Holstein model in infinite dimensions

Floquet nonadiabatic mixed quantum-classical dynamics in periodically driven solid systems

In this paper, we introduce the Floquet mean-field dynamics and Floquet surface hopping approaches to study the nonadiabatic dynamics in periodically driven solid systems. We demonstrate that these two approaches can be formulated in both real and reciprocal spaces. Using the two approaches, we are able to simulate the interaction between electronic carriers and phonons under periodic drivings, such as strong light-matter interactions. Employing the Holstein and Peierls models, we show that strong light-matter interactions can effectively modulate the dynamics of electronic population and mobility. Notably, our study demonstrates the feasibility and effectiveness of modeling low-momentum carriers' interactions with phonons using a truncated reciprocal space basis, an approach impractical in real space frameworks. Moreover, we reveal that even with a significant truncation, carrier populations derived from surface hopping maintain greater accuracy compared to those obtained via mean-field dynamics. These results underscore the potential of our proposed methods in advancing the understanding of carrier-phonon interactions in various periodically driven materials.

A stability bound on the [Formula: see text]-linear resistivity of conventional metals

Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is 1/τtr = 2πλT, where λ is a dimensionless strength of the electron-phonon coupling. The fact that measured values satisfy λ ≲ 1 has been noted in the context of a possible "Planckian" bound on transport. However, since the electron-phonon scattering is quasielastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a "stability" bound on λ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.

Charge Order in the Holstein Model on a Honeycomb Lattice

The effect of electron-electron interactions on Dirac fermions, and the possibility of an intervening spin-liquid phase between the semimetal and antiferromagnetic (AF) regimes, has been a focus of intense quantum simulation effort over the last five years. We use determinant quantum Monte Carlo simulations to study the Holstein model on a honeycomb lattice and explore the role of electron- phonon interactions on Dirac fermions. We show that they give rise to charge-density-wave (CDW) order and present evidence that this occurs only above a finite critical interaction strength. We evaluate the temperature for the transition into the CDW which, unlike the AF transition, can occur at finite values owing to the discrete nature of the broken symmetry.

Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems

Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.

Inhomogeneous dynamical mean-field theory of the small polaron problem

We present an inhomogeneous dynamical mean field theory (I-DMFT) that is suitable to investigate electron-lattice interactions in non-translationally invariant and/or inhomogeneous systems. The presented approach, whose only assumption is that of a local, site-dependent self-energy, recovers both the exact solution of an electron for a generic random tight-binding Hamiltonian in the non-interacting limit and the DMFT solution for the small polaron problem in translationally invariant systems. To illustrate its full capabilities, we use I-DMFT to study the effects of defects embedded on a two-dimensional surface. The computed maps of the local density of states reveal Friedel oscillations, whose periodicity is determined by the polaron mass. This can be of direct relevance for the interpretation of scanning-tunneling microscopy experiments on systems with sizable electron-lattice interactions. Overall, the easy numerical implementation of the method, yet full self-consistency, allows one to study problems in real-space that were previously difficult to access.

Supersolid phase accompanied by a quantum critical point in the intermediate coupling regime of the Holstein model

We reveal that electron-phonon systems described by the Holstein model on a bipartite lattice exhibit, away from half filling, a supersolid (SS) phase characterized by coexisting charge order (CO) and superconductivity (SC), and an accompanying quantum critical point (QCP). The SS phase, demonstrated by the dynamical mean-field theory with a quantum Monte Carlo impurity solver, emerges in the intermediate-coupling regime, where the peak of the Tc dome is located and the metal-insulator crossover occurs. On the other hand, in the weak- and strong-coupling regimes the CO-SC boundary is of first order with no intervening SS phases. The QCP is associated with the continuous transition from SS to SC and characterized by a reentrant behavior of the SS around it. We further show that the SS-SC transition is hallmarked by diverging charge fluctuations and a kink (peak) in the superfluid density.

Superconductivity of composite particles in a two-channel Kondo lattice

Emergence of odd-frequency s-wave superconductivity is demonstrated in the two-channel Kondo lattice by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. Around half filling of the conduction bands, divergence of an odd-frequency pairing susceptibility is found, which signals instability toward the superconductivity. The corresponding order parameter is equivalent to a staggered composite-pair amplitude with even frequencies, which involves both localized spins and conduction electrons. A model wave function is constructed for the composite order with the use of symmetry operations such as charge conjugation and channel rotations. Given a certain asymmetry of the conduction bands, another s-wave superconductivity is found that has a uniform order parameter. The Kondo effect in the presence of two channels is essential for both types of unconventional superconductivity.

