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arXiv:1608.06866 · Physical review. B./Physical review. B

Anderson-Mott transition in a disordered Hubbard chain with correlated hopping

Francesca Battista, Alberto Camjayi, Liliana Arrachea

Published Jul 12, 2017• 4 citations
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Abstract

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 $U$ 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 $t$. We identify three different phases as functions of the disorder amplitude $W$ and Coulomb interaction strength $U>0$. When $U<4t$ the system shows a metallic phase: (i) only when no disorder is present $W=0$ or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When $U>4t$ 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.

DOI
10.1103/physrevb.96.045413

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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)(\ensuremath{-}W,+W)(\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≠0W\ensuremath{\ne}0W\ensuremath=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.
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We study the interplay between electron correlation and disorder in the two-dimensional Hubbard model at half filling by means of a variational wave function that can interpolate between Anderson and Mott insulators. We give a detailed description of our improved variational state and explain how the physics of the Anderson-Mott transition can be inferred from equal-time correlations functions, which can be easily computed within the variational Monte Carlo scheme. The ground-state phase diagram is worked out in both the paramagnetic and the magnetic sector. Whereas in the former a direct second-order Anderson-Mott transition is obtained, when magnetism is allowed variationally, we find evidence for the formation of local magnetic moments that order before the Mott transition. Although the localization length increases before the Mott transition, we have no evidence for the stabilization of a true metallic phase. The effect of a frustrating next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ is also studied in some detail. In particular, we show that ${t}^{\ensuremath{'}}$ has two primary effects. The first one is the narrowing of the stability region of the magnetic Anderson insulator, also leading to a first-order magnetic transition. The second and most important effect of a frustrating hopping term is the development of a ``glassy'' phase at strong couplings, where many paramagnetic states, with disordered local moments, may be stabilized.
In this thesis we consider a variational wave function approach as a possible route to describe the competition between disorder and strong electron-electron interaction in two dimensions. In particular we aim to obtain a transparent and physically intuitive understanding of the competition between these two localizing forces within the simplest model where they both are active, namely the disordered Hubbard model at half filling and in a square lattice. Our approach is based on an approximate form of the ground-state wave function, which we believe contains the physically relevant ingredients for a correct description of both the Mott and the Anderson insulators, where electrons are localized by the Coulomb repulsion and by disorder, respectively. For strongly interacting fermionic systems, a standard variational wave function is constructed by a correlation term acting on a Slater determinant, the latter being an uncorrelated metallic state. Previous variational calculations showed that a long-range density-density correlation factor, so called Jastrow factor, is needed to correctly describe the Mott insulator [9]. This term, which is collective by definition, correlates spatially charge uctuations, thus preventing their free motion that would otherwise imply metallic conductance. For this reason, our variational wave function does include such a term. Anderson localization is instead mostly a matter of single-particle wave functions, hence it pertains to the uncorrelated Slater determinant which the Jastrow factor acts onto. We consider both the case in which we enforce paramagnetism in the wave function and the case in which we allow for magnetic ordering. Summarizing briefly our results, we find that, when the variational wave function is forced to be paramagnetic, the Anderson insulator to Mott insulator transition is continuous. This transition can be captured by studying several quantities. In particular, a novel one that we have identified and that is easily accessible variationally is the disconnected density-density fluctuation at long wavelength, defined by lim where ^nq is the Fourier transform of the charge density at momentum q, (...) denotes quantum average at fixed disorder and the overbar represents the average over disorder configurations. We find that Ndisc q!0 is everywhere finite in the Anderson insulator and vanishes critically at the Mott transition, staying zero in the Mott insulator. When magnetism is allowed and the hopping only connects nearest neighbor sites, upon increasing interaction the paramagnetic Anderson insulator first turns antiferromagnetic and finally the magnetic and compressible Anderson insulator gives way to an incompressible antiferromagnetic Mott insulator. The optimized uncorrelated Slater determinant is always found to be the eigenstate of a disordered non-interacting effective Hamiltonian, which suggests that the model is never metallic. Finally, when magnetism is frustrated by a next to nearest neighbor hopping, the overall sequence of phases does not change. However, the paramagnetic to magnetic transition within the Anderson insulator basin of stability turns first order. Indeed, within the magnetically ordered phase, we find many almost degenerate paramagnetic states with well defined local moments. This is suggestive of an emerging glassy behavior when the competition between disorder and strong correlation is maximum.
Interplay of electron correlation and randomness is studied by using the Anderson-Hubbard model within the Hartree-Fock approximation. Under the coexistence of short-range interaction and diagonal disorder, we obtain the ground-state phase diagram in three dimensions, which includes an antiferromagnetic insulator, an antiferromagnetic metal, a paramagnetic insulator (Anderson-localized insulator) and a paramagnetic metal. Although only the short-range interaction is present in this model, we find unconventional soft gaps in the insulating phases irrespective of electron filling, spatial dimensions and long-range order, where the single-particle density of states (DOS) vanishes with a power-law scaling in one dimension (1D) or even faster in two dimensions (2D) and three dimensions (3D) toward the Fermi energy. We call it soft Hubbard gap. Moreover, exact-diagonalization results in 1D support the formation of the soft Hubbard gap beyond the mean-field level. The formation of the soft Hubbard gap cannot be attributed to a conventional theory by Efros and Shklovskii (ES) owing the emergence of soft gaps to the long-range Coulomb interaction. Indeed, based on a picture of multivalley energy landscape, we propose a phenomenological scaling theory, which predicts a scaling of the DOS in perfect agreement with the numerical results. We further discuss a correction of the scaling of the DOS by the long-range part of the Coulomb interaction, which modifies the scaling of Efros and Shklovskii. Furthermore, explicit formulae for the temperature dependence of the DC resistivity via variable-range hopping under the influence of the soft gaps are derived. Finally, we compare the present theory with experimental results of SrRu_{1-x}Ti_xO_3.
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Abstract We study the half-filled Hubbard model with Anderson and Coulomb disorder by mean of dynamical mean field theory using the geometrically averaged local density of states. The paramagnetic phase diagram of the model as a function of the Coulomb interaction and Anderson disorder strength is obtained. The spectral phase diagrams of the ground states for the model are also constructed and discussed. We show that in the intermediate and strong interaction regimes, the Coulomb disorder leads the metallic and Mott insulator phase regions shrink, while the Anderson insulator region is enlarged.