Correlation effects in low dimensional quantum systems
Chun Yang
This dissertation discussed four low-dimensional systems: Hubbard ladder and its 2D extension, anisotropic Hubbard ladder, one-dimensional two-orbital t-J model, and Kondo model. All of them are of strongly correlated. Doped cuprates, as strongly correlated systems, have attracted a lot of attention in the condensed matter physics community, not just from the purely theoretical perspective, but also due to the novel applications beyond the conventional semiconductor paradigm. They display complicated phase diagram, defying the conventional rigid band theory, shaking our common sense and driving us to wrestle with many-body physics. With the aid of advanced experimental techniques such as ARPES, its various exotic electronic structure, such as waterfalls, hole pockets, Fermi arcs and kinks have been unveiled and remain open to interpretation. To attack such complicated problems, people usually build various models to mimic the CuO2 planes, which is the common feature of various cuprate compounds and is believed to be mainly responsible for their complicated properties, especially the high temperature superconductivity. In Chapter 3, we simulated the spectral properties of the 2- leg single-band Hubbard ladder and its 2-dimensional extension at and away from half-lling using the numerical tool: the combination of Cluster Perturbation Theory (CPT) with the time-dependent density matrix renormalization group method (tDMRG) as a solver. The main features of the spectrum can be described with a mean-eld dispersion, with kinks and pseudogap traced back to scattering between spin and charge degrees of freedom. As a bonus, we nd that the spectrum of hubbard ladder involves spin-polaron, the bound state of spinon and holon. Interacting one-dimensional electron systems generically behave dierent from higher dimensional systems in the sense that its low-energy excitations are described by Luttinger liquid theory as collective bosonic modes carrying spin and charge separately, the so-called spinons and holons, rather than the coherent quasi-particles in Fermi liquid theory. This phenomenon is known as spin-charge separation, an intrinsic property of 1D system. It can be thought of as a particular case of electron fractionalization. When multiple 1D chains get coupled, how the picture changes? In Chapter 4, we study the spectral function of the anisotropic 2-leg Hubbard ladder, one of the simplest multiple-chain systems. The spectrum can be understood as the scattering resultants of spinon and holons: As the inter-chain hopping is increased, the continuum in the bonding channel moves to higher energies and spinon and holon branches merge into a single coherent quasi-particle band. Simultaneously, the spectrum undergoes a crossover from a regime with two minima at incommensurate values of kx (a Mott insulator), to one with a single minimum at kx = (a band insulator). In addition, the spectrum contains a continuum of scattering states consisting of a triplon and a polaron, accompanied by the formation of bound states with higher spin 3 2 , ferromagnetic \spin bags" in which the hole can move freely. To analyze the formation of quasi-particle, we study the time-evolution of charge and spin degrees of freedom in real space after a hole is injected, which indicates that incoherent holons and spinons can emerge into polarons, that can propagate coherently, after a characterstic time . Multiorbital systems can involve Mott and Hund physics, and are rich in various phenomena, including orbital selective Mott transitions, spin-orbital separations, and pairing density wave due to the complex interplay between spin, charge and orbital degrees of freedom. Therefore, it can capture many unique features in real strongly correlated systems, such as iron pnictides and ruthenates, and thus attract a lot of investigations. In Chapter 5, we comprehensively study a one-dimensional two-orbital model at and below quarter lling, which realizes a number of unconventional phases, by means of DMRG and some analytical calculations. In particular, we nd that the system supports an extensive density wave in which excitons quasicondense with nite center-of-mass momentum. In this phase, excitons behave as hardcore bosons without charge order. In addition, excitons can pair to form biexcitons in a state that is close to a charge density wave instability. Finally, a genuine orbital-selective paired state (metallic plus spin-gapped superconductor) can be realized when pairing dominates over the interorbital repulsion. Kondo problem, as one of the most studied and best understood correlated systems, has been studied by various techniques, but the internal structure of its ground state has two deeply con icting pictures: At strong coupling limit, the system is essentially composed of a scattering center, which is a tightly bound singlet formed by the impurity and a localized electron at r0, and the remaining conduction electrons that are decoupled to the impurity and remain almost \free". At weak enough couplings, the singlet extends to the entire volume and the impurity will couple mostly to one electron at the Fermi level. In chapter 6, we provide a coherent picture to unveil the puzzle in the context of quantum information theory by deconstructing the Kondo singlet, both in real and energy space, and measuring the spin correlations between the impurity and the invididual free electron eigenstate based on two dierent measures. As a bonus, we can identify \projected natural orbitals" that can be used as a \good" approximate wavefunctions for simulations, and a quasi-order parameter that determines the crossover from weak to strong coupling regimes and furthermore oers the means to measure the Kondo screening length K. This screening length might be used to characterize the \size" of the Kondo cloud.
•Jan 1, 2018•0 citations