In this thesis we study the strongly-correlated-electron physics of the longstanding H-Tc-superconductivity problem using a non-perturbative method, the Dynamical Mean Field Theory (DMFT), capable to go beyond standard perturbation-theory techniques. DMFT is by construction a local theory which neglects spatial correlation. Experiments have however shown that the latter is a fundamental property of cuprate materials. In a first step, we approach the problem of spatial correlation in the normal state of cuprate materials using a phenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop in detail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT), capable of considering short-ranged spatial correlation in a system, and we implement it using the exact diagonalization algorithm . After benchmarking CDMFT with the exact one-dimensional solution of the Hubbard Model, we employ it to study the density-driven Mott metal-insulator transition in the two-dimensional Hubbard Model, focusing in particular on the anomalous properties of the doped normal state close to the Mott insulator. We finally study the superconducting state. We show that within CDMFT the one-band Hubbard Model supports a d-wave superconductive state, which strongly departs from the standard BCS theory. We conjecture a link between the instabilities found in the normal state and the onset of superconductivity.
Comment on "Z2-slave-spin theory for strongly correlated fermions" + Reply to the Reply to the "Comment on ?Z2-slave-spin theory for strongly correlated" fermions?
Coherent cellular dynamical mean-field theory: a real-space quantum embedding approach to disorder in strongly correlated electron systems
Max-Planck-Institut für Festkörperforschung（马克斯·普朗克固体研究所）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究院计算量子物理中心）；Institute of Information Systems Engineering, TU Wien（维也纳工业大学信息系统工程学院）；Institute of Solid State Physics, TU Wien（维也纳工业大学固体物理研究所）；Department of Physics, Friedrich-Alexander-Universität Erlangen/Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学物理系）
This thesis describes the development of the density matrix embedding theory (DMET) and its applications to lattice strongly correlated electron problems, including a review of DMET theory and algorithms (Ch 2), investigation of finite size scaling (Ch 3), Applications to high-temperature superconductivity (Ch 4-6), a framework for finite-temperature DMET (Ch 7).
The effects associated with exciton Bose condensate formation in strongly correlated spin crossover systems are considered within the effective Hamiltonian obtained from the two-orbital Hubbard-Kanamori model. The collective excitations spectrum at various points of the temperature-crystal field phase diagram is calculated. The role of the electron-phonon interaction is discussed. The exciton and magnetic order photoenhancement (induction) in strongly correlated spin crossover systems a new mechanism based on the cooperative effect of electron-phonon and interatomic exchange interactions and t…
We show how strongly correlated materials could be described within the framework of an excitonic insulator formalism, and delineate the relationship between inter- and intra-band ordering phenomena. Our microscopic model of excitons clarifies the fundamental role of Van-Hove-singularity-nesting in driving both inter- and intra-band ordering transitions, and uncovers an interesting connection with resonating-valence-bond physics.
An exact formula for the temperature dependent Hall number of metals is derived. It is valid for non-relativistic fermions or bosons, with arbitrary potential and interaction. This DC transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.
High transition temperature superconductors in cuprates exhibit the charge-density-wave fluctuations and the ferromagnetic time-reversal-symmetry-breaking fluctuation in the polar Kerr rotation experiments. We demonstrate that they share the same root of origin, and the underlying mechanism also leads to the pseudogap formation. The pseudogap formation, the charge-density-wave fluctuation, and the time-reversal-symmetry-breaking fluctuation are the consequent phenomena of the correlation. They are the basic notions in strongly correlated electron systems.
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The strongly-correlated subspace is identified from the occupation number band structure as opposed to a mean-field energy band structure. The self-consistent solution of the many-body model Hamiltonian and a generalized Kohn-Sham equation exactly incorporates momentum-dependent and crystal-symmetric correlations into electronic structure calculations in a way that…
Strongly correlated systems of fermions have a number of exciting collective properties. Among them, the creation of a lattice that is occupied by doublons, i.e. two quantum particles with opposite spins, offers interesting electronic properties. In the past a variety of methods have been proposed to control doublon formation, both, spatially and temporally. Here, a novel mechanism is proposed and verified by exact diagonalization and nonequilibrium Green functions simulations---fermionic doublon creation by the impact of energetic ions. We report the formation of a nonequilibrium steady state…
A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the solution of a Schrödinger equation with an effective Hamiltonian that can be viewed as embedding the marginal wave function in the environment of weakly correlated electrons. Here, the complementary equation for the conditional amplitude is replaced by a generalized Kohn-Sham equation, for which an orbital-dependent functional approximation is shown to reproduce th…
This is a reply to A. A. Katanin's comment [A. A. Katanin, Nat. Commun. 12, 1433 (2021); arXiv:2103.02966] on our paper [X. Deng et al., Nat. Commun. 10, 2721 (2019); arXiv:1708.05752].
We present a Gutzwiller von Neumann dynamics (GvND) method for simulating equilibrium and nonequilibrium phenomena in strongly correlated electron systems. Our approach is a real-space formulation of the time-dependent Gutzwiller approximation method. Applying the GvND method to simulate interaction quenches in the Peierls-Hubbard model, we demonstrate the amplification of initial inhomogeneities, which in turn results in the collapse of quench-induced synchronized oscillation. Moreover, we find a dynamical phase transition separating two quasi-stationary regimes with rather distinct spatial d…
We investigated kinetic properties of correlated pairing states in strongly correlated phase of the Hubbard model in two space dimensions. We employ an optimization variational Monte Carlo method, where we use the improved wave function $ψ_λ= e^{-λK}ψ_G$ for the Gutzwiller wave function $ψ_G$ with $K$ being the kinetic part of the Hamiltonian. The Gutzwiller-BCS state is stabilized as the potential energy driven superconductivity because the Coulomb interaction energy is lowered while the kinetic energy increases in this state. In contrast, we show that in the $ψ_λ$-BCS wave function $ψ_{λ-BCS…
The effective lattice models in strongly correlated electron systems are \emph{derived} in particular for the cuprate superconductors, that incorporate the quantum fluctuations of the spin Berry's phase and the antiferromagnetic fluctuation. Consistent with the field-theoretical approach, the density modulation, the weak ferromagnetism, and the superconductivity are reproduced. We discussed the pros and cons of the effective-model approach and demonstrate that both positive and negative Hubbard model are the effective models subject to the occurrence of the quantum fluctuations of the correlat…
