We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal–insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled to external electrodes. In both cases, we focus on the impact of the correlated (assisted) hopping (CH) interaction. For superconductors, CH acts as a driving mechanism for the phase transition and modifies the spectral properties of the system. We present the evolution of the spectral function as the system approaches the Mott-type transition under varying model parameters. In quantum-dot-based devices, CH influences the tunneling amplitude between the dot and metallic leads. We demonstrate that the characteristic changes in the conductance of a normal metal–quantum dot–normal metal structure provide a clear signature of the presence and sign of CH interaction. Abstract Published by the Jagiellonian University 2026 authors
We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal–insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled to external electrodes. In both cases, we focus on the impact of the correlated (assisted) hopping (CH) interaction. For superconductors, CH acts as a driving mechanism for the phase transition and modifies the spectral properties of the system. We present the evolution of the spectral function as the system approaches the Mott-type transition under varying model parameters. In quantum-dot-based devices, CH influences the tunneling amplitude between the dot and metallic leads. We demonstrate that the characteristic changes in the conductance of a normal metal–quantum dot–normal metal structure provide a clear signature of the presence and sign of CH interaction. Abstract Published by the Jagiellonian University 2026 authors
We investigate the role of strong Coulomb interactions beyond the standard Hubbard model in two distinct physical contexts. First, we analyze the superconducting phase transition occurring near the Mott metal-insulator transition. Second, we study transport properties of artificial nano-scale structures containing quantum dots coupled to external electrodes. In both cases, we focus on the impact of the correlated (assisted) hopping (CH) interaction. For superconductors, CH acts as a driving mechanism for the phase transition and modifies the spectral properties of the system. We present the evolution of the spectral function as the system approaches the Mott-type transition under varying model parameters. In quantum-dot-based devices, CH influences the tunneling amplitude between the dot and metallic leads. We demonstrate that the characteristic changes in the conductance of a normal metal-quantum dot-normal metal structure provide a clear signature of the presence and sign of CH interaction.
Slave boson mean-field studies of the ground state of the Hubbard model with correlated hopping were performed. The approach qualitatively recovers the exact results for the case when the hopping integral t equals the correlated hopping integral X. The phase diagram for the strongly correlated state with only singly occupied sites, the weakly correlated state, where single and double occupation is allowed, and for the superconducting state, was determined for any value of X and any electron concentration n. At the half-filled band (n=1) a direct transition from the superconductor to the Mott insulator was found. In the region of strong correlations the superconducting solution is stable for n close to 1, in contrast to the case of weak correlations, in which superconductivity occurs at $n\ensuremath{\approx}0$ and $n\ensuremath{\approx}2.$ We have also found that strong correlations change the characteristics of the superconducting phase, e.g., the gap in the excitation spectrum exhibits a nonexponential dependence on the on-site Coulomb integral U close to the phase-transition point.
For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength U, temperature T, and filling n shows that, upon increasing n toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T = 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.
As the characteristic dimensions of a physical system shrink to the nanometer scale, its behavior is governed primarily by quantum mechanics rather than by classical laws. In this regime, effects such as barrier tunnelling, energy quantization, and quantum coherence play a central role in how nanoscale devices function. These phenomena are particularly prominent in platforms such as graphene and semiconductor quantum dots, where they have a pronounced impact on transport properties, optical behavior, and overall device performance. In parallel, lattice-based many-body models offer a concise theoretical framework for describing collective quantum states in engineered structures. The present work provides a conceptually oriented survey that links quantum phenomena at the nanoscale to two benchmark lattice Hamiltonians, namely the Jaynes-Cummings-Hubbard (JCH) and Bose-Hubbard (BH) models. The approach is qualitative and literature-based: results from quantum optics, cold-atom physics, and condensed-matter research are combined to interpret how the parameters of these models relate to experimentally tunable quantities, such as coupling strengths, confinement scales, and interaction energies. The main outcome of the review is threefold. First, tunnelling, graphene, and quantum dots can be viewed as natural settings where effective Hubbard-type descriptions arise. Second, despite describing different degrees of freedom-hybrid light-matter polaritons in the JCH case and interacting bosons in the BH case, both models display analogous phase structures with insulating and superfluid-like regimes. Third, reliable implementation of these phases in nanotechnological devices requires a careful mapping between abstract Hamiltonian parameters and specific design variables. The discussion indicates that JCHand BH-type models should be regarded not only as abstract theoretical constructs but also as practical tools for guiding the design of future quantum technologies. Extensions to driven-dissipative dynamics and topological band structures are identified as promising directions for next-generation quantum simulators and nanoscale sensors. Keywords: quantum tunnelling, graphene, quantum dots, Jaynes-Cummings-Hubbard model, Bose-Hubbard model, quantum simulators
A generalized Hubbard model with correlated hoppings is studied at half filling using exact diagonalization methods. For certain values of the hopping parameters our results for several static properties, the Drude weight and the single-particle spectra function, suggest the occurrence of a metal-insulator transition (MIT) at a finite value of the local Coulomb interaction Uc. We identify the regions of the hopping parameters where the MIT is of the Mott type. In these regions, for large UUc, we find a ferromagnetic ground state.
An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.