effect on next-nearest-neighbor (NNN) exchange interaction J′ (frustration) on the hole pairing and the thermodynamic properties of the system is considered. Two holes initially remain unbound at smaller value of J′/t, but tend to bind at larger value. The maximum possibility of pair formation has been observed to be at NNN sites. Entropy calculation shows that the system goes to more disordered state with J′. The specific heat curves show a single peak structure. A decrease in effective exchange energy is observed due to the frustration.
The influence of the next-nearest-neighbor (NNN) antiferromagnetic interaction J ’has been examined within t-t'-J-J ’model in an exact technique. An 8-site square cluster is chosen as the representative of the system. The effect of the next-nearest-neighbor (NNN) antiferromagnetic interaction on various ground state properties such as electron-electron correlation, spin-spin correlation, effective hopping amplitude etc. has been studied. Temperature variation of the susceptibility shows that J ’suppresses short range antiferromagnetic order. Applying periodic boundary conditions, the calculations have been extended beyond the 8-site limit.
The role of next nearest neighbor (NNN) hopping (t') and next to NNN hopping (t'') on hole pairing and thermodynamic properties such as specific heat, entropy have been investigated using two dimensional (2D) hole-doped t-t'-t''-J model based on exact diagonalization (ED) method. Standard Periodic boundary conditions are applied to minimize error due to finite size effect as the calculations are made using small sized cluster geometry. The attraction between holes increases with the inclusion of third neighbor hopping term. The maximum probability of hole pairing is at NNN site. The system goes to more disordered and ordered state with the increase of long range hopping terms at temperature T≤0.35t and T>0.35t, respectively. A single peak nature is observed in specific heat graph.