This thesis investigates how bosonic environments reshape electronic correlations in quantum many-body systems, with emphasis on two complementary classes of mediators: lattice vibrations and quantized electromagnetic modes. The central question is how such bosonic degrees of freedom renormalize electronic motion, generate effective interactions, and open routes toward controlling correlated states. The first part of the thesis focuses on phonon-mediated correlations in the Holstein–Hubbard model. We study how dispersive optical phonons modify bipolaron binding, mobility, and single-particle spectra. We show that phonon dispersion can substantially reshape both the stability of bound pairs and their spectroscopic fingerprints. We further demonstrate that electron-removal spectra can already contain clear signatures of preformed pairs: a liquid of incoherent bipolarons exhibits a depletion of low-energy spectral weight near the chemical potential while remaining metallic, and its spectra can be understood in terms of a simple Bose-sea picture of hard-core pairs. The second part addresses nonequilibrium control of phonon-mediated interactions. For a system with nonlinear electron–phonon coupling driven by a short optical pulse, numerically exact time evolution reveals that phonon driving can switch the effective electron–electron interaction between attraction and repulsion. In the oscillator-softening regime, the pulse can create a long-lived metastable bound state that persists after the field is turned off, reflecting a configuration-selective redistribution of phonon excitations rather than a purely Floquet mechanism. The final part turns to photon-mediated correlations in structured electromagnetic environments. Within extended dynamical mean-field theory, we study a system in which intrinsic static interactions coexist with retarded photon-mediated couplings. The results reveal a superradiant-like ordered phase driven by the softening of a collective polaritonic mode and show that static interactions can assist the emergence of this order. Taken together, the thesis highlights bosons not only as mediators of correlations, but also can serve as a tool for controlling correlated electronic behavior.
This thesis investigates how bosonic environments reshape electronic correlations in quantum many-body systems, with emphasis on two complementary classes of mediators: lattice vibrations and quantized electromagnetic modes. The central question is how such bosonic degrees of freedom renormalize electronic motion, generate effective interactions, and open routes toward controlling correlated states. The first part of the thesis focuses on phonon-mediated correlations in the Holstein–Hubbard model. We study how dispersive optical phonons modify bipolaron binding, mobility, and single-particle spectra. We show that phonon dispersion can substantially reshape both the stability of bound pairs and their spectroscopic fingerprints. We further demonstrate that electron-removal spectra can already contain clear signatures of preformed pairs: a liquid of incoherent bipolarons exhibits a depletion of low-energy spectral weight near the chemical potential while remaining metallic, and its spectra can be understood in terms of a simple Bose-sea picture of hard-core pairs. The second part addresses nonequilibrium control of phonon-mediated interactions. For a system with nonlinear electron–phonon coupling driven by a short optical pulse, numerically exact time evolution reveals that phonon driving can switch the effective electron–electron interaction between attraction and repulsion. In the oscillator-softening regime, the pulse can create a long-lived metastable bound state that persists after the field is turned off, reflecting a configuration-selective redistribution of phonon excitations rather than a purely Floquet mechanism. The final part turns to photon-mediated correlations in structured electromagnetic environments. Within extended dynamical mean-field theory, we study a system in which intrinsic static interactions coexist with retarded photon-mediated couplings. The results reveal a superradiant-like ordered phase driven by the softening of a collective polaritonic mode and show that static interactions can assist the emergence of this order. Taken together, the thesis highlights bosons not only as mediators of correlations, but also can serve as a tool for controlling correlated electronic behavior.
