The interaction of time-dependent electromagnetic fields with electrons in quantum materials can give rise to many both fundamentally interesting as well as technologically relevant phenomena like transient band structure manipulations or the emergence of prethermal states of matter, which are not a result of heating. This thesis contributes theoretical insights to both these topics: We model the interference of Floquet and Volkov side bands, which are a result of the dressing of electron states by light, in a time-resolved angle-resolved photoemission spectroscopy (ARPES) experiment. Furthermore, we analyze the emergence of a band-like feature in the non-equilibrium spectral function of a one-dimensional charge-density wave insulator upon periodic driving. Secondly, we use the fermionic truncated Wigner approximation (fTWA), a phase space method for the time evolution of interacting fermions, to study the light-induced order parameter dynamics in SU(N)-symmetric fermionic lattice models. By comparison with exact analytical results for an interaction quench in the Hubbard model, we find that dephasing-induced prethermalization is correctly described by fTWA. We discuss photoinduced prethermal transitions between competing phases of matter in the large-N Hubbard-Heisenberg model and find a pronounced frequency-dependence of the transition. This work contributes to a better understanding of photoinduced order parameter dynamics from a microscopic perspective.
The interaction of time-dependent electromagnetic fields with electrons in quantum materials can give rise to many both fundamentally interesting as well as technologically relevant phenomena like transient band structure manipulations or the emergence of prethermal states of matter, which are not a result of heating. This thesis contributes theoretical insights to both these topics: We model the interference of Floquet and Volkov side bands, which are a result of the dressing of electron states by light, in a time-resolved angle-resolved photoemission spectroscopy (ARPES) experiment. Furthermore, we analyze the emergence of a band-like feature in the non-equilibrium spectral function of a one-dimensional charge-density wave insulator upon periodic driving. Secondly, we use the fermionic truncated Wigner approximation (fTWA), a phase space method for the time evolution of interacting fermions, to study the light-induced order parameter dynamics in SU(N)-symmetric fermionic lattice models. By comparison with exact analytical results for an interaction quench in the Hubbard model, we find that dephasing-induced prethermalization is correctly described by fTWA. We discuss photoinduced prethermal transitions between competing phases of matter in the large-N Hubbard-Heisenberg model and find a pronounced frequency-dependence of the transition. This work contributes to a better understanding of photoinduced order parameter dynamics from a microscopic perspective.
Periodically driven quantum systems provide a versatile platform for engineering and exploring non-equilibrium states of matter that have no equilibrium counterparts– a field commonly re- ferred to as Floquet engineering. The research presented in this thesis addresses the microscopic interpretation of experimental spectroscopic signatures, the stability of these driven states in the presence of strong many-body interactions, and the emergence of novel forms of non-equilibrium criticality encoded in quantum entanglement. The first part of the thesis focuses on the interpretation of time- and angle-resolved photo- emission spectroscopy (tr-ARPES), the primary experimental tool for detecting Floquet–Bloch sidebands (FBs). The measured signal reflects interference between processes occurring both inside the material and in the vacuum. In particular, Floquet-dressed initial states coexist and interfere with Volkov-dressed final states arising from the laser-assisted photoelectric effect (LAPE). Their experimental identification requires careful comparison with theoretical predic- tions. Using graphene as a model Dirac material, we perform a systematic comparison between two theoretical frameworks: the first-order perturbative Born approximation (PB1) and time- dependent nonequilibrium Green’s functions (tdNEGF), and compare them with experimental results. We disentangle intrinsic Floquet states, LAPE, and their interference, and quantify how polarization, incidence angle, and near-surface screening shape the observed spectra. Our findings show that, once matrix elements are included, both methods capture qualitative trends, but tdNEGF is necessary to describe the full energy–momentum-resolved features, including hybridization gaps. While non-interacting systems exhibit well-defined FBs, interacting systems absorb energy and can evolve toward an infinite-temperature state. To study this competition between coherent driving and many-body heating, in the second part we consider a one-dimensional chain of interacting spinless fermions using exact diagonalization (ED) and matrix product state (MPS) methods. We compute time-dependent spectral functions and correlation measures, and compare the spectral width of the many-body excitation continuum with the driving frequency to define low- and high-frequency regimes. In our parameter regime, low-frequency driving leads to strong overlap between Floquet sectors, resulting in rapid heating and loss of coherence. For weakly populated continua, we find a transient timescale for the suppression of FBs. When the driving frequency exceeds the continuum width, FBs are well separated and long-lived. Thefinalpartofthethesisinvestigatesnon-equilibriumphenomenafromaninformation-theoretic perspective. Wereportanewclassofdynamicalphasetransitions,termedtemporalentanglement transitions (TET) characterized by non-analytic reorganizations of the entanglement spectrum, in a periodically driven transverse-field Ising chain. These transitions occur in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking, marked by the closure of the Schmidt gap and parity flips. These transitions remain invisible to conventional local observables. Finite-size scaling reveals that TET belong to a universality class with a correlation-length exponent ν = 1, mirroring equilibrium Ising universality despite their purely dynamical origin.
