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The main flaw of the well-known Brinkman-Rice description, obtained through the Gutzwiller approximation, of the paramagnetic Mott transition in the Hubbard model is in neglecting high-energy virtual processes that generate, for instance, the antiferromagnetic exchange J∼t2/U. Here, we propose a way to capture those processes by combining the Brinkman-Rice approach with a variational Schrieffer-Wolff transformation, and apply this method to study the single-band metal-to-insulator transition in a Bethe lattice with infinite coordination number, where the Gutzwiller approximation becomes exact. We indeed find for the Mott transition a description very close to the real one provided by the dynamical mean-field theory, an encouraging result in view of possible applications to more involved models.

We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multiband lattice Hamiltonian without any assumption about the dynamics of the variational correlation parameters that define the Gutzwiller wave function, and which thus behave as genuine dynamical degrees of freedom that add on those of the variational uncorrelated Slater determinant. We apply the method to the standard half-filled single-band Hubbard model. We are able to recover known results, but, as a by-product, we also obtain a few other results. In particular, we show that quantum fluctuations can reproduce, almost quantitatively, the behavior of the uniform magnetic susceptibility uncovered by dynamical mean-field theory, which, though enhanced by correlations, is found to be smooth across the paramagnetic Mott transition. By contrast, the simple Gutzwiller approximation predicts that susceptibility to diverge at the transition.

We study how the non-Fermi-liquid nature of the overscreened multichannel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap Δ. We find that the low-energy spectrum in the limit Δ→0 actually does not correspond to the spectrum strictly at Δ=0. In particular, in the two-channel Kondo model, the Δ→0 ground state is an orbitally degenerate spin singlet, while it is an orbital singlet with a residual spin degeneracy at Δ=0. In addition, there are fractionalized spin-1/2 subgap excitations whose energy in units of Δ tends toward a finite and universal value when Δ→0, as if the universality of the anomalous power-law exponents that characterize the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by Δ≠0. This intriguing phenomenon can be explained by the renormalization flow toward the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi-liquid features at finite Δ: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a nonmonotonic function of temperature. The persistent subgap excitations are characteristic of the non-Fermi-liquid fixed point of the model, and thus depend on the impurity spin and the number of screening channels.

The study of photoexcited strongly correlated materials is attracting growing interest since their rich phase diagram often translates into an equally rich out-of-equilibrium behaviour. With femtosecond optical pulses, electronic and lattice degrees of freedom can be transiently decoupled, giving the opportunity of stabilizing new states inaccessible by quasi-adiabatic pathways. Here we show that the prototype Mott-Hubbard material V 2 O 3 presents a transient non-thermal phase developing immediately after ultrafast photoexcitation and lasting few picoseconds. For both the insulating and the metallic phase, the formation of the transient configuration is triggered by the excitation of electrons into the bonding a 1g orbital, and is then stabilized by a lattice distortion characterized by a hardening of the A 1g coherent phonon, in stark contrast with the softening observed upon heating. Our results show the importance of selective electron-lattice interplay for the ultrafast control of material parameters, and are relevant for the optical manipulation of strongly correlated systems.

We introduce a variational implementation of cluster perturbation theory (CPT) to address the dynamics of spin systems driven out of equilibrium. We benchmark the method with the quantum Ising model subject to a sudden quench of the transverse magnetic field across the transition or within a phase. We treat both the one-dimensional case, for which an exact solution is available, as well the two-dimensional case, for which we have to resort to numerical results. Comparison with exact results shows that the approach provides a quite accurate description of the real-time dynamics up to a characteristic timescale τ that increases with the size of the cluster used for CPT. In addition, and not surprisingly, τ is small for quenches across the equilibrium phase transition point, but can be quite larger for quenches within the ordered or disordered phases.

The quantum physics of ions and electrons behind low-energy spectra of strongly correlated molecular conductors, superconductors and Mott insulators is poorly known, yet fascinating especially in orbitally degenerate cases. The fulleride insulator Cs3C60 (A15), one such system, exhibits infrared (IR) spectra with low temperature peak features and splittings suggestive of static Jahn-Teller distortions with a breakdown of orbital symmetry in the molecular site. That is puzzling, since there is no detectable static distortion, and because the features and splittings disappear upon modest heating, which they should not. Taking advantage of the Mott-induced collapse of electronic wavefunctions from lattice-extended to nanoscale localized inside a caged molecular site, we show that the unbroken spin and orbital symmetry of the ion multiplets explains the IR spectrum without adjustable parameters. This demonstrates the importance of a fully quantum treatment of nuclear positions and orbital momenta in the Mott insulator sites, dynamically but not statically distorted. The observed demise of these features with temperature is explained by the thermal population of a multiplet term whose nuclear positions are essentially undistorted, but whose energy is very low-lying. That term is in fact a scaled-down orbital excitation analogous to that of other Mott insulators, with the same spin 1/2 as the ground state, but with a larger orbital momentum of two instead of one.

