We present a novel approach for a systematic large–spin expansion of the t-J Hamiltonian which enables us to work without the constraint of no double occupancy. In our scheme we can perform the large–spin limit ensuring that the low energy spin excitations are in exact correspondence with the physical excitations of the s = 1 2 Hilbert space. As a consequence, we expect a smooth dependence of the physical quantities on the expansion parameter 1/s. As a first application of the method we study the case of a single hole in a Néel background. A systematic expansion in fluctuations about this stable solution indicates that by increasing t/J the quasiparticle weight strongly depends on the momentum carried by the hole. Results, obtained on small lattice sizes, are found in excellent agreement with exact diagonalization data.
We present a novel approach for a systematic large–spin expansion of the t-J Hamiltonian which enables us to work without the constraint of no double occupancy. In our scheme we can perform the large–spin limit ensuring that the low energy spin excitations are in exact correspondence with the physical excitations of the s = 1 2 Hilbert space. As a consequence, we expect a smooth dependence of the physical quantities on the expansion parameter 1/s. As a first application of the method we study the case of a single hole in a Néel background. A systematic expansion in fluctuations about this stable solution indicates that by increasing t/J the quasiparticle weight strongly depends on the momentum carried by the hole. Results, obtained on small lattice sizes, are found in excellent agreement with exact diagonalization data.
We develop an efficient numerical method for the description of a single-hole motion in the antiferromagnetic background. The method is free of finite-size effects and allows the calculation of physical properties at an arbitrary wave vector. A methodical increase of the functional space leads to results that are valid in the thermodynamic limit. We found good agreement with cumulant expansion, exact-diagonalization approaches on finite lattices as well as self-consistent Born approximations. The method allows a straightforward addition of other inelastic degrees of freedom, such as lattice effects. Our results confirm the existence of a finite quasiparticle weight near the band minimum for a single hole and the existence of stringlike peaks in the single-hole spectral function.
We investigate the phase diagram of the two-dimensional $t\ensuremath{-}J$ model using a recently developed technique that allows one to solve the mean-field model Hamiltonian with a variational calculation. The accuracy of our estimate is controlled by means of a small parameter q1, analogous to the inverse spin magnitude s1 employed in studying quantum spin systems. The mathematical aspects of the method and its connection with other large-spin approaches are discussed in detail. In the large-q limit the problem of strongly correlated electron systems turns into the minimization of a total-energy functional. We have performed this optimization numerically on a finite but large $L\ifmmode\times\else\texttimes\fi{}L$ lattice. For a single hole the static small-polaron solution is stable except for small values of J, where polarons of increasing sizes have lower energy. At finite doping we recover phase separation above a critical J and for any electron density, showing that the Emery et al. picture represents the semiclassical behavior of the $t\ensuremath{-}J$ model. Quantum fluctuations are expected to be very important, especially in the small-J-small-doping region, where phase separation may also be suppressed.
The novel slave-free (i.e. without slave bosons and fermions) approach to the problem of strong correlations is used in studying the Hubbard (t-J) model, where the self-energy is expressed in terms of charge and spin vertex functions of Hubbard operators. A systematic 1/N expansion (N is the number of spin components) of the self-energy is carried out. In O(1) it gives the same quasiparticle spectrum as the slave boson theory. The next order O(1/N) of the self-energy Σ(k, ω) is calculated exactly by solving analytically the integral equations for the charge and spin vertices. As an example for the feasibility of the proposed method explicit results for Σ(k, ω) are given in the case J=0. Dealing only with observable quantities our method is transparent and easily applicable to models which exclude double occupancy on lattice sites, such as the Anderson model and the Emery model for high temperature superconductors.
