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Physical review. B, Condensed matter

Renormalization-group study of the Anderson-Hubbard model

Michael Ma

Published Nov 1, 1982• 69 citations
Publisher

Abstract

We study the half-filled Hubbard model with random on-site energies with the use of a real-space renormalization group. For $d=1$, we find a transition from an Anderson insulator to a Hubbard insulator as the Hubbard $U$ is increased. We find no metallic phase. For $d=3$, we find a metallic phase which, surprisingly, is stabilized against Anderson localization by a small Hubbard $U$.

DOI
10.1103/physrevb.26.5097

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We study the half-filled Hubbard model with random on-site energies with the use of a real-space renormalization group. For d=1d=1d=1, we find a transition from an Anderson insulator to a Hubbard insulator as the Hubbard UUU is increased. We find no metallic phase. For d=3d=3d=3, we find a metallic phase which, surprisingly, is stabilized against Anderson localization by a small Hubbard UUU.
We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction UUU reaches a critical value UcU_cUc​. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.
We study the ground state of the two-dimensional Anderson-Hubbard model using a quantum real space renormalization group method. We obtain the phase diagram near half filling. The system is always insulating with disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insulator as the interaction U reaches a critical value Uc{\mathit{U}}_{\mathit{c}}Uc​. Away from half filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one-dimensional system and suggests strongly the importance of the electron-electron correlation in this gapless insulating phase.
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 nonrandom repulsion, the Hubbard UUU. 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 MMM theory, which generalizes the SU(2) spin symmetry to SU(M)\mathrm{SU}(M)SU(M) and obtains exponents for the electron and spin correlators which agree with those of Cha et al. This critical point is expected to have the maximal quantum Lyapunov exponent. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small UUU.
The tight-binding diagonally disordered Anderson model with on-site Coulomb interaction is solved in the mean-field hopping approach. Phase diagrams of the metal-insulator transition are obtained from the free energy for the half-filled band and the binary-alloy distribution. For attractive interaction (U<0), the Coulomb term gives additional localizing effect and for some values of the microscopic parameters the temperature induced two transitions (insulator to metal to insulator). For U>0 two different types of behavior are distinguished. For small disorder (W\ensuremath{\le}U/2), the metallic phase can be induced by disorder, while for large W, the disorder always destroys the phase of extended states.
The ground state of the half-filled Hubbard model is studied using a real-space renormalization-group technique. We first study in detail the one-dimensional case. We find the ground state to be insulating for all finite coupling, in agreement with the exact solution. We compute the ground-state energy, localization length, energy gap, magnitude of the local moment, and spin-density autocorrelation function. For those quantities that are exactly known we find good agreement with the exact results. Using a simple extension of our one-dimensional calculation, we are able to study approximately two- and three-dimensional lattices. We find a Mott transition at finite interaction for these cases. The critical exponents for these transitions are found to satisfy an approximate interdimensional scaling law.
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.