In this thesis, I investigate the behavior of particles dressed by quantum field excitations and random interactions. First I consider two-carrier states in the Peierls model describing the modulation of the particle hopping due to lattice distortions. I compute the spectral response using the Momentum Average approximation. Combining accurate numerical techniques and analytical arguments, I provide a complete picture of the Peierls bipolarons. It is found that polarons bind into strongly bound yet light bipolarons in the singlet sector, even at large values of the electron-phonon coupling strength. At finite electron fillings, these bipolarons may condense into a high-Tc superconductor. On the other hand, phonons mediate a repulsive interaction in the triplet sector, or equivalently (in one dimension), between two hard-core particles, in which case the ground-state dimers bound by sufficiently attractive bare interactions exhibit two sharp transitions, one of which is the first known example of a self-trapping transition at the two-carrier level. In both situations, phonons mediate pair-hopping effective interactions between the carriers. I further study some aspects of the excited spectrum for the two hard-core particles, a situation relevant to ultracold quantum simulators. It is found that the repulsive phonon-mediated interaction binds a repulsive bipolaron embedded in the excited spectrum. I then turn to the study of quenched randomness in an ultracold molecular plasma. I argue that the quenched ultracold plasma presents an experimental platform for studying quantum many-body physics of disordered systems in the long-time and finite energy-density limits. I analyze an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. I develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered non-equilibrium physics of this system. This thesis thus examines the quantum many-body response in interacting systems coupled to bosonic fields or in disordered environments.
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]
Optimizing various properties of materials have been under intensive focus for many decades. In recent years, the exposure of ultrafast techniques enhance the possibility of seizing this goal. As by employing these techniques, one can expose the system under strong short fields, and investigate the transient response of various low-lying excitations. Such studies will strengthen our understanding of interplays among various degrees of freedom in correlated materials, and thereby facilitate the chance to manipulate different properties of these systems. Of our particular attention is the electron-lattice dynamics, where modulating a particular vibrational mode of the crystal lattice, will lead to the emergence of new quasi stable'' lattice structures as well as novel transient phenomena. Aside from these experimental prospects, the above mentioned goals were also the subject of an extensive theoretical studies. In this thesis, we investigated the in and out of equilibrium dynamics of electronic systems which are interacting with lattice degrees of freedom. We employed the two-time Keldysh Green's function within the framework of the dynamical mean field theory to conduct our researches on this subject. In our first attempt, we studied the dynamical response of a one-electron system under a linear electron-lattice interaction. We explored the real-time formation of a bound quasiparticle, known as a polaron, under various parameter regimes of the model. We presented that when the carrier is suddenly coupled to the lattice degrees of freedom, the long-time response of the system in the strong coupling limit exhibits both bound, polaronic, and unbound, delocalized, states. We characterized the nature of such a mixed state using the adiabatic picture of the model. We also showed that the formed polaron is dressed by excited phononic states, in contrast to its equilibrium counterpart, where the ground-state phononic states are bounding the electron. We also addressed the response of a many-body electronic system, weakly coupled to a bosonic bath, under various time dependent excitations, which brings the system to a bad-metallic phase. We employed a model which treated the Coulomb repulsive interaction locally. We presented that the relaxation of this excited state varies by the strength of the electron-electron interaction. We demonstrated that, for both insulating and metallic regimes of the system, a slow relaxation dynamics can be observed close to the phase transition from the metallic to insulating regimes of the system. Our analysis revealed that in the metallic side, this slow evolution is rooted in the spin-related physics of the problem. However, in the insulating regimes of the model, our results showed that presence of a gap in the spectral density of the insulating system prohibits the relaxation of the excited particles. We also studied the associated timescale for the adiabatic dynamics near the Mott transition. Our results exhibited that there is a nonadiabatic window'' in the metallic side of the phase transition, in which the adiabatic timescale is extremely long. We pointed out that the presence of such a window is intertwined with the slow relaxation timescale of the spin-related dynamics close to the Mott transition. We also captured an induced metallic phase near metal-to-insulator transition out of equilibrium. We initiated this study using the slave-rotor impurity solver, which is been coupled to the self-energies obtained from the first-order Luttinger-Ward functional for the Phonon degrees of freedom. We presented the emergence of the larger spectral density at small frequencies both in metallic and insulating phases close to the phase transition, which is surrounded by pseudo gaps. We explored the physics of such spectral densities as well as their dependencies on the phononic parameters. We postulated that this response of the system is due to the evolution of the system, in a non-thermal mechanism, towards a temperature which is less than the initial temperature of the system, before coupling to the bath. We also pointed out that the associated very slow relaxation dynamics is the result of the formation of psuedo-gaps around the quasiparticle peak.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.