Mott insulators are "unsuccessful metals" in which Coulomb repulsion prevents charge conduction despite a metal-like concentration of conduction electrons. The possibility to unlock the frozen carriers with an electric field offers tantalizing prospects of realizing new Mott-based microelectronic devices. Here we unveil how such unlocking happens in a simple model that shows the coexistence of a stable Mott insulator and a metastable metal. Considering a slab subject to a linear potential drop, we find, by means of the dynamical mean-field theory, that the electric breakdown of the Mott insulator occurs via a first-order insulator-to-metal transition characterized by an abrupt gap collapse in sharp contrast to the standard Zener breakdown. The switch on of conduction is due to the field-driven stabilization of the metastable metallic phase. Outside the region of insulator-metal coexistence, the electric breakdown occurs through a more conventional quantum tunneling across the Hubbard bands tilted by the field. Our findings rationalize recent experimental observations and may offer a guideline for future technological research.

We show that the inclusion of nonlocal correlation effects in a variational wave function for the ground state of a topological Anderson lattice Hamiltonian is capable of describing both topologically trivial insulating phases and nontrivial ones characterized by an indirect gap, as well as its closure at the transition into a metallic phase. The method, though applied to an oversimplified model, thus captures the metallic and insulating states that are indeed observed in a variety of Kondo semiconductors, while accounting for topologically nontrivial band structures.

We compare two different notions of dynamical phase transitions in closed quantum systems. The first is identified through the time-averaged value of the equilibrium-order parameter, whereas the second corresponds to non-analyticities in the time behaviour of the Loschmidt echo. By exactly solving the dynamics of the infinite-range XYmodel, we show that in this model non-analyticities of the Loschmidt echo are not connected to standard dynamical phase transitions and are not robust against quantum fluctuations. Furthermore, we show that the existence of either of the two dynamical transitions is not necessarily connected to the equilibrium quantum phase transition.

Scanning tunnelling microscopy and break-junction experiments realize metallic and molecular nanocontacts that act as ideal one-dimensional channels between macroscopic electrodes. Emergent nanoscale phenomena typical of these systems encompass structural, mechanical, electronic, transport, and magnetic properties. This Review focuses on the theoretical explanation of some of these properties obtained with the help of first-principles methods. By tracing parallel theoretical and experimental developments from the discovery of nanowire formation and conductance quantization in gold nanowires to recent observations of emergent magnetism and Kondo correlations, we exemplify the main concepts and ingredients needed to bring together ab initio calculations and physical observations. It can be anticipated that diode, sensor, spin-valve and spin-filter functionalities relevant for spintronics and molecular electronics applications will benefit from the physical understanding thus obtained.

We consider nonequilibrium phenomena in a very simple model that displays a zero-temperature first-order phase transition. The quantum Ising model with a four-spin exchange is adopted as a general representative of first-order quantum phase transitions that belong to the Ising universality class, such as for instance the order-disorder ferroelectric transitions, and possibly first-order T=0 Mott transitions. In particular, we address quantum quenches in the exactly solvable limit of infinite connectivity and show that, within the coexistence region around the transition, the system can remain trapped in a metastable phase, as long as it is spatially homogeneous so that nucleation can be ignored. Motivated by the physics of nucleation, we then study in the same model static but inhomogeneous phenomena that take place at surfaces and interfaces. The first-order nature implies that both phases remain locally stable across the transition, and with that the possibility of a metastable wetting layer showing up at the surface of the stable phase, even at T=0. We use mean-field theory plus quantum fluctuations in the harmonic approximation to study quantum surface wetting.

In the last two decades non-equilibrium spectroscopies have evolved from avant-garde studies to crucial tools for expanding our understanding of the physics of strongly correlated materials. The possibility of obtaining simultaneously spectroscopic and temporal information has led to insights that are complementary to (and in several cases beyond) those attainable by studying the matter at equilibrium. From this perspective, multiple phase transitions and new orders arising from competing interactions are benchmark examples where the interplay among electrons, lattice and spin dynamics can be disentangled because of the different timescales that characterize the recovery of the initial ground state. For example, the nature of the broken-symmetry phases and of the bosonic excitations that mediate the electronic interactions, eventually leading to superconductivity or other exotic states, can be revealed by observing the sub-picosecond dynamics of impulsively excited states. Furthermore, recent experimental and theoretical developments have made it possible to monitor the time-evolution of both the single-particle and collective excitations under extreme conditions, such as those arising from strong and selective photo-stimulation. These developments are opening the way for new, non-equilibrium phenomena that can eventually be induced and manipulated by short laser pulses. Here, we review the most recent achievements in the experimental and theoretical studies of the non-equilibrium electronic, optical, structural and magnetic properties of correlated materials. The focus will be mainly on the prototypical case of correlated oxides that exhibit unconventional superconductivity or other exotic phases. The discussion will also extend to other topical systems, such as iron-based and organic superconductors, (Formula presented.) and charge-transfer insulators. With this review, the dramatically growing demand for novel experimental tools and theoretical methods, models and concepts, will clearly emerge. In particular, the necessity of extending the actual experimental capabilities and the numerical and analytic tools to microscopically treat the non-equilibrium phenomena beyond the simple phenomenological approaches represents one of the most challenging new frontiers in physics.