We study the microscopic dynamics of competing ordered phases in a two-dimensional correlated electron model, which is driven with a pulsed electric field of finite duration. In order to go beyond a mean-field treatment of the electronic interactions we adopt a large-N generalization of the Hubbard model and combine it with the semiclassical fermionic truncated Wigner approximation as a time evolution method. This allows us to calculate dephasing corrections to the mean-field dynamics and to obtain stationary states, which we interpret as prethermal order. We use this framework to simulate the light-induced transition between two competing phases (bond density wave and staggered flux) and find that the postpulse stationary state order parameter values are not determined alone by the amount of absorbed energy but depend explicitly on the driving frequency and field direction. While the transition between the two prethermal phases takes place at similar total energies in the low- and high-frequency regimes, we identify an intermediate-frequency regime for which it occurs with minimal heating.
The study of nonequilibrium phenomena in interacting lattice systems can provide new perspectives on correlation effects, and information on metastable states of matter. Mott insulators are a promising class of systems for nonequilibrium studies, since they exhibit exotic phenomena and complex phase diagrams upon doping, and because a large Mott gap provides protection against fast thermalization and heating after photo-excitations. We can thus expect the emergence of interesting transient states and photo-induced phases in Mott systems. This review presents the current understanding of the mechanisms which control the time evolution of photo-doped charge carriers and the properties of photo-induced metastable states. We focus on recent theoretical progress, identify the relevant underlying concepts, and link them to experimental observations. The review starts with a general discussion of field-induced nonequilibrium setups and an overview of key experiments which revealed characteristic properties of photo-excited Mott states, proceeds with a compact overview of the theoretical tools which have been developed to investigate these strongly correlated nonequilibrium states, and then analyzes Mott insulators driven out of equilibrium by static electric fields, periodic fields, and short laser pulses. We also discuss the appearance of nonthermal electronic orders in photo-excited Mott systems, including nonthermal spin and orbital orders, η pairing states, and novel types of excitonic orders.
This thesis explores non-equilibrium phenomena in quantum many-body systems, with a focus on correlated electron systems and photon Bose-Einstein condensates. The first part develops the theoretical foundation, beginning with the Lindblad master equation and the construction of non-equilibrium quantum field theory. The two-particle irreducible effective action formalism is introduced, from which the Kadanoff-Baym equations for real-time evolution and the Dyson equation for steady-states are derived. The theoretical groundwork continues with a treatment of strongly correlated electron systems, where non-equilibrium dynamical mean-field theory (DMFT), auxiliary particles, and the non-crossing approximation (NCA) are introduced. These techniques, together with the Lindblad and Kadanoff-Baym approaches, are used throughout the subsequent chapters. The second part presents the main research projects of this thesis. The first two projects are concerned with the fate of the heavy fermion state under irradiation of light. To accurately incorporate light-matter interactions in this case, dipole transitions must be included. In the first project a periodically driven system is considered, where the light can be treated semiclassically. A Floquet DMFT+NCA framework is developed, revealing the mechanisms and conditions under which the heavy fermion state is most strongly suppressed. The second project analyzes a THz spectroscopy experiment performed on CeCu6. In this case a semi-classical treatment of the light field is no longer sufficient, and a full two-time evolution of all the non-equilibrium Green functions is necessary. This approach reveals the microscopic mechanisms underlying the collapse and revival of the Kondo state observed in the experiment. The next project investigates a recent experiment regarding an observation of a non-Hermitian phase transition in EuO. The equilibrium properties of EuO are first analyzed, and then an exciton model is constructed that gives rise to the non-Hermitian phase transition, in good agreement with experimental observations. In the final project, a photon Bose-Einstein condensate in a dye-filled microcavity is studied. A stabilization mechanism, distinct from thermalization, is revealed which admits a condensate phase for orders of magnitude longer than the experimentally relevant timescales.
Correlated electron systems represent a wide class of materials which at equilibrium display fascinating properties. Several recent experimental breakthroughs in the field of femtosecond spectroscopy and cold atomic gases allow nowadays to investigate the real time dynamics of these many-body quantum systems. Since strongly correlated systems usually escape single particle approaches, the theoretical study of their dynamics constitutes a formidable problem which necessitates the development of novel techniques. In this Thesis we investigate the out-of-equilibrium physics of simple paradigmatic models that are believed to capture some essential physics of interacting fermions by means of the time dependent extension of the Gutzwiller Variational Approach. After an introductory Chapter on the recent results in this field, in Chapter 2 we present the Gutzwiller Approach in-and-out of equilibrium. In Chapter 3 we investigate the dynamics for the single band Hubbard model after a linear ramp of the Coulomb interaction. We will show that a dynamical transition appears for any duration of the ramp; this dynamical point is adiabatically connected to the zero temperature Metal-to-Insulator transition. We will then consider the role of quantum fluctuations beyond mean field. In Chapter 4 we consider the dynamics of an initial antiferromagnetic state under a quench of the interaction in the single band fermionic Hubbard model. We will show that non-thermal ordered states survive more than expected and that two different nonequilibrium antiferromagnets can be distinguished. Finally in Chapter 5 we will consider a two-band Hubbard model which we believe captures the main physics of the paradigmatic compound vanadium sesquioxide, V2 O3 . After an investigation of the equilibrium properties for this model, we will provide evidences that non-thermal metallic phases can emerge upon an excitation of a Mott insulator.
We propose to combine the Floquet formalism for systems in ac fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively include both the correlation effects and nonlinear effects due to the driving field, which is imperative in analyzing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single-band noninteracting systems. As a demonstration, we have applied the method to the Falicov-Kimball model in intense ac fields to calculate the spectral function. The result shows that photoinduced midgap states emerge from strong ac fields, triggering an insulator-metal transition.