Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. The Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of charge gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time-dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed: 1) the recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and 2) the Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible–near-infrared domains.
Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. The Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of charge gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time-dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed: 1) the recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and 2) the Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible–near-infrared domains.
Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of Charge Gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed:(1) Recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and (2) Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible-near-infrared domains.
In this thesis, we theoretically investigate exotic quantum phenomena underlying periodically-driven systems.We discuss three distinct systems, noninteracting Dirac systems, lattice systems with a strong repulsive interaction, and lattice systems with a strong attractive interaction.We reveal various novel phenomena underlying these systems, and provide clear understanding of them.Periodically-driven systems, i.e., systems with a discrete time-translational symmetry, are described by the Floquet formalism, which maps the time-dependent Hamiltonian to a static "photon-dressed Hamiltonian".While a perturbative expansion of this Hamiltonian from the limit of high driving frequency has clarified various novel phenomena peculiar to periodically-driven systems, such an approach suffers from serious heating or damage when it is applied to realistic condensed matters.In this thesis, we focus on a lower-frequency regime, especially when the heating should be suppressed due to the small driving amplitude or an energy gap larger than the driving frequency.There, the high-frequency expansion cannot capture the relevant physics, so that we first formulate various perturbative expansions for three distinct regimes, i.e., high-frequency, small-amplitude, and strong-coupling regimes.We apply the small-amplitude expansion to two-and three-dimensional Dirac electrons driven by a circularly-polarized light to explore their behavior in the lowfrequency regime.We find an emergence of infinite numbers of topological gaps for the former and Weyl nodes for the latter.We also discuss how a regularization of the model affects this topological structure.We then introduce a strong repulsive interaction, and discuss behaviors of spins using the strong-coupling expansion.We predict an emergence of scalar spin chirality when a circularly-polarized light is illuminated, and discuss possible applications to photo-induced chiral spin liquids, and optical probing of spin chirality.Finally we turn to a strong attractive interaction to discuss the fate of the ordinary s-wave superconductivity under the periodic driving.We demonstrate an emergence of long sought-after η-pairing superconductivity, first as a ground state of the photon-dressed Hamiltonian, and then as a consequence of a dynamical phase transition in an isolated system such as an optical lattice system.
A review of the physical properties of small systems described by various model Hamiltonians is given. Their physical properties are found either exactly or by using Monte-Carlo methods, and are compared with properties of bulk systems. It is shown that (i) clusters differ in an essential way from the bulk, having electronic states strongly dependent on the geometry and cluster size, but, at the same time, (ii) important insights into the nature of electron correlation and low-energy excitations in solids may be gained by cluster studies. In particular, the cluster calculations allow one to identify the tendencies to various kinds of symmetry-broken states in the (extended) Hubbard model and give a simple qualitative understanding of the low temperature properties of the Kondo and the heavy-fermion systems. Furthermore, cluster calculations allow one to study such problems as the development of magnetic moment at chemisorbed atoms for strong correlations and the suppression of frustration by quantum fluctuations. Recently, cluster calculations gave important information about the possible role of charge transfer processes and magnetic interactions in the microscopic mechanism of pairing in high temperature superconducting oxides.
We propose a method to study the time evolution of correlated electrons driven by a harmonic perturbation. Combining Floquet formalism to include the time-dependent field and cluster perturbation theory to solve the many-body problem in the presence of short-range correlations, we treat the electron double dressing, by photons and by $e\text{\ensuremath{-}}e$ interactions, on the same footing. We apply the method to an extended Hubbard chain at half occupation, and we show that in the regime of small field frequency and for given values of field strength, the zero-mode Floquet band is no longer gapped and the system recovers a metallic state. Our results are indicative of an omnipresent mechanism for insulator-to-metal transitions in one-dimensional systems.
We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is analyzed by comparing it to an equivalent implementation in undriven systems. The dynamics of double occupancies for the near- and off-resonant driving regime indicate that the effective Hamiltonian picture is valid for several orders of magnitude in modulation time. Furthermore, we show that driving a hexagonal lattice compared to a simple cubic lattice allows us to modulate the system up to 1 s, corresponding to hundreds of tunneling times, with only minor atom loss. Here, driving at a frequency close to the interaction energy does not introduce resonant features to the atom loss.
"We have studied the extended Hubbard and the Peierls-extended Hubbard models in one dimension using primarily computational methods. We discuss the derivation of the models and the computational methods used to study them, focusing primarily on our extensions over existing numerical methods. In particular, we present the construction of ""operator-loop"" updates for spin-1/2 fermions and the inclusion of electron-phonon interactions in the Stochastic Series Expansion Quantum Monte Carlo method and the use of Quantum Parallel Tempering to improve the quality of the numerical data. For the extended Hubbard model at half-filling, we have confirmed the existence of a recently reported bond-order wave phase for the ground state in a small region of parameter space between the well-known charge- and spin-density wave phases. We have studied in detail the nature of the associated quantum phase transitions between all the phases. Upon doping away from half-filling, the doubly-degenerate, spin and charge gapped long-range-ordered ground states of the model are shown to evolve to a Luther-Emery liquid with no charge gap but a finite spin gap. For the Peierls-extended Hubbard model, which includes both electron-phonon and electron-electron interactions, we have studied the dimerization transition of the half-filled system in the presence of fully quantum mechanical phonons. We show that the transition to a dimerized state occurs only when the electron-phonon coupling exceeds a finite critical value that depends on the bare phonon frequency. This is in contrast to previous studies in similar models with adiabatic phonons that had predicted a dimerized state for arbitrarily small values of the electron-phonon coupling."