PHYSICAL REVIEW B VOLUME 44, NUMBER 18 1 NOVEMBER 1991-II Renormalized pseudoparticle description of the one-dimensional Hubbard-model thermodynamics J. Carmelo' and P. Horsch Max Pla-nck Ins-tm'tut fii r Festkorperforschung, D 700-0 Stuttgart 80, Federal Republic of Germany and Institute for Scientgc Interchange Foundation, Villa Gualino, 1-10189 Torino, Italy P. A. Bares~ Theoretische Physik, Eidgenossische Technische IIochschule-IIonggerberg, CII-8098 Zurich, Sei tzerland A. A. Ovchinnikov~ Institute for ScientijicIn'terchange Foundation, Villa Guahno, I 101$8 -Torino, Italy (Received 15 November 1990; revised manuscript received 19 April 1991) It is shown that the Hubbard chain in a magnetic field of arbitrary strength H can be treated as a liquid of interacting pseudoparticles which at T = 0 has only forward scattering. The excitation spectra can be understood in terms of particle-hole processes in the pseudoparticle renormalized bands. Within this framework, we are able to study in detail the low-temperature thermodynamics of the Hubbard model. Explicit expressions for the specific heat c, for a nearly half-filled band and for values of the magnetic field close to the ferromagnetic saturated state are derived. The renormalized charge and spin masses which regulate the crossover regime to the exponential behavior of several physical quantities close to the metal-insulator and ferromagnetic transitions, respectively, are calculated. I. INTRODUCTION Much attention has been given recently to the Hubbard model in connection with the low-dimensional strongly correlated materials (high-T, superconductors, quasi- one-dimensional synthetic metals, etc. ). Despite con- siderable efforts our understanding of the model is still far from complete. Lieb and Wu showed that in one dimension the Hamiltonian can be diagonalized by the Bethe-ansatz technique. The low-lying excitation spec- trum of the one-dimensional model has been studied by many authors. Nonetheless, almost all the investiga- tions have concentrated on the zero magnetic field case. More recently, the asymptotic behavior of correlation functions in the presence of an external magnetic field has been calculated using the finite-size analysis in con- formal field theory. In this paper we investigate in detail both the gapless and across-gap low-lying excitation spectra of the repul- sive one-dimensional Hubbard model in the presence of an external magnetic field. Our central motivation is to show that, as in a zero magnetic field, the low-lying exci- tation spectra can be understood in terms of particle-hole processes taking place in the pseudoparticle bands of the renormalized Landau-Lut tinger approach introduced in Ref. 10. A crucial point is that, in contrast to Fermi- liquid theory where the quasiparticles describe approxi- mate eigenstates of finite lifetime near the Fermi surface, the pseudoparticles of the present Landau liquid refer to exact eigenstates of the many-body system for all val- ues of pseudomorT. enta of the pseudoparticles. This fea- ture of the one-dimensional system follows from the fact that, at T = 0, the renormalized Landau-Luttinger liquid has only forward scattering. There are previous studies on one-dimensional systems where the designations "for- ward scattering" and "backward scattering" are used in a different context. In order to avoid misunderstand- ings of pure terminology we emphasize that our present designation "forward scattering" refers to the same pro- cesses as in Landau s Fermi-liquid theory — interactions where there is neither energy nor momentum exchange. The only consequence of these scattering events is a shift in the phases of the pseudoparticles. The pseudoparticle phase shifts follow in a natural way from our formalism. Moreover, they regulate all the low-energy physics. It is well known that the description of the many-body inter- actions by the Bethe-ansatz wave functions can be un- derstood in terms of phase shifts. We show in this paper that the usual Bethe-ansatz phase shifts can be related to the pseudoparticle phase shifts of the renormalized liquid. We are also able to study the low-temperature thermo- dynamics and derive explicit expressions for the specific heat. The derivation of these expressions requires the evaluation of the charge and spin renormalized masses which regulate the crossover regime to the exponential behavior of the specific heat and other physical quanti- ties due to the Hubbard (charge) and triplet (spin) gaps. The paper is organized as follows. In Sec. II we con- sider the energy spectra of the low-lying excitations of the model in the presence of a magnetic field, which are cal- culated by the standard method usually used in Bethe ansatz. The renormalized theory is introduced in Sec. 9967 1991 The American Physical Society