We extend to initial ground states with zero spin density m = 0 the expressions provided by the pseudofermion dynamical theory (PDT) for the finite-energy one- and two-electron spectral-weight distributions of a one-dimensional (1D) correlated metal with on-site particle-particle repulsion. The spectral-function expressions derived in this paper were used in recent successful and detailed theoretical studies of the finite-energy singular features in photoemission of the organic compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) metallic phase. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. Expressions for the spectral functions in the vicinity of the singular border lines which also appear in the TTF- TCNQ spectral-weight distribution are derived. In addition, the PDT expressions are generalized for electronic densities in the vicinity of half filling. Further details on the processes involved in the applications to TTF-TCNQ are reported. Our results are useful for the further understanding of the unusual spectral properties observed in low-dimensional organic metals and also provide expressions for the one- and two-atom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.
The momentum, electronic density, spin density, and interaction dependences of the exponents that control the ( k , ω ) -plane singular features of the σ = ↑ , ↓ one-electron spectral functions of the 1D Hubbard model at finite magnetic field are studied. The usual half-filling concepts of one-electron lower Hubbard band and upper Hubbard band are defined in terms of the rotated electrons associated with the model Bethe-ansatz solution for all electronic density and spin density values and the whole finite repulsion range. Such rotated electrons are the link of the non-perturbative relation between the electrons and the pseudofermions. Our results further clarify the microscopic processes through which the pseudofermion dynamical theory accounts for the one-electron matrix elements between the ground state and excited energy eigenstates.
This pre-print deals with the one dimensional Hubbard model, as described by the Pseudofermion Dynamical Theory (PDT), with the purpose of (1) deriving a novel expression for the one electron spectral function for all values of the on-site repulsion
U/t and filling
n∈(0,1), at vanishing magnetisation
m→0, and (2) discover how to correctly compare the results originating from two different theoretical frameworks in the
U/t→∞ limit, as a first-test of the novel expressions obtained in this paper. Thus, an exact expression of the spectral function is obtained, which is furthermore successfully compared with previously known results in the
U→∞ limit. Following the PDT, the expression for the one electron spectral function factorises into a spin part and a charge part for all values of the on-site repulsion
U/t, where the dynamical quantum objects are spin zero and
η-spin (charge) zero singlet pairs of so-called rotated electrons, which in turn are obtained from the original electrons by a unitary transformation. The spectral function is exemplified for
U/t=400, with the purpose of comparing it with the same function obtained by other authors (and other means) in the
U→∞ limit. The main pillars of the PDT is presented in a summarised form. For example, we will only be interested in excited energy eigenstates which originate the most significant singular features of the spectral map in the
(k,ω) plane, safely ignoring higher order contributions. Even though emphasis is given on step-by-step derivations where necessary, derivations that have been done elsewhere and/or do not notably contribute to the physical understanding, are sometimes avoided. Therefore, references for further study are given throughout the paper.
We describe a low-temperature approach to the two-dimensional half-filled Hubbard model which allows us to study both antiferromagnetism and single-particle properties. This approach ignores amplitude fluctuations of the antiferromagnetic (AF) order parameter and is valid below a crossover temperature
TX which marks the onset of AF short-range order. Directional fluctuations (spin waves) are described by a nonlinear sigma model $(\mathrm{NL}\ensuremath{\sigma}\mathrm{M})$ that we derive from the Hubbard model. The parameters of the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$---the spin stiffness and spin-wave velocity---are calculated as a function of the Coulomb repulsion U. The $\mathrm{NL}\ensuremath{\sigma}\mathrm{M}$ is solved by a saddle-point approximation within the
CP1 representation where the N\'eel field is parametrized by two Schwinger bosons. At zero temperature, there is always Bose condensation of the Schwinger bosons, which signals AF long-range order for any value of the Coulomb repulsion. At finite temperature, the AF long-range order is suppressed (in agreement with the Mermin-Wagner theorem), but the AF correlation length remains exponentially large. In the
CP1 representation, the fermion field is naturally expressed as the product of a Schwinger boson and a pseudofermion whose spin is quantized along the (fluctuating) N\'eel field. This allows us to write the fermion Green's function as the product (in direct space) of the Schwinger boson propagator (which is derived from the $\mathrm{NL}\ensuremath{\sigma}\mathrm{M})$ and the pseudofermion propagator. At zero temperature and weak coupling, our results are typical of a Slater antiferromagnet. The AF gap is exponentially small; there are well-defined Bogoliubov quasiparticles (QP's) (carrying most of the spectral weight) coexisting with a high-energy incoherent excitation background. As U increases, the Slater antiferromagnet progressively becomes a Mott-Heisenberg antiferromagnet. The Bogoliubov bands evolve into Mott-Hubbard bands separated by a large AF gap. A significant fraction of spectral weight is transferred from the Bogoliubov QP's to incoherent excitations. At finite temperature, there is a metal-insulator transition between a pseudogap phase at weak coupling and a Mott-Hubbard insulator at strong coupling. Finally, we point out that our results straightforwardly translate to the half-filled attractive Hubbard model, where the $\mathbf{q}=(\ensuremath{\pi},\ensuremath{\pi})$ charge and
q=0 pairing fluctuations combine to form an order parameter with SO(3) symmetry.