Material scientists and condensed matter physicists have long been divided on the issue of choosing the conceptual framework for explaining why open-shell transition-metal oxides tend to be insulators, whereas otherwise successful theories such as DFT often predict them to be (false) metals. Strong correlation becomes the recommended medicine. We point out that strong correlation can be mitigated by allowing DFT to lower the energy by breaking structural, magnetic or dipolar symmetries. Such local motifs are observed experimentally by local probes beyond the 'average structure' determined by X-Ray diffraction. Observed broken symmetries can arise from slow fluctuations that persist over the observation time or longer. The surprising fact is that when symmetry breaking motifs are used as input to electronic structure calculations, false metals are converted into real insulators without the recommended medicine of strong correlation. Consistently, DFT calculations that show energy lowering symmetry breaking correct most cases where DFT, even with advanced exchange-correlation functionals, previously missed the correct metal vs insulator designation. Total energy calculations distinguish systems that support energy-lowering symmetry breaking from those that do not. This approach distinguishes between paramagnetic insulating and metallic phases and shows mass enhancement in Mott metals. The reason is that symmetry breaking removes many of the degeneracies that exist in a symmetry-unbroken system, reducing significantly the need for strong correlation. If one chooses to ignore symmetry breaking, the persistent degeneracies often call for strong correlation treatment. Thus, symmetry breaking transforms strong to normal correlation and false metals to true insulators. This view sheds light on the historic controversy between Mott and Slater that still reverberates today.
Material scientists and condensed matter physicists have long been divided on the issue of choosing the conceptual framework for explaining why open-shell transition-metal oxides tend to be insulators, whereas otherwise successful theories such as DFT often predict them to be (false) metals. Strong correlation becomes the recommended medicine. We point out that strong correlation can be mitigated by allowing DFT to lower the energy by breaking structural, magnetic or dipolar symmetries. Such local motifs are observed experimentally by local probes beyond the 'average structure' determined by X-Ray diffraction. Observed broken symmetries can arise from slow fluctuations that persist over the observation time or longer. The surprising fact is that when symmetry breaking motifs are used as input to electronic structure calculations, false metals are converted into real insulators without the recommended medicine of strong correlation. Consistently, DFT calculations that show energy lowering symmetry breaking correct most cases where DFT, even with advanced exchange-correlation functionals, previously missed the correct metal vs insulator designation. Total energy calculations distinguish systems that support energy-lowering symmetry breaking from those that do not. This approach distinguishes between paramagnetic insulating and metallic phases and shows mass enhancement in Mott metals. The reason is that symmetry breaking removes many of the degeneracies that exist in a symmetry-unbroken system, reducing significantly the need for strong correlation. If one chooses to ignore symmetry breaking, the persistent degeneracies often call for strong correlation treatment. Thus, symmetry breaking transforms strong to normal correlation and false metals to true insulators. This view sheds light on the historic controversy between Mott and Slater that still reverberates today.
