We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first-order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in
d=3 spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices in $d\ensuremath{\geqslant}2$. In a given realization, the hopping disorder breaks time-reversal invariance but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low-energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein nonlinear sigma model $(\mathrm{FNL}\ensuremath{\sigma}\mathrm{M})$ (A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983) [Sov. Phys. JETP 57, 97 (1983)]). We analyze the $\mathrm{FNL}\ensuremath{\sigma}\mathrm{M}$ using a perturbative, one-loop renormalization group analysis controlled via an
ϵ expansion in
d=2+ϵ dimensions. We find that in
d=2 dimensions, the interactions destabilize the conducting phase known to exist in the disordered, noninteracting system. The metal-insulator transition that we identify in
d>2 dimensions
(ϵ>0) occurs for disorder strengths of order
ϵ, and is therefore perturbatively accessible for
ϵ⪡1. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase and the transition into it can only appear due to the presence of the interactions.
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
U. 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
M theory, which generalizes the SU(2) spin symmetry to
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
U.
We study the effects of generic short-ranged interactions on a system of two-dimensional (2D) Dirac fermions subject to a special kind of static disorder, often referred to as ``chiral.'' The noninteracting system is a member of the disorder class
BDI [M. R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)]. It emerges, for example, as a low-energy description of a time-reversal invariant tight-binding model of spinless fermions on a honeycomb lattice, subject to random hopping, and possessing particle-hole symmetry. It is known that, in the absence of interactions, this disordered system is special in that it does not localize in 2D, but possesses extended states and a finite conductivity at zero energy, as well as a strongly divergent low-energy density of states. In the context of the hopping model, the short-range interactions that we consider are particle-hole symmetric density-density interactions. Using a perturbative one-loop renormalization group analysis, we show that the same mechanism responsible for the divergence of the density of states in the noninteracting system leads to an instability, in which the interactions are driven strongly relevant by the disorder. This result should be contrasted with the limit of clean Dirac fermions in 2D, which is stable against the inclusion of weak short-ranged interactions. Our work suggests a mechanism wherein a clean system, initially insensitive to interaction effects, can be made unstable to interactions upon the inclusion of weak static disorder. We dub this mechanism a ``disorder-driven Mott transition.'' Our result for 2D fermions also contrasts sharply with known results in one dimension, where a similar delocalized phase has been shown to be robust against the inclusion of weak interaction effects.
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.
Local moment formation is ubiquitous in disordered semiconductors such as Si:P, where it is observed both in the metallic and the insulating regimes. Here, we focus on local moment behavior in disordered insulators, which arises from short-ranged, repulsive electron-electron interactions. Using density matrix renormalization group and strong-disorder renormalization group methods, we study paradigmatic models of interacting insulators: one-dimensional Hubbard chains with quenched randomness. In chains with either random fermion hoppings or random chemical potentials, both at and away from half-filling, we find exponential decay of disorder-averaged charge and fermion two-point correlations, but power-law decay of disorder-averaged spin correlations that are indicative of the random singlet phase. The numerical results can be understood qualitatively by appealing to the large-interaction limit of the Hubbard chain, in which a remarkably simple picture emerges.
We introduce a Cellular Dynamical Cluster Approximation (CDCA) to study the nature of the Mott insulator-metal transition in the extended Hubbard model on a square lattice. At strong coupling, a d-wave Mott insulator is obtained. Hole doping drives a first order Mott transition to a non-Fermi (nFL) liquid metal. Remarkably, this nFL is caused by an Anderson orthogonality catastrophe at low energies due to the non-trivial competition between strong, non-local interactions and hopping. This constitutes the first explicit realisation of Anderson's Luttinger liquid idea in two dimensions. Many experimental responses in the ``strange metal'' phase found around optimal doping in cuprates are understood naturally within our approach.