The phase diagram of the 2D t-J model is investigated using high-temperature expansions. Series for the Heimholtz free energy, the inverse compressibility, the chemical potential, and the uniform spin susceptibility through tenth order are calculated and analyzed. A region of phase separation is found at 7=0 for Jit lying above a line extending from Jit =3.8 at zero filling to Jit = 1.2 at half filling. For very small Jit near half filling where the Nagaoka effect is possible, we find a region of divergent uniform magnetic susceptibility at T-0.
We have calculated the high temperature series for the momentum distribution function n k of the 2D t-J model to twelfth order in inverse temperature. By extrapolating the series to T = 0.2J we searched for a Fermi surface of the 2D t-J model. We find that three criteria used for estimating the location of a Fermi surface violate Luttinger's Theorem, implying the t-J model does not have an adiabatic connection to a non-interacting model.Models for two-dimensional strongly correlated electrons play a central role in attempts to understand high temperature superconductors [1]. However, the 2D models themselves are at present poorly understood. One of the main points of interest in studies of 2D strongly correlated electrons is how similar the 2D models are to Fermi liquid theory, the standard model for conventional metals [2]. Many-body calculations for conventional metals are generally perturbative, assuming an adiabatic relation to a non-interacting model, with low energy excitations describable by quasiparticles.By summing a perturbative expansion to all orders Luttinger [3] was able to show that a sharp Fermi surface can exist for interacting electrons. He defined the Fermi surface to be the locus of points in k-space where the renormalized single particle energy is equal to the zero temperature chemical potential E k = µ. This requires the imaginary part of the retarded self-energy to vanish on the Fermi surface. Luttinger was able to show [4] ImΣ ret (ω) ∝ (ω − µ) 2 , satisfying this requirement. An immediate consequence of this perturbative calculation is that the volumes (areas in 2D) enclosed by the interacting and non-interacting Fermi surfaces are the same, a statement generally known as Luttinger's Theorem.Using high temperature series we investigated the momentum distribution function for the 2D t-J model on a square lattice, with the Hamiltonian for the t-J model given bywhere the sums are over pairs of nearest neighbor sites and the projection operators P eliminate from the Hilbert space states with doubly occupied sites. We calculated the high temperature series for the momentum distribution function to twelfth order in inverse temperature β = 1/k B T , extending a previous eighth order calculation by Singh and Glenister [5]. The definition of the single spin momentum distribution function iswith n r = c † 0σ c rσ . For the calculations reported here we fix J/t = 0.4 and the electron density n = 0.8. A wider range of parameters will be explored in a future publication.To reach low temperatures we need to analytically continue the series for n k . A standard way to do this is to use Padé approximants. However, for n k the straightforward application of Padés does not work very well. One way to improve the convergence of Padé approximants is to change the functional form before calculating Padés [6]. Exactly which change to make is difficult to know for unknown functions. One way to proceed is to use the function itself as a scaling function. To do this we first form the high temperature series for t...
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