We present a nonperturbative method for deriving a quasiparticle description of the low-energy excitations in the t-J model for strongly correlated electrons. Using the exact diagonalization technique we evaluated exactly the spectral functions of composite operators, which describe an electron or hole dressed by antiferromagnetic spin fluctuations as expected in the string or spin bag picture. For hole doping up to 1/8, use of the composite operators leads to a drastic simplification of the single-particle spectral function: at half-filling it takes free-particle form, for the doped case it resembles a system of weakly interacting fermions corresponding to the doped holes. We conclude that for all doping levels studied, the elementary electronic excitations next to the Fermi level are adequately described by the antiferromagnetic spin-fluctuation picture.
Solid state physics, a very broad field in natural science, aims to explain physical properties of materials modeled as a many-body ensemble of the order of ∼ 10^23 interacting particles. For interacting metallic systems, one of the most powerful tools for unraveling the consequences of the collective interaction is the Fermi liquid theory. While still being an approximation, it excellently models many materials especially in the low-temperature and low-energy regime by treating themany-body problem as being equivalent to effectively non-interacting ”particles”, which is done by introducing the concept of quasiparticles. During the last few decades, several exotic phases of matter have been discovered, which originate from strong Coulomb interactions between the electrons, whose description is beyond the Fermi liquid theory. This thesis addresses the question of the validity of Fermi liquid theory once a single hole is introduced into an antiferromagnet with completely localized spins due to the strong interactions. Here, the most-studied case concerns the so-called 2D t − J model, which hosts a well-defined quasiparticle, the spin polaron. Focusing on a more tractable case, the t − Jz model without quantum spin fluctuations, we study the stability of the spin polaron solution once the nextnearest neighbor hopping t′ is introduced into the system. We focus on observations at the Γ-point and the X-point of systems with fixed Jz = 0.4t and varying t′ ∈ [−0.5t, 0.5t]. The model is numerically solved using exact diagonalization on finite-size lattices of up to 32 sites. A study of the quasiparticle weight under finite-size scaling reveals an “anomalous” regime at the Γ-point fort′ ≤ −0.3t, indicated by a vanishing quasiparticle weight. In order to characterize the low-energy dynamics within this “anomalous” regime, we investigated the spin correlation centered around the hole, as well as the magnon number distribution of a single-doped 20-site system. Based on the results, we present a preliminary picture of the antiferromagnetic ground state doped with one hole within that “anomalous” regime (t′ ≤ −0.3t) that deviates from the standard spin polaron as the cloud of magnetic fluctuations, typically localized around the hole, delocalizes over the whole finite-size lattice. Consequently, such systems show a weakly suppressed antiferromagnetic configuration under single-hole doping.
The spectral functions of one hole in the t-J and one-band Hubbard models are calculated using exact diagonalization techniques on small lattices. Results for the t-Jz model are also presented. For the t-J model we found that there is a quasiparticle at the bottom of the hole spectrum with an energy well approximated by Eh=-3.17+2.83J0.73 (for 0.1\ensuremath{\le}J\ensuremath{\le}1.0, t=1) on a 4\ifmmode\times\else\texttimes\fi{}4 lattice. The rest of the spectrum is not incoherent: We identified at least two other peaks following a similar power-law behavior with J. We speculate that the J dependence of the results can be explained by a model where the hole is trapped in a confining potential as in the Ising limit. The bandwidth of the hole is linear in J in the region 0.1\ensuremath{\le}J\ensuremath{\le}0.4 although a power-law behavior is not excluded. The spectral weight of the quasiparticle grows like J0.5 in the same region. We present new analytical results in the large J/t limit to understand the motion of the hole: In perturbation theory it can be shown that the momentum of the hole at large J/t is k=(\ensuremath{\pi},\ensuremath{\pi}) changing to k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) at intermediate J/t in agreement with numerical and spin-waves results. We show analytically and numerically that the bandwidth of the quasiparticle is of order t in the large J/t limit. This result corresponds to a spin-liquid state. The one-hole spectral function of the Hubbard model is obtained for lattices with 8 and 10 sites. A quasiparticle is also observed in this case. The bandwidth and the relation with the t-J model are discussed and a comparison with recent Monte Carlo results is made. We also review and extend previous results for the ground-state properties of the t-J model.