We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical Uc1 and remains zero within a metallic phase. At a larger Uc2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but nonzero insulating gap for all finite U.
We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical Uc1 and remains zero within a metallic phase. At a larger Uc2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but nonzero insulating gap for all finite U.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.
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
We study a model of a covalent band insulator with on-site Coulomb repulsion at half filling using dynamical mean-field theory. Upon increasing the interaction strength the system undergoes a discontinuous transition from a correlated band insulator to a Mott insulator with hysteretic behavior at low temperatures. Increasing the temperature in the band insulator close to the insulator-insulator transition we find a crossover to a Mott insulator at elevated temperatures. Remarkably, correlations decrease the energy gap in the correlated band insulator. The gap renormalization can be traced to the low-frequency behavior of the self-energy, analogously to the quasiparticle renormalization in a Fermi liquid. While the uncorrelated band insulator is characterized by a single gap for both charge and spin excitations, the spin gap is smaller than the charge gap in the correlated system.
We investigate the ground state phase diagram of the half-filled repulsive Hubbard model in two dimensions in the presence of a staggered potential Delta, the so-called ionic Hubbard model, using cluster dynamical mean-field theory. We find that for large Coulomb repulsion, U >> Delta, the system is a Mott insulator (MI). For weak to intermediate values of Delta, on decreasing U, the Mott gap closes at a critical value Uc1(Delta) beyond which a correlated insulating phase with possible bond order is found. Further, this phase undergoes a first-order transition to a band insulator (BI) at Uc2(Delta) with a finite charge gap at the transition. For large Delta, there is a direct first-order transition from a MI to a BI with a single metallic point at the phase boundary.
In this thesis, several aspects of correlation effects in band insulators that were hitherto not addressed, both in equilibrium and non-equilibrium, are studied using the Ionic Hubbard model (IHM) at half-filling and Dynamical mean-field theory (DMFT). The IHM is an extension of the Hubbard model on a bipartite lattice with a staggered on-site “ionic potential Δ added in. The Hubbard model by itself is a tight-binding model of electrons hopping between (orbitals localized on) lattice sites, with amplitudes t and t’ for first neighbor and second neighbor hopping respectively, together with a coulomb repulsion energy cost of U for double occupancy (i.e., with both up and down spin electrons) at any lattice site. The studies in this thesis address strong correlation effects in this model using DMFT techniques which map the lattice problem to a self consistently embedded quantum impurity problem. The impurity problem itself is solved using state of the art continuous time quantum monte-carlo (CTQMC) techniques (Ch.s 3 and 4) as well as the somewhat simpler Iterated Perturbation Theory (IPT) (Ch.s 3, 5 and 6).
Chapter 3 of the thesis is devoted to a detailed analysis of the properties of the half-filled t-U-Δ IHM (i.e., with t’=0) on a Bethe lattice of infinite connectivity. It is shown conclusively here that for a finite Δ and at zero temperature (T=0), the IHM has a first order transition from the Band Insulator (BI) phase to an antiferromagnetic insulating (AFI) phase at a threshold U = UAF (which increases with Δ) such that the BI to AFI transition preempts the transition from the BI to the correlation induced paramagnetic metallic (PM) phase. Evidence is also presented for a quantum transition to a sliver of half-metal (HM) phase just after the AF order turns on, followed by a return to the AFI phase on further increasing U. With increasing T, the AF order is lost via a first-order transition for weak to intermediate U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, the transition from the AFI to the paramagnetic Mott insulating phase (adiabatically connected to the BI phase) is of second order. As T increases, the range of U over which the AF order is stable shrinks, collapsing eventually to a line of tricritical points that separates the surfaces of first- and second-order phase transitions in the T-U-Δ space.
In Chapter 4 of the thesis the t-t’-U-Δ IHM on a square lattice is studied using DMFT+CTQMC. It is shown here that the presence of t’ frustrates the AF order for weak to intermediate correlations, resulting in the stabilization of the correlation induced PM phase over a broad region of the parameter space, although the AFI is always the stable phase for large enough U. In the intermediate coupling regimes, two other interesting phases show up as a result of the competition among U, Δ and t’ : a Ferrimagnetic metallic (FM) phase which has non-zero values of the uniform as well as staggered magnetization; and even more interesting, an…
Correlated electrons in a binary alloy ${A}_{x}{B}_{1\ensuremath{-}x}$ are investigated within the Hubbard model and dynamical mean-field theory (DMFT). The random energies ${\ensuremath{\epsilon}}_{i}$ have a bimodal probability distribution and an energy separation $\ensuremath{\Delta}.$ We solve the DMFT equations by the numerical renormalization-group method at zero temperature and calculate the spectral density as a function of disorder strength $\ensuremath{\Delta}$ and interaction U at different fillings. For filling factors $\ensuremath{\nu}=x$ or 1+x the lower or upper alloy subband is half filled and the system becomes a Mott insulator at strong interactions, with a correlation gap at the Fermi level. At the metal-insulator transition hysteresis is observed. We also analyze the effective theory in the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty}$ limit and find good agreement between analytical and numerical results for the critical interaction Uc at which the metal-insulator transition occurs.