Vanadium sesquioxide (V2O3) is an antiferromagnetic insulator below TN≈155K. The magnetic order does not consist of only antiferromagnetic nearest-neighbor bonds, possibly excluding the interplane vanadium pairs, as one would infer from the bipartite character of the hexagonal basal plane in the high-temperature corundum structure. In fact, a magnetic structure with one ferromagnetic bond and two antiferromagnetic ones in the honeycomb plane is known experimentally to be realized, accompanied by a monoclinic distortion that makes the ferromagnetic bond inequivalent from the other two. We show here that the magnetic ordering, the accompanying monoclinic structural distortion, the magnetic anisotropy, and also the recently discovered high-pressure nonmagnetic monoclinic phase, can all be accurately described by conventional electronic structure calculations within GGA and GGA+U. Remarkably, our calculations yield that the corundum phase would be unstable to a monoclinic distortion even without magnetic ordering, thus suggesting that magnetism and lattice distortion are independent phenomena, though they reinforce each other. By means of GGA+U, we find a metal-to-insulator transition at a critical Uc. Both metal at U≤Uc and insulator above Uc have the same magnetic order as that actually observed below TN, but different monoclinic distortions. Reassuringly, the distortion on the insulating side agrees with the experimental one. Our results are in line with DMFT calculations for the paramagnetic phase [A. I. Poteryaev, Phys. Rev. B 76, 085127 (2007)]10.1103/PhysRevB.76.085127, which predict that the insulating character is driven by a correlation-enhanced crystal-field splitting between egπ and a1g orbitals that pushes the latter above the chemical potential. We find that the a1g orbital, although almost empty in the insulating phase, is actually responsible for the unusual magnetic order as it leads to magnetic frustration whose effect is similar to a next-nearest-neighbor exchange in a Heisenberg model on a honeycomb lattice.

The Kondo zero-bias anomaly of Co adatoms probed by scanning tunneling microscopy is known to depend on the height of the tip above the surface, and this dependence is different on different low index Cu surfaces. On the (100) surface, the Kondo temperature first decreases then increases as the tip approaches the adatom, while on the (111) surface it is virtually unaffected. These trends are captured by combined density functional theory and numerical renormalization-group calculations. The adatoms are found to be described by an S=1 Anderson model on both surfaces, and ab initio calculations help identify the symmetry of the active d orbitals. We correctly reproduce the Fano line shape of the zero-bias anomaly for Co/Cu(100) in the tunneling regime but not in the contact regime, where it is probably dependent on the details of the tip and contact geometry. The line shape for Co/Cu(111) is presumably affected by the presence of surface states, which are not included in our method. We also discuss the role of symmetry, which is preserved in our model scattering geometry but most likely broken in experimental conditions.

The infinite-dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a Z2 gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local Z2 gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactly solving the effective spin-fermion model by dynamical mean-field theory both at zero and at finite temperature.

We investigate by means of the time-dependent Gutzwiller approximation the transport properties of a strongly correlated slab subject to Hubbard repulsion and connected with to two metallic leads kept at a different electrochemical potential. We focus on the real-time evolution of the electronic properties after the slab is connected to the leads and consider both metallic and Mott insulating slabs. When the correlated slab is metallic, the system relaxes to a steady state that sustains a finite current. The zero-bias conductance is finite and independent of the degree of correlations within the slab as long as the system remains metallic. On the other hand, when the slab is in a Mott insulating state, the external bias leads to currents that are exponentially activated by charge tunneling across the Mott-Hubbard gap, consistent with the Landau-Zener dielectric breakdown scenario.

We study the nonequilibrium dynamics of a simple model for V2O3 that consists of a quarter-filled Hubbard model for two orbitals that are split by a weak crystal field. Peculiarities of this model are (1) a Mott insulator whose gap corresponds to transferring an electron from the occupied lower orbital to the empty upper one, rather than from the lower to the upper Hubbard subbands; (2) a Mott transition generically of first order even at zero temperature. We simulate by means of time-dependent Gutzwiller approximation the evolution within the insulating phase of an initial state endowed by a nonequilibrium population of electrons in the upper orbital and holes in the lower one. We find that the excess population may lead, above a threshold, to a gap collapse and drive the insulator into the metastable metallic phase within the coexistence region around the Mott transition. This result foresees a nonthermal pathway to revert a Mott insulator into a metal. Even though this physical scenario is uncovered in a very specific toy model, we argue it might apply to other Mott insulating materials that share similar features.

We find evidence that superconductivity intrudes into the paramagnetic-to-magnetic transition of the Kondo lattice model if magnetic frustration is added. Specifically, we study by the variational method the model on a square lattice in the presence of both nearest-neighbor (t) and next-nearest-neighbor (t′) hopping of the conduction electrons. We find that, when t′/t>0, a d-wave superconducting dome emerges between the magnetic and paramagnetic metal phases and close to the compensated regime, i.e., the number of conduction electrons equals the number of localized spin-1/2 moments. Superconductivity is further strengthened by a direct antiferromagnetic exchange, JH, between the localized moments, to such an extent that we observe coexistence with magnetic order.