The present Thesis aims to deepen the understanding of the physics of strongly-correlated systems along diverse directions with a common denominator, namely a focus on the physical role played by the collective modes shaping quantum many-body correlations. This investigation has been mostly led through the heuristic application of the Quantum Gutzwiller Approach, a recently developed theory of the quantised excitations above the Gutzwiller approximation for strongly-interacting systems on a lattice. In the first place, the intertwining between quantum correlations and collective effects is explored in the context of Bose-Hubbard models, intended both as simple yet highly non-trivial realisations of complex many-body scenarios, and as controllable environments for the quantum simulation of impurity problems. In particular, we are able to provide a comprehensive and semi-analytical description of quantum fluctuations across the critical regimes induced by the proximity of a Mott transition (Mottness), ranging from accurate predictions for the superfluid density and pair correlations across quantum critical regimes to the Andreev-Bashkin effect in a two-component bosonic mixture. As case studies for the effectiveness and flexibility of our approach, we give a detailed account of the rich behaviours of a quantum impurity, either fixed or itinerant, immersed in a Bose-Hubbard environment, showing that both the decoherence dynamics of spinful particle and the resulting Bose polaron in the second case are extremely sensitive probes of the type of critical fluctuations experienced by the surrounding system. Additionally, we extend our analysis of quantum fluctuations to the Fermi-Hubbard model, where we uncover the interplay between low-energy quasiparticles and bosonic elementary excitations in determining two-particle correlations. A more complex physical scenario addressed in this Thesis is represented by driven-dissipative interacting systems, which find a state-of-the-art technological implementation in circuit QED platforms, among others. Inspired by the experimental interest in these systems as a potential toolbox for the generation of exotic quantum states of light, we consider a strongly-correlated fluid of photons on a lattice stabilised via incoherent drive and dissipation, and examine its collective fluctuations across the out-of-equilibrium insulator-to-superfluid transition of the system. Specifically, establishing a conceptual parallelism with our approach to fluctuations at equilibrium, we develop a linear-response theory of the excitations on top of the Gutzwiller stationary state of the Lindblad dynamics, and characterise their physical role in quantum observables and response functions. Taking advantage of our formalism, we describe also dynamical instabilities and novel physical regimes arising in the ultrastrong coupling limit of the superfluid phase. Among the most remarkable results, we bring to light the paradoxical nature of the Mott-like insulating phase of the system, whose peculiar one-body dynamical fluctuations are shown to echo the behaviour of a lasing state. Encompassing diverse modern domains of many-body physics, our investigation goes in the direction of solidifying the interpretation of collective modes as fundamental actors in correlation-induced phenomena under a unified physical picture.
In the first part of the thesis we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We describe the single particle evolution of the system during expansion and establish criteria for a far-field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including: Bogoliubov theory, mean-field decoupling, and particle-hole perturbative expantion about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on system correlations. We justify a Gaussian approximation from which we develop a general three-dimensional theoretical formalism for an inhomogeneous lattice system by comparison with the directly calculated correlation functions. \nIn the second part of the thesis we show how the conventional wisdom that increasing tem- perature means decreasing quantum coherence in system can be faulty. We explore a practical example that can be explored in optical lattice experiments. Using finite temperature perturbation theory and exact calculations we show that the short-range coherence of the Mott-insulating phase of bosons in an optical lattice can increase substantially with increasing temperature. We demonstrate that this phenomenon originates from thermally produced defects that can tunnel with ease. Since the near zero temperature coherence properties have been measured with high precision we expect these results to be verifiable in current experiments. \nIn the last part of the thesis we turn our attention to one dimensional Bose gases. We fo- cus on the moderate temperature weakly interacting regime namely the high temperature quasicondensate and quantum decoherent regimes, which we investigate using the stochas- tic projected Gross-Pitaevskii equation (SPGPE) formalism. Here we compare the SPGPE results against the Bethe ansatz and a mean-field formalism adapted to the quasicondensate regime. This theory covers a regime not addressed by other formalism.