Low-energy properties of the Kondo lattice model

We study the zero-temperature properties of the Kondo lattice model within the dynamical mean-field theory. As an impurity solver we use the numerical renormalization group. We present results for the paramagnetic case showing the anticipated heavy-fermion physics, including direct evidence for the appearance of a large Fermi surface for antiferromagnetic exchange interaction. Allowing for the formation of a Néel state, we observe at finite doping an antiferromagnetic metal below a critical exchange interaction, which shows a crossover from a local moment antiferromagnet with a small Fermi surface for weak exchange coupling to a heavy-fermion antiferromagnet with a large Fermi surface for increasing exchange. Including lattice degrees of freedom via an additional Holstein term we observe a significant suppression of the Kondo effect, leading to a strongly reduced low-energy scale. For too large electron-phonon coupling we find a complete collapse of the heavy Fermi liquid and the formation of polarons.

A DFT + DMFT approach for nanosystems

We propose a combined density-functional-theory-dynamical-mean-field-theory (DFT + DMFT) approach for reliable inclusion of electron-electron correlation effects in nanosystems. Compared with the widely used DFT + U approach, this method has several advantages, the most important of which is that it takes into account dynamical correlation effects. The formalism is illustrated through different calculations of the magnetic properties of a set of small iron clusters (number of atoms 2 ≤ N ≤ 5). It is shown that the inclusion of dynamical effects leads to a reduction in the cluster magnetization (as compared to results from DFT + U) and that, even for such small clusters, the magnetization values agree well with experimental estimations. These results justify confidence in the ability of the method to accurately describe the magnetic properties of clusters of interest to nanoscience.

Temperature dependence of the angle resolved photoemission spectra in the undoped cuprates: self-consistent approach to the t-J Holstein model

We develop a novel self-consistent approach for studying the angle resolved photoemission spectra (ARPES) of a hole in the t-J Holstein model giving perfect agreement with numerically exact diagrammatic Monte Carlo (DMC) data at zero temperature for all regimes of electron-phonon coupling. Generalizing the approach to finite temperatures, we find that the anomalous temperature dependence of the ARPES in undoped cuprates is explained by cooperative interplay of coupling of the hole to magnetic fluctuations and strong electron-phonon interaction.

Polaronic and nonadiabatic phase diagram from anomalous isotope effects

Isotope effects (IEs) are powerful tools to probe directly the dependence of many physical properties on lattice dynamics. In this Letter we investigate the onset of anomalous IEs in the spinless Holstein model by employing the dynamical mean field theory. We show that the isotope coefficients of the electron effective mass and of the dressed phonon frequency are sizable also far away from the polaronic crossover and mark the importance of nonadiabatic lattice fluctuations. We draw a nonadiabatic phase diagram in which we identify a novel crossover, not related to polaronic features, where the IEs attain their largest anomalies.

Polaron crossover and bipolaronic metal-insulator transition in the half-filled Holstein model

The formation of a finite-density polaronic state is analyzed in the context of the Holstein model using the dynamical mean-field theory. The spinless and spinful fermion cases are compared to disentangle the polaron crossover from the bipolaron formation. The exact solution of dynamical mean-field theory is compared with weak-coupling perturbation theory, noncrossing (Migdal), and vertex correction approximations. We show that polaron formation is not associated with a metal-insulator transition, which is instead due to bipolaron formation.

First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory

We propose a dynamical mean-field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean-field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional "LDA+DMFT," such as Hubbard interaction parameters and double-counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.

Gap formation and soft phonon mode in the Holstein model

We investigate electron-phonon coupling in many-electron systems using the dynamical mean-field theory in combination with the numerical renormalization group. This nonperturbative method reveals significant precursor effects to the gap formation at intermediate coupling strengths. The emergence of a soft phonon mode and very strong lattice fluctuations can be understood in terms of Kondo-like physics due to the development of a double-well structure in the effective potential for the ions.

Dynamical mean-field theory for pairing and spin gap in the attractive hubbard model

We solve the attractive Hubbard model for arbitrary interaction strengths within dynamical mean-field theory. We compute the transition temperature for superconductivity and analyze electron pairing in the normal phase. The normal state is a Fermi liquid at weak coupling and a non-Fermi-liquid state with a spin gap at strong coupling. Away from half filling, the quasiparticle weight vanishes discontinuously at the transition between the two normal states.

Metal-insulator transitions: influence of lattice structure, jahn-teller effect, and Hund's rule coupling

We study the influence of the lattice structure, the Jahn-Teller effect, and the Hund's rule coupling on a metal-insulator transition in A(n)C60 (A = K,Rb). The difference in the lattice structure favors A3C60 (fcc) being a metal and A4C60 (bct) being an insulator, and the coupling to H(g) Jahn-Teller phonons favors A4C60 being nonmagnetic. The coupling to H(g) ( A(g)) phonons decreases (increases) the value U(c) of the Coulomb integral at which the metal-insulator transition occurs. There is an important partial cancellation between the Jahn-Teller effect and the Hund's rule coupling.