Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCritical scaling of the renormalized single-particle wave function near the Mott-Hubbard transition
170
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a quantum critical behavior of the renormalized single-particle Wannier function, calculated in the Gutzwiller correlated state near the insulator-metal transition (IMT) for cubic lattices. The wave function size and its maximum, as well as the system energy scale with increasing lattice parameter $R$ as $R^{n}$. Such scaling is interpreted as the evidence of a dominant role of the Coulomb repulsion. Relation of the insulator-metal transition lattice-parameter value $R=R_{C}$ to the original {em Mott criterion} is obtained. The method is tested by comparing our results with the exact approach for the Hubbard chain.
rate research
Read More
Identifying the fingerprints of the Mott-Hubbard metal-insulator transition may be quite elusive in correlated metallic systems if the analysis is limited to the single particle level. However, our dynamical mean-field calculations demonstrate that the situation changes completely if the frequency dependence of the two-particle vertex functions is considered: The first non-perturbative precursors of the Mott physics are unambiguously identified well inside the metallic regime by the divergence of the local Bethe-Salpeter equation in the charge channel. At low temperatures this occurs in the region where incoherent high-energy features emerge in the spectral function, while at high temperatures it is traceable up to the atomic-limit.
We analyze the highly non-perturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory calculations at the two-particle level. By extending the results of Schafer, et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. These divergence lines accumulate around the critical Mott endpoint in accordance with the interpretation as precursors of the MIT. By comparing our numerical data with analytical calculations of increasing complexity, such as for the disordered Binary Mixture and Falicov-Kimball (FK) models, as well as for the atomic limit (AL) case, (i) we identify two different kinds of divergences lines; (ii) we classify them in terms of the frequency-structure of the associated singular eigenvectors; (iii) we investigate their relation to the multiple branches in the Luttinger-Ward formalism. Moreover, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, unique energy scale $ u^*$ below which perturbation theory does no longer apply, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the non-perturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime.
We have studied the impact of non-local electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -- irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
Correlation-driven screening of disorder is studied within the typical-medium dynamical mean-field theory (TMT-DMFT) of the Mott-Anderson transition. In the strongly correlated regime, the site energies epsilon_R^i characterizing the effective disorder potential are strongly renormalized due to the phenomenon of Kondo pinning. This effect produces very strong screening when the interaction U is stronger then disorder W, but applies only to a fraction of the sites in the opposite limit (U<W).
We apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction~$U$ equals the band width, $U_{rm c}=W$, where the single-particle gap opens linearly, $Delta(Ugeq W)=U-W$. The simple nature of the elementary excitations permits to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $n_k$ at the Fermi wave number $k_{rm F}=0$ cannot be used to locate accurately $U_{rm c}$ from finite-size systems. However, the slope of $n_k$ at the band edges, $k_{rm B}=pm pi$, reveals the formation of a single-particle bound state which can be used to determine $U_{rm c}$ reliably from $n_k$ using accurate finite-size data.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
