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arXiv:2008.09714 · Physical review. B./Physical review. B

Anderson localization effects on the doped Hubbard model

Nathan Giovanni, Marcello Civelli, Maria C. O. Aguiar

Published Jun 23, 2021• 6 citations
arXivHTMLPDF

Abstract

We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.

DOI
10.1103/physrevb.103.245134

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We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.
The interplay between Mott and Anderson routes to localization in disordered interacting systems gives rise to different transitions and transport regimes. Here, we investigate the phase diagram at finite temperatures using dynamical mean-field theory combined with typical medium theory, which is an effective theory of the Mott-Anderson metal-insulator transition. We mainly focus on the properties of the coexistence region associated with the Mott phase transition. For weak disorder, the coexistence region is found to be similar to that in the clean case. However, as we increase disorder, Anderson localization effects are responsible for shrinking the coexistence region, and at sufficiently strong disorder (approximately equal to twice the bare bandwidth) it drastically narrows, the critical temperature Tc{T}_{c}Tc​ abruptly goes to zero, and we observe a phase transition in the absence of a coexistence of the metallic and insulating phases. In this regime, the effects of interaction and disorder are found to be of comparable importance for charge localization.
We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion UUU and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude ttt. We identify three different phases as functions of the disorder amplitude WWW and Coulomb interaction strength U>0U>0U>0. When U<4tU<4tU<4t the system shows a metallic phase: (i) only when no disorder is present W=0W=0W=0 or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When U>4tU>4tU>4t the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.
We study the Anderson-Hubbard model to examine the interplay between the disordered potential and the Hubbard interactions. We use the dynamical mean-field theory (DMFT) with an exact diagonalization as an impurity solver to effectively deal with the quantum fluctuations due to the local interactions. In order to characterize the paramagnetic metal-insulator transition in disordered systems, we compute the typical local density of states, as well as the arithmetically-averaged local density of states. Our approach is found to reproduce the characteristic features of the metal-insulator transition in infinite dimensions, such as the existence of the disorder-driven metallic phase for moderate values of disorder strength and interactions, as observed in earlier studies. In two dimensions, the system turns out to exhibit more insulating behavior when we increase the cluster size in the cellular DMFT. The metallic phase, which is induced from weak Mott insulators by the introduction of a disordered potential, is not observed in two dimensions.
Abstract We consider Anderson localization in the half-filled Anderson–Hubbard model in the presence of either random on-site interactions or spatially alternating interactions in the lattice. By using dynamical mean field theory with the equation of motion method as an impurity solver, we calculate the arithmetically and geometrically averaged local density of states and derive the equations determining the critical value for the phase transition between metallic, Anderson and Mott insulating phases. The nonmagnetic ground state phase diagrams are constructed numerically. We figure out that the presence of Coulomb disorder drives the system toward the Anderson localized phase that can occur even in the absence of Anderson structural disorder. For the spatially alternating interactions, we find that the metallic region is reduced and the Anderson insulator one is enlarged with increasing interaction modulation. Our obtained results are relevant to current research in ultracold atoms in disordered optical lattices where metal–insulator transition can be observed experimentally by using ultracold atom techniques.
We review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the dynamical mean-field theory (DMFT), to interacting disordered lattice fermions. In particular, we demonstrate that DMFT combined with geometric averaging over disorder can capture Anderson localization and Mott insulating phases on the level of one-particle correlation functions. Results are presented for the ground state phase diagram of the Anderson–Hubbard model at half-filling, both in the paramagnetic phase and in the presence of antiferromagnetic order. We find a new antiferromagnetic metal which is stabilized by disorder. Possible realizations of these quantum phases with ultracold fermions in optical lattices are discussed.