We investigate the localized-electron character of the Mott-insulating phase in A$_3$C$_{60}$ using a single-site multiorbital electron model coupled to anisotropic molecular vibrations (Jahn--Teller phonons). We apply the spherical-tensor formalism, a framework originally developed in nuclear physics, to analyze the electron--phonon-coupled ground-state multiplet. Focusing on multipole moments, we find that both the conventional electronic quadrupole moment and the lattice displacement associated with the molecular vibrations vanish, even though the degenerate ground-state multiplet implies the presence of quadrupolar degrees of freedom. By analyzing these degrees of freedom within the spherical-tensor framework, we introduce composite (two-body) quadrupole operators involving both electrons and phonons and study their parameter dependence numerically. Furthermore, using quasispin selection rules, we demonstrate that the composite quadrupole does not couple to either the conventional quadrupole or lattice-displacement operators, thereby distinguishing it fundamentally from standard quadrupolar degrees of freedom. In addition, we investigate the nature of the electron--phonon entanglement and characterize it from the viewpoint of angular momentum. Analysis of the entanglement spectrum reveals that the ground state consists of superpositions of multi-phonon states with angular momenta $L_{\rm ph}=2$ and $L_{\rm ph}=3$, formed through coupling to three-electron states with $L=1$ and $L=2$.
We investigate the localized-electron character of the Mott-insulating phase in A3C60 using a single-site multiorbital electron model coupled to anisotropic molecular vibrations (Jahn--Teller phonons). We apply the spherical-tensor formalism, a framework originally developed in nuclear physics, to analyze the electron--phonon-coupled ground-state multiplet. Focusing on multipole moments, we find that both the conventional electronic quadrupole moment and the lattice displacement associated with the molecular vibrations vanish, even though the degenerate ground-state multiplet implies the presence of quadrupolar degrees of freedom. By analyzing these degrees of freedom within the spherical-tensor framework, we introduce composite (two-body) quadrupole operators involving both electrons and phonons and study their parameter dependence numerically. Furthermore, using quasispin selection rules, we demonstrate that the composite quadrupole does not couple to either the conventional quadrupole or lattice-displacement operators, thereby distinguishing it fundamentally from standard quadrupolar degrees of freedom. In addition, we investigate the nature of the electron--phonon entanglement and characterize it from the viewpoint of angular momentum. Analysis of the entanglement spectrum reveals that the ground state consists of superpositions of multi-phonon states with angular momenta Lph=2 and Lph=3, formed through coupling to three-electron states with L=1 and L=2.
We discuss a hopping model of electrons between idealized molecular sites with a local orbital degeneracy and a dynamical Jahn-Teller effect, for crystal field environments of sufficiently high symmetry. For the Mott-insulating case (one electron per site and large Coulomb repulsions), in the simplest twofold degenerate situation, we are led to consider a particular exchange Hamiltonian, describing two isotropic spin-1/2 Heisenberg problems coupled by a quartic term on equivalent bonds. This twin-exchange Hamiltonian applies to a physical regime in which the interorbital singlet is the lowest-energy intermediate state available for hopping. This regime is favored by a relatively strong electron-phonon coupling. Using variational arguments, a large-n limit, and exact diagonalization data, we find that the ground state, in the one dimensional case, is a solid valence-bond state. The situation in the two dimensional case is less clear. Finally, the behavior of the system upon hole doping is studied in one dimension.
We calculate the spectral function of the one-dimensional Hubbard-Holstein model using the time-dependent density matrix renormalization group, focusing on the regime of large local Coulomb repulsion, and away from electronic half-filling. We argue that, from weak to intermediate electron-phonon coupling, phonons interact only with the electronic charge, and not with the spin degrees of freedom. For strong electron-phonon interaction, spinon and holon bands are not discernible anymore and the system is well described by a spinless polaronic liquid. In this regime, we observe multiple peaks in the spectrum with an energy separation corresponding to the energy of the lattice vibrations (i.e., phonons). We support the numerical results by introducing a well controlled analytical approach based on Ogata-Shiba's factorized wave function, showing that the spectrum can be understood as a convolution of three contributions, originating from charge, spin, and lattice sectors. We recognize and interpret these signatures in the spectral properties and discuss the experimental implications.
