Field-dependent dynamics in the metallic regime of the half-filled Hubbard model

Abstract

A systematic study of the effect of magnetic field (h) on Hubbard model has been carried out at half filling within dynamical mean field theory. In agreement with previous studies, we find a zero temperature itinerant metamagnetic transition, reflected in the discontinuous changes in magnetization as well as in the hysteresis, from a paramagnetic (PM) metallic state to a polarized quasi-ferromagnetic (QFM) state, at intermediate and large interaction strength (U ). The jump in magnetization vanishes smoothly with decreasing interaction strength, and at a critical U , the transition becomes continuous. The region of 'coexistence' of the PM and QFM solutions in the field-U plane obtained in this study agrees quantitatively with recent numerical renormalization group calculations, thus providing an important benchmark. We highlight the changes in dynamics and quasiparticle weight across this transition. The effective mass increases sharply as the transition is approached, exhibiting a cusp-like singularity at the critical field, and decreases with field monotonically beyond the transition. We conjecture that the first order metamagnetic transition is a result of the competition between Kondo screening, that tries to quench the local moments, and Zeeman coupling, which induces polarization and hence promotes local moment formation. A comparison of our theoretical results with experiments on 3 He indicate that, a theory of 3 He based on the half-filled Hubbard model places it in a regime of intermediate interaction strength.

Properties of an almost localized Fermi liquid in an applied magnetic field revisited: a statistically consistent Gutzwiller approach

“…Namely, a relatively small value of U ∼ 5|t| ≪ W (where W ≡ 24|t| is bare band width) obtained from the m(h) best fit places the liquid 3 He at ambient pressure as a moderately correlated system. This seemingly unexpected conclusion is also in agreement with the DMFT analysis [21]. In this way, the Hubbard-model approach squares also qualitatively with the fundamental Fermi-liquid theory assumption that the interaction between quasiparticles can be essentially limited to the region very close to the Fermi surface (U substantially smaller than W ).…”

“…In other words, we have not obtained any first-order metamagnetic transition which limits the original Gutzwiller approach (GA) applicability to real systems such as liquid 3 He (see also the discussion in Ref. [21]). Apart from that, GA approach is not statistically consistent, as discussed in detail in the text.…”

“…Minimally, it plays the role of a mean field theory. Among other techniques frequently applied to the Hubbard model are also the dynamical mean-field theory (DMFT) [21] or the quantum Monte Carlo (QMC) [22] methods.…”

Feasibility of a metamagnetic transition in correlated systems

“…For h < t, we can compare our results with the previous work. For T= 0, we compare the value of U/U c below which there is no MMT (as h rises to t): our single-site SRMF theory gives a value close to 0.5 while in GA it is about 0.44 5 and in DMFT, about 0.61 2,20 . We also compare GA with SR MFT.…”

“…However, it is a theory for the ground state only and neglects spin correlations entirely. Theoretical attempts 2,19,20 have recently been brought to bear upon this problem recently to understand it using more powerful techniques. The emergence of dynamical mean-field theory (DMFT) has seen a major paradigm shift in the study of strongly correlated systems.…”