Electronic States and Geometrical Structures of Hubbard Clusters with an Impurity

Aleksandr Krinitsyn, Sergey V. Nikolaev, Sergey G. Ovchinnikov

Kristjan Haule

We generalized the recently introduced impurity solver [P. Werner et al., Phys. Rev. Lett. 97, 076405 (2006)] based on the diagrammatic expansion around the atomic limit and quantum Monte Carlo summation of the diagrams. We present generalization to the cluster of impurities, which is at the heart of the cluster dynamical mean-field methods, and to realistic multiplet structure of a correlated atom, which will allow a high-precision study of actinide and lanthanide based compounds with the combination of the dynamical mean-field theory and band-structure methods. The approach is applied to both the two-dimensional Hubbard and $t\text{\ensuremath{-}}J$ models within cellular dynamical mean-field method. The efficient implementation of the algorithm, which we describe in detail, allows us to study coherence of the system at low temperature from the underdoped to overdoped regime. We show that the point of maximal superconducting transition temperature coincides with the point of maximum scattering rate, although this optimal doped point appears at different electron densities in the two models. The power of the method is further demonstrated in the example of the Kondo volume collapse transition in cerium. The valence histogram of the dynamical mean-field theory solution is presented, showing the importance of the multiplet splitting of the atomic states.

Elbio R. Dagotto

Sadulla Mamarazhabovich Tashpulatov

We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors.Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a ν -dimensional lattice.We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator.We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.

Hideki Matsumoto, Ferdinando Mancini

Md Fahad Equbal, M. A. H. Ahsan

We investigate the emergence of correlation-driven altermagnetism in simple and extended Hubbard model on geometrically frustrated lattice-clusters using exact diagonalization. By systematically tuning the degree of geometric frustration across different cluster geometries -- including the fully frustrated 3x3 torus, the partially frustrated 2x3 cylinder and the unfrustrated 2x4 cylindrical lattice -- we isolate the necessary conditions for compensated anisotropic spin order. At half-filling on 3x3 lattice, the average altermagnetic spin-response <Δ_spin> remains small despite robust local moment formation, indicating that localized moments alone are insufficient to break directional symmetry. In contrast, the introduction of a single mobile charge carrier (hole or electron) induces a finite <Δ_spin> that increases monotonically with on-site interaction U . This altermagnetic phase is characterized by a d-wave-like alternating sign structure in real-space correlations, a broad momentum-space distribution in the altermagnetic structure factor S_alm(q) and a distinct particle-hole asymmetry with significantly enhanced response for one-electron-doped system. We demonstrate that these correlations remain zero on the unfrustrated 2x4 lattice, establishing geometric frustration as a fundamental prerequisite. The inclusion of nearest-neighbor Coulomb repulsion V weakens the altermagnetic correlations in 3x3 lattice through enhanced electronic localization but facilitates the onset of altermagnetic order in 2x3 lattice beyond a critical threshold. Finally, we show that the anisotropy parameter A is non-zero only for degenerate ground states, revealing that macroscopic symmetry breaking on finite clusters requires a confluence of geometric frustration and ground-state degeneracy.