Dynamical functions of a 1D correlated quantum liquid

Abstract

Abstract. The dynamical correlation functions in the one-dimensional electronic systems show power-law behavior at low energies and momenta close to integer multiples of the charge and spin Fermi momenta. These systems are usually referred to as Tomonaga-Luttinger liquids. However, near well-dfined lines of the (k, ω) plane the power-law behaviour extends beyond the low-energy cases mentioned above, and also appears at higher energies leading to singular features in the photoemission spectra and other dynamical correlation functions. The general spectral-function expressions derived in this paper were used in recent theoretical studies of the finiteenergy singular features in photoemission of the organic compound tetrathiafulvalenetetracyanoquinodimethane (TTF-TCNQ) metallic phase. They are based on a so called pseudofermion dynamical theory (PDT), which allows us to systematically enumerate and describe the excitations in the Hubbard model starting from the Bethe-Ansatz, as well as to calculate the charge and spin objects phase shifts appearing as exponents of the power laws. In particular, we concentrate on the spin-density m → 0 limit and in effects of the vicinity of the singular border lines, as well as close to half filling. Our studies take into account spectral contributions from types of microscopic processes that do not occur for finite values of the spin density. In addition, the specific processes involved in the spectral features of TTF-TCNQ are studied. 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 twoatom spectral functions of a correlated quantum system of ultracold fermionic atoms in a 1D optical lattice with on-site two-atom repulsion.

Threshold singularities in the one-dimensional Hubbard model

“…Finally, singularity exponents obtained by completely different methods have been reported in Ref. 29. We have checked that the numerical results for the exponent 0,− in the range ͉P͉ Ͻ k F , density n c = 0.59 and several values of u͑u = 0.25, 1.225, 2.5͒ are in agreement with ours.…”

“…It would be interesting to demonstrate the equivalence of the expressions for the exponents of Ref. 29 and our results analytically.…”

Finite-temperature dynamics of the Mott insulating Hubbard chain

“…with energy − (p) relative to the ground state, and the momenta are quantized according to (18). We note that one-hole states have to be taken into account as we are working in the grand canonical ensemble, where the total number of spinless fermions is not fixed.…”

An Application of the Extended Global SO(3) × SO(3) × U(1) Symmetry of the Hubbard Model on a Square Lattice: The Spinon, η-Spinon, and c Fermion Description

“…They merely give rise to phase shifts whose expressions may be extracted from the BA solution. This allows the introduction of a pseudofermion dynamical theory, which provides finite-energy spectral and correlation function expressions involving phase shifts [28,29]. Hence in 1D such interactions do not involve interchange of energy and momentum.…”

“…In contrast to the 1D case where a suitable c and s1 fermion dynamical theory is available [28,29], for the square-lattice quantum liquid there are within the present status of the theory no suitable tools to calculate matrix elements between the ground state and one-and two-electron excited states. Hence, one cannot calculate explicitly spin-spin correlation functions.…”