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arXiv:1611.00047 · Physical Review Letters

Localization of Interacting Dirac Fermions

Tianxing Ma, Lufeng Zhang, Chia‐Chen Chang, Hsiang-Hsuan Hung, Richard T. Scalettar

Published Mar 12, 2018• 46 citations
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Abstract

Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.

DOI
10.1103/physrevlett.120.116601

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Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.
Using large-scale quantum Monte Carlo simulations, the authors unbiasedly demonstrate the existence of a topological Mott insulator -- an interaction-driven topological insulator emerging from a strongly correlated Dirac semimetal. The model designed here consists of Dirac fermions and fluctuating Ising fields mediating interactions between fermions. By tuning the fluctuation strength of the Ising fields, the authors show the existence of a topological quantum phase transition between the topological Mott insulator phase and the Dirac-semimetal phase. Furthermore, the quantum critical point was found to be in the (2+1)D NNN=8 Chiral Ising universality class.
We study the quantum phase diagram of a three dimensional noninteracting Dirac semimetal in the presence of either quenched axial or scalar potential disorder, by calculating the average and the typical density of states as well as the inverse participation ratio using numerically exact methods. We show that as a function of the disorder strength a half-filled (i.e., undoped) Dirac semimetal displays three distinct ground states, namely an incompressible semimetal, a compressible diffusive metal, and a localized Anderson insulator, in stark contrast to a conventional dirty metal that only supports the latter two phases. We establish the existence of two distinct quantum critical points, which respectively govern the semimetal-metal and the metal-insulator quantum phase transitions and also reveal their underlying multifractal nature. Away from half-filling the (doped) system behaves as a diffusive metal that can undergo Anderson localization only, which is shown by determining the mobility edge and the phase diagram in terms of energy and disorder.
Disorder or sufficiently strong interactions can render a metallic state unstable, causing it to turn into an insulating one. Despite the fact that the interplay of these two routes to a vanishing conductivity has been a central research topic, a unifying picture has not emerged so far. Here, we establish that the two-dimensional Falicov-Kimball model, one of the simplest lattice models of strong electron correlation, does allow for the study of this interplay. In particular, we show that this model at particle-hole symmetry possesses three distinct thermodynamic insulating phases and exhibits Anderson localization. The previously reported metallic phase is identified as a finite-size feature due to the presence of weak localization. We characterize these phases by their electronic density of states, staggered occupation, conductivity, and the generalized inverse participation ratio. The implications of our findings for other strongly correlated systems are discussed.
Effects of electron correlations on Anderson insulators have been one of the central themes for recent two decades, suggesting that the Anderson insulating phase turns into a novel insulating state referred to as many body localization (MBL). However, the role of spin degrees of freedom in this dynamical phase transition still remains unclarified as a function of the interaction strength. In this study, we perform real-space spin-resolved Hartree-Fock-Anderson simulations to investigate metal-insulator transitions above a critical disorder strength in three spatial dimensions, where all single-particle states are Anderson-localized without interactions. Here, relatively weak correlations below the Mott regime are taken into account in the mean-field fashion but disorder effects are introduced essentially exactly. We find two types of single-particle mobility edges, where the multifractal spectrum of the interaction-driven low-energy mobility edge deviates from that of the high-energy one smoothly connected with the multifractal spectrum of the metal-insulator transition without interactions. We show that the weakly interacting insulating phase remains to be a paramagnetic Anderson insulating state up to the temperature of the order of the band width. On the other hand, we uncover that the relatively strongly interacting insulating phase still below the Mott regime is ferromagnetic, which turns into a ferromagnetic metallic state at a critical temperature much lower than the order of the bandwidth. Based on all these results, we propose a quantum phase transition from a paramagnetic Anderson insulating state to a ferromagnetic MBL insulating phase via an intermediate ferromagnetic metallic state, which intervenes between these two insulators at the Fermi energy.
The topological Anderson and Mott insulators are two phases that have so far been separately and widely explored beyond topological band insulators. Here we combine the two seemingly different topological phases into a system of spin-1/2 interacting fermionic atoms in a disordered optical lattice. We find that the topological Anderson and Mott insulators in the noninteracting and clean limits can be adiabatically connected without gap closing in the phase diagram of our model. Lying between the two phases, we uncover a disordered correlated topological insulator, which is induced from a trivial band insulator by the combination of disorder and interaction, as the generalization of topological Anderson insulators to the many-body interacting regime. The phase diagram is determined by computing various topological properties and confirmed by unsupervised and automated machine learning. We develop an approach to provide a unified and clear description of topological phase transitions driven by interaction and disorder. The topological phases can be detected from disorder-/interaction-induced edge excitations and charge pumping in optical lattices.
By performing exact quantum Monte Carlo simulations of a model of interacting Dirac Fermions with staggered potential, we reveal a novel intermediate phase where the electronic correlations drive a band insulator metallic, and at a larger interaction, drive the metal-to-Mott insulator. We also show that the Mott insulating phase is antiferromagnetic. A complete phase diagram is achieved by studying the phase transitions at large staggered potential and interaction strengths, which shows that the intermediate state is robust and occupies a large part of the phase diagram and that it should be more feasible to be detected experimentally.