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Register a new userThermodynamics of the metal-insulator transition in the extended Hubbard model
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In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.
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We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site non-random repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et al. (arXiv:2002.07181) can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $M$ theory which generalizes the SU(2) spin symmetry to SU($M$), and obtain exponents for the electron and spin correlators which agree with those of Cha et al. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small $U$.
In this work we study the two-orbital Hubbard model on a square lattice in the presence of hybridization between nearest-neighbor orbitals and a crystal-field splitting. We use a highly reliable numerical technique based on the density matrix renormalization group to solve the dynamical mean field theory self-consistent impurity problem. We find that the orbital mixing always leads to a finite local density states at the Fermi energy in both orbitals when at least one band is metallic. When one band is doped, and the chemical potential lies between the Hubbard bands in the other band, the coherent quasiparticle peak in this orbital has an exponential behavior with the Hubbard interaction $U$.
To understand how charge transport is affected by a background medium and vice versa we study a two-channel transport model which captures this interplay via a novel, effective fermion-boson coupling. By means of (dynamical) DMRG we prove that this model exhibits a metal-insulator transition at half-filling, where the metal typifies a repulsive Luttinger liquid and the insulator constitutes a charge density wave. The quantum phase transition point is determined consistently from the calculated photoemission spectra, the scaling of the Luttinger liquid exponent, the charge excitation gap, and the entanglement entropy.
In this article, we discuss the non-trivial collective charge excitations (plasmons) of the extended square-lattice Hubbard model. Using a fully non-perturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly-correlated phase. The momentum-resolved charge susceptibility is also computed on the basis of the Euclidean charge density-density correlator. In agreement with previous EDMFT studies, we find that at large strength of the electron-electron interaction, the plasmon dispersion develops two branches.
We study the phase diagram of the frustrated $t{-}t^prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {it ansatz} can be achieved both at weak and strong coupling. We present the evidence that an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^prime/t$.
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