Jahn-Teller systems exhibit strong coupling between the electronic and nuclear degrees of freedom. We analyse how linear and quadratic coupling affect the electron-nuclear entanglement in the E⊗ϵ system. A measure of quantum entanglement, recently developed by Shimony [Ann. New York Acad. Sci. 755, 675 (1995)], is used. States in the adiabatic regime with quadratic coupling are analysed. The electron-nuclear entanglement in vibronic states of the linear Exe model is calculated numerically. The physical significance of electron-nuclear entanglement is discussed in terms of reduction factors and magnetic vibrational circular dichroism.
In this work we investigate some aspects of the physics of strongly correlated systems by taking into account both electron-electron and electron-phonon interactions as basic mechanisms for reproducing electronic correlations in real materials. The relevance of the electron-electron interactions is discussed in the first part of this thesis in the framework of a self-consistent theoretical approach, named Composite Operator Method (COM), which accounts for the relevant quasi-particle excitations in terms of a set of composite operators that appear as a result of the modification imposed by the interactions on the canonical electronic fields. We show that the COM allows the calculation of all the relevant Green’s and correlation functions in terms of a number of unknown internal parameters to be determined self-consistently. Therefore, depending on the balance between unknown parameters and self-consistent equations, exact and approximate solutions can be obtained. By way of example, we discuss the application of the COM to the extended t-U- J-h model in the atomic limit, and to the two-dimensional single-band Hubbard model. In the former case, we show that the COM provides the exact solution of the model in one dimension. We study the effects of electronic correlations as responsible for the formation of a plethora of different charge and/or spin orderings. We report the phase diagram of the model, as well as a detailed analysis of both zero and finite temperature single-particle and thermodynamic properties. As far as the single-band Hubbard model is concerned, we illustrate an approximated selfconsistent scheme based on the choice of a two-field basis. We report a detailed analysis of many unconventional features that arise in single-particle properties, thermodynamics and system’s response functions. We emphasize that the accuracy of the COM in describing the effects of electronic correlations strongly relies on the choice of the basis, paving the way for possible multi-pole extensions to the twofield theory. To this purpose, we also study a three-field approach to the single-band Hubbard model, showing a significant step forward in the agreements with numerical data with respect to the two-pole results. The role of the electron-phonon interaction in the physics of strongly correlated systems is discussed in the second part of this thesis. We show that in highly polarizable lattices the competition between unscreened Coulomb and Fröhlich interactions results in a short-range polaronic exchange term Jp that favours the formation of local and light pairs of bosonic nature, named bipolarons, which condense with a critical temperature well in excess of hundred kelvins. These findings, discussed in the framework of the so-called polaronic t-Jp model, are further investigated in the presence of a finite on-site potential ~U , coming from the competition between on-site Coulomb and Fröhlich interactions. We discuss the role of ~U as the driving parameter for a small-to-large bipolaron transition, providing a possible explanation of the BEC-BCS crossover in terms of the properties of the bipolaronic ground state. Finally, we show that a hard-core bipolarons gas, studied as a charged Bose-Fermi mixture, allows for the description of many non Fermi liquid behaviours, allowing also for a microscopic explanation of pseudogap features in terms of a thermal-induced recombination of polarons and bipolarons, without any assumption on preexisting order or broken symmetries. [edited by Author]
Mott insulators, in which strong Coulomb interactions fully localize electrons on single atomic sites, play host to an incredibly rich and exciting array of strongly correlated physics. One can naturally extend this concept to cluster Mott insulators, wherein electrons localize not on single atoms but across clusters of atoms, forming "molecules in solids". The resulting localized degrees of freedom incorporate the full spectrum of electronic degrees of freedom, spin, orbital, and charge. These serve as the building blocks for cluster Mott insulators, and understanding them is an important first step toward understanding the many-body physics that emerges in candidate cluster Mott insulators. Here, we focus on elementary building blocks, neglecting some of the complexity present in real materials which can often obfuscate the underlying principles at play. Through an extensive set of exact theoretical calculations on clusters of varying geometry, number of orbitals, and number of electrons, we uncover some of the basic organizing principles of cluster Mott phases, particularly when interactions dominate and negate a simple single-particle picture. These include, for example, the identification of an additional "cluster Hund's rule", of cluster ground states that are best understood from a purely interacting perspective, and of several localized degrees of freedom which are protected by an unusual combination of discrete spatial or orbital symmetries. Finally, we discuss the impact of adding additional terms, relevant to material candidates, on the phase diagrams presented throughout, as well as the potential next steps in the journey to building a more complete picture of cluster Mott insulators.