Abstract: The metal–insulator transition (MIT) constitutes one of the most profound and persistent problems in condensed matter physics, sitting at the intersection of electronic structure theory, many-body physics, and emergent quantum phenomena. Conventional band theory, which successfully classifies materials as metals or insulators according to the filling of their electronic bands, fails dramatically when confronted with a class of compounds transition metal oxides chief among them that ought to be metallic by band-counting arguments yet are robustly insulating in the laboratory. The resolution of this paradox required abandoning the independent-electron picture entirely and recognizing that strong Coulomb repulsion between electrons can, by itself, drive localization. This insight, formalized by Mott and later distilled into the Hubbard model, established correlation-driven insulation as a phenomenon distinct from band insulation. The present paper offers a theoretical exploration of the MIT problem, tracing its conceptual development from the Mott criterion through the Hubbard Hamiltonian, the Brinkman–Rice scenario of quasiparticle mass divergence, and the watershed development of dynamical mean-field theory (DMFT), which rendered the Mott transition quantitatively tractable for the first time. We argue that the competition between the electronic bandwidth and the on-site interaction encoded in the ratio U/W provides the unifying organizing principle for the field. Building toward the modern frontier, we examine how the Mott transition connects to quantum phase transitions and quantum criticality, where zero-temperature instabilities governed by quantum rather than thermal fluctuations produce non-Fermi-liquid behavior and anomalous scaling. Case studies of vanadium oxides, rare-earth nickelates, and doped cuprates illustrate the diversity and subtlety of real correlated materials. We conclude that the MIT remains a central and unresolved problem whose continued study is increasingly entangled with the development of quantum materials and quantum technologies. Keywords: Metal–Insulator Transition; Mott Insulator; Strongly Correlated Electrons; Hubbard Model; DMFT; Quantum Criticality; Quantum Materials; Condensed Matter Physics
Numerous transition-metal oxides have low-temperature, long-range-ordered antiferromagnetic (AFM) states that are generally insulating, and high-temperature, disordered paramagnetic (PM) phases. The latter can be either insulating (predicted here for NaFeO3), or metallic (predicted here and previously observed in NaOsO3). Similar distinctions have been traditionally affected in strongly correlated models by the value used for Coulomb repulsion U. Here we show an alternative, strong-correlation-free (U=0) view suggesting that the distinction between insulating and metallic PM phases is governed by the competition between local magnetic moment disorder and the polymorphous distribution of off-center atomic displacements. Such parameter-free, energy-lowering symmetry breaking density functional calculations provide a framework for understanding metal-insulator behaviors across different quantum materials in terms of measurable local structural and magnetic parameters.
In the widely-used Kohn-Sham density functional theory for the manyelectron ground state, only the density functional for the exchange-correlation energy is approximated. While the exact density functional minimizes at the exact ground-state energy for any system, widely used approximations can at best describe normally-correlated ground states. A “proper” approximation for a given problem is defined as one that well describes relevant normally-correlated states. Strong correlation, present in many quantum materials, can arise due to abnormally high degeneracy of the Kohn-Sham occupied and unoccupied one-electron energies near the Fermi level. In such situations, the approximate functional may lower its energy by spontaneously breaking symmetries that the ground-state density shares with the many-electron Hamiltonian, reducing the degeneracies that lead to strong correlation. Here the Levy constrained search is invoked to argue that the total energy of a “proper” functional with maximal spontaneous symmetry breaking is bounded from below by the exact total energy, and that the bound may be close to the extent that the abnormal degeneracies are removed. This is a consequence of a variational principle, and it may not hold in non-variational but more accurate approaches to normal correlation such as coupled cluster theory. Since the correlation energy of any one-electron state is zero, a widely “proper” approximate functional should be nearly or exactly self-interaction free, and progress toward a proper self-interaction correction is reviewed here. The time-centered physical interpretation of symmetry breaking is also discussed.
Addressing the many-body electronic-structure problem is a central goal of modern condensed-matter physics. Paramagnetic Mott insulators, in particular, have long represented a challenge for standard approaches, such as density-functional theory. Historically, these systems have been tackled either by considering many-body dynamics, as in the case of dynamical mean-field theory (DMFT), or, more recently, by invoking a polymorphous description consisting of large supercells populated with static symmetry-broken motifs whose spatial average restores the paramagnetic state. Inspired by these viewpoints, we introduce the on-site dephased ensemble (DE) approximation, in which the local electronic-structure problem is described by a thermal ensemble of all accessible local static solutions; this gives rise to a strong frequency dependence of the local electronic self-energy, as seen in DMFT or in the coherent-potential approximation of disordered alloys. We show that the DE successfully recovers defining hallmarks of strongly correlated Mott systems, both in terms of the self-energy as well as the persistence of local moments in time, in quantitative agreement with DMFT. By bypassing expensive quantum Monte Carlo solvers or large supercell calculations, this approach offers efficient routes to treating paramagnetic Mott systems in a first-principles setting, and highlights a deeper connection between the physics of strong correlations and that of disorder.
Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.