Quantum phase transitions in strongly correlated electron materials are one of the most intriguing phenomena in condensed matter physics. In fact, the rich phase-diagrams of these systems usually allow for the presence of several quantum phase transitions. At the same time, a comprehensive theoretical description of the quantum critical properties of correlated electrons has been not fully developed yet. For one of the most fundamental model in solid state physics, the 3D Hubbard model, quantum critical behaviour appears to violate the conventional Hertz-Millis- Moriya theory. This unexpected finding has been ascribed to the presence of specific features on the Fermi surface (FS), such as Kohn points and/or lines. If this is the case, the correct description of 3D correlated metal should be already accessible by means of Dynamical Mean Field Theory (DMFT) calculations. DMFT, in fact, preserves the information about the FS geometry and correctly captures temporal fluctuations, crucial for the description of quantum criticality. The main aim of this work is to test the hypothesis that DMFT treatment is sufficient to describe the quantum critical behaviour of 3D correlated metals, without resorting to more advanced (and much heavier!) quantum many-body schemes. Our DMFT results for the hole-doped 3D-Hubbard model have allowed to determine the location of the quantum-critical point of the magnetic transition and to highlight promising trends for the associated quantum critical exponents.
Quantum phase transitions in strongly correlated electron materials are one of the most intriguing phenomena in condensed matter physics. In fact, the rich phase-diagrams of these systems usually allow for the presence of several quantum phase transitions. At the same time, a comprehensive theoretical description of the quantum critical properties of correlated electrons has been not fully developed yet. For one of the most fundamental model in solid state physics, the 3D Hubbard model, quantum critical behaviour appears to violate the conventional Hertz-Millis- Moriya theory. This unexpected finding has been ascribed to the presence of specific features on the Fermi surface (FS), such as Kohn points and/or lines. If this is the case, the correct description of 3D correlated metal should be already accessible by means of Dynamical Mean Field Theory (DMFT) calculations. DMFT, in fact, preserves the information about the FS geometry and correctly captures temporal fluctuations, crucial for the description of quantum criticality. The main aim of this work is to test the hypothesis that DMFT treatment is sufficient to describe the quantum critical behaviour of 3D correlated metals, without resorting to more advanced (and much heavier!) quantum many-body schemes. Our DMFT results for the hole-doped 3D-Hubbard model have allowed to determine the location of the quantum-critical point of the magnetic transition and to highlight promising trends for the associated quantum critical exponents.
We investigate magnetic quantum phase-transitions in bulk correlated metals. To this end, we focus on the Hubbard model on different cubic lattices as a function of temperature and electronic density, determining the relevant regimes around its quantum magnetic transition, i.e. classical, quantum critical, and quantum disordered, as well as the corresponding (thermal/non-thermal) quantum critical exponents. Our numerical results, based on dynamical mean-field theory, together with supporting analytical derivations, rigorously demonstrate how and why the presence of different kinds of Kohn anomalies on the underlying Fermi surface (i) drives the quantum critical behavior above the quantum critical point and (ii) shapes the whole phase diagram around it. Our findings highlight the importance of an explicit inclusion of such Fermi surface geometrical properties into the universality class definition for magnetic quantum phase-transitions in correlated metals.
A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that-in contradiction to the conventional Hertz-Millis-Moriya theory-its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electronic correlations become strong.
Almost 50 years after the invention of the Hubbard model [1–3] and despite modern petaflop supercomputers, a precise analysis of the criticality of this most basic model for electronic correlations has not been achieved so far, at least not in three dimensions. Dynamical mean field theory (DMFT) [4–6] was a big step forward to quantitatively calculate the three dimensional Hubbard model since the major contribution of electronic correlations, i.e., the local ones, are well captured within this theory. Local correlations give rise to quasiparticle renormalization, the Mott-Hubbard transition, magnetism, and even more subtle issues such as kinks in a purely electronic models [7]. However, non-local spatial correlations are also naturally generated by a purely local Hubbard interaction, and, as it is well known, they become of essential importance in the vicinity of secondorder phase transitions. As these correlations are neglected in DMFT, this scheme can provide only for a conventional mean-field (MF) description of the critical properties. To overcome this shortcoming cluster extensions to DMFT such as the dynamical cluster approximation (DCA) and cluster-DMFT have been proposed, see Ref. 8 for a review. In these approaches non-local correlations beyond DMFT are taken into account, however only within the range of the cluster size; and due to computational limitations the actual size of the cluster is severely restricted to about 3-5 sites for each direction. Hence, short-range correlations are included by these approaches, whereas long-range ones are not. Nonetheless, Kent et al. [9] were able to extrapolate the cluster size of so-called Betts clusters to infinity, albeit assuming from the very beginning the critical exponents to be those of the Heisenberg model. This way they extrapolated the critical temperature of the paramagnetic-toantiferromagnetic phase transition which was found to be in agreement with earlier quantum Monte Carlo (QMC) simulations of Staudt et al. [10] on finite lattices.
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
Dynamical Mean-Field Theory (DMFT) has opened new perspectives for the investigation of strongly correlated electron systems and greatly improved our understanding of correlation effects in models and materials. In contrast to Hartree-Fock-type approximations the mean field of DMFT is dynamical, whereby local quantum fluctuations are fully taken into account. DMFT becomes exact in the limit of high spatial dimensions or coordination number. Using DMFT the dynamics of correlated electron systems can be investigated non-perturbatively at all interaction strengths, electron densities and temperatures. By merging density functional theory with DMFT a powerful method for the calculation of the properties of correlated electron materials has become available, which is applicable to bulk systems and heterostructures, including topological states of matter. The inclusion of non-local correlations into DMFT makes it possible to explore unconventional superconductivity and the critical behavior at thermal or quantum phase transitions. By generalizing DMFT to non-equilibrium states also the real-time dynamics of correlated systems can be investigated. In this brief review the foundations and current status of DMFT are discussed along with characteristic physical insights obtained with this approach.
A new approach is proposed which encompasses the dynamical mean field theory (DMFT) for strongly correlated electron systems and the self-consistent renormalization (SCR) theory of spin fluctuations. The latter is incorporated into DMFT as a O(1/d) correction, where d is the spatial dimensionality, but in a phenomenological way. The DMFT is completely recovered when the effect of spin fluctuation is omitted, whereas the properties at the quantum critical point (QCP) is the same as the SCR theory. An example of calculation is presented for the single band Hubbard model and the non-Fermi liquid behavior is demonstrated at QCP.