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arXiv:2206.03890 · Physical review. B./Physical review. B

Metal-insulator transition in the disordered Hubbard model of the Lieb lattice

Yueqi Li, Lingyu Tian, Tianxing Ma, Hai‐Qing Lin

Published Nov 28, 2022• 7 citations
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Abstract

Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transition in the interacting disordered Hubbard model of a Lieb lattice in which the system characterizes the flat band centered at the Fermi level. By choosing suitable electron densities, we ensure the weak interaction sign problem to improve the reliability of our results. It is found that disorder and on-site Coulomb repulsive interaction produce interesting effects that induce the metal-insulator transition which is impossible in the half-filled case. The density of states at the Fermi energy is still finite in the thermodynamic limit, suggesting that the system is an Anderson insulator rather than a Mott insulator. Moreover, this doping system is paramagnetic, unlike the half-filled system which is ferrimagnetic.

DOI
10.1103/physrevb.106.205149

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Using the determinant quantum Monte Carlo method, we investigate the metal-insulator transition in the interacting disordered Hubbard model of a Lieb lattice in which the system characterizes the flat band centered at the Fermi level. By choosing suitable electron densities, we ensure the weak interaction sign problem to improve the reliability of our results. It is found that disorder and on-site Coulomb repulsive interaction produce interesting effects that induce the metal-insulator transition which is impossible in the half-filled case. The density of states at the Fermi energy is still finite in the thermodynamic limit, suggesting that the system is an Anderson insulator rather than a Mott insulator. Moreover, this doping system is paramagnetic, unlike the half-filled system which is ferrimagnetic.
We study the effect of disorder and doping on the metal-insulator transition in a repulsive Hubbard model on a square lattice using the determinant quantum Monte Carlo method. First, with the aim of making our results reliable, we compute the sign problem with various parameters such as temperature, disorder, on-site interactions, and lattice size. We show that in the presence of randomness in the hopping elements, the metal-insulator transition occurs and the critical disorder strength differs at different fillings. We also demonstrate that doping is a driving force behind the metal-insulator transition.
The properties of a phase at finite interactions can be significantly influenced by the underlying dispersion of the noninteracting Hamiltonian. We demonstrate this by studying the repulsive Hubbard model on the two-dimensional Lieb lattice, which has a flat band for vanishing interaction UUU. We perform real-space dynamical mean-field theory calculations at different temperatures and dopings using a continuous-time quantum Monte Carlo impurity solver. Studying the frequency dependence of the self-energy, we find that a nonmagnetic metallic region at finite temperature displays non-Fermi-liquid behavior, which is a concomitant of the flat-band singularity. At half-filling, we also find a magnetically ordered region, where the order parameter varies linearly with the interaction strength, and a strongly correlated Mott insulating phase. The double occupancy decreases sharply for small UUU, highlighting the flat-band contribution. Away from half-filling, we observe the stripe order, i.e., an inhomogeneous spin and charge density wave of finite wavelength, which turns into a sublattice ordering at higher temperatures.
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.
While the Hubbard model is the standard model to study Mott metal-insulator transitions, it is still unclear to what extent it can describe metal-insulator transitions in real solids, where nonlocal Coulomb interactions are always present. By using a variational principle, we clarify this issue for short- and long-range nonlocal Coulomb interactions for half-filled systems on bipartite lattices. We find that repulsive nonlocal interactions generally stabilize the Fermi-liquid regime. The metal-insulator phase boundary is shifted to larger interaction strengths to leading order linearly with nonlocal interactions. Importantly, nonlocal interactions can raise the order of the metal-insulator transition. We present a detailed analysis of how the dimension and geometry of the lattice as well as the temperature determine the critical nonlocal interaction leading to a first-order transition: for systems in more than two dimensions with nonzero density of states at the Fermi energy the critical nonlocal interaction is arbitrarily small; otherwise, it is finite.
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 investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U . With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.