In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [Abdelwahab et al., preceding paper, Phys. Rev. B 96, 035445 (2017)]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely, paramagnetic Mott insulators, Luttinger liquids, and spin-$1/2$ Heisenberg chains. The validity of the effective ladder models is assessed for selected parameters by studying the dependence of results on the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate.
In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [Abdelwahab et al., preceding paper, Phys. Rev. B 96, 035445 (2017)]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely, paramagnetic Mott insulators, Luttinger liquids, and spin-1/2 Heisenberg chains. The validity of the effective ladder models is assessed for selected parameters by studying the dependence of results on the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate.
We present a theoretical study of correlated atomic wires deposited on substrates in two parts. In this first part, we propose lattice models for a one-dimensional quantum wire on a three-dimensional substrate and map them onto effective two-dimensional lattices using the Lanczos algorithm. We then discuss the approximation of these two-dimensional lattices by narrow ladder models that can be investigated with well-established methods for one-dimensional correlated quantum systems, such as the density-matrix renormalization group or bosonization. The validity of this approach is studied first for noninteracting electrons and then for a correlated wire with a Hubbard electron-electron repulsion using quantum Monte Carlo simulations. While narrow ladders cannot be used to represent wires on metallic substrates, they capture the physics of wires on insulating substrates if at least three legs are used. In the second part [Abdelwahab et al., following paper, Phys. Rev. B 96, 035446 (2017)], we use this approach for a detailed numerical investigation of a wire with a Hubbard interaction on an insulating substrate.
It is now possible to create wires consisting of a single chain of atoms on an insulating substrate, with possible applications in nanoscale circuitry. However, experimental data on such systems are currently rather limited and as such a thorough theoretical investigation of such systems is required. In particular, it is useful to know to what extent the behaviour of such wires is one-dimensional - purely one-dimensional systems display Luttinger liquid behaviour, as opposed to the Fermi liquid behaviour characteristic of higher dimensional systems. However, conventional techniques in theoretical surface science are unable to provide a description of electronic correlations at the level required for one dimensional systems. The existing literature on such atomic wire systems is first reviewed. A discussion of physics in one spatial dimension follows, with a thorough introduction to both the Luttinger liquid and the analytical solutions of the Luttinger model. These concepts are then applied to a simplified model of an atomic wire system - two coupled chains of atoms, on just one of which electron-electron interactions are included. The chain which includes interactions thus represents the wire, while the non-interacting chain represents, albeit incompletely, the influence of the insulating substrate upon which the wire is embedded. Evidence for Luttinger liquid behaviour would be found in the excitation spectra and correlation functions of the system. A Fortran 90 code was written to implement the above, and both a description of the code and numerical results are presented. The results from excitations and correlation functions of the system indicate that, within the limitations of the model, Luttinger liquid behaviour may well survive. It is possible to calculate for larger and more complicated systems by use of the Density Matrix Renormalization Group (DMRG) algorithm, which relies on keeping only those states of the many particle system needed to describe the ground state and the low-energy excitations. The underlying theory of DMRG is discussed and followed with presentation of preliminary results based on a Hubbard model Hamiltonian.
We present a theoretical study of two spinless fermion wires coupled to a three-dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block Lanczos algorithm. We then approximate the resulting system by narrow ladder models, which can be investigated using the density-matrix renormalization group method. In the absence of any direct wire-wire hopping we find that the substrate can mediate an effective wire-wire coupling so that the wires could form an effective two-leg ladder with a Mott charge-density-wave insulating ground state for arbitrarily small nearest-neighbor repulsion. In other cases the wires remain effectively uncoupled even for strong wire-substrate hybridizations leading to the possible stabilization of the Luttinger liquid phase at finite nearest-neighbor repulsion as found previously for single wires on substrates. These investigations show that it may be difficult to determine under which conditions the physics of correlated one-dimensional electrons can be realized in arrays of atomic wires on semiconducting substrates because they seem to depend on the model (and consequently material) particulars.
In a previous paper [Bischoff and Jeckelmann, Phys. Rev. B 96, 195111 (2017)] we introduced a density-matrix renormalization group method for calculating the linear conductance of one-dimensional correlated quantum systems and demonstrated it on homogeneous spinless fermion chains with impurities. Here we present extensions of this method to inhomogeneous systems, models with phonons, and the spin conductance of electronic models. The method is applied to a spinless fermion wire-lead model, the homogeneous spinless Holstein model, and the Hubbard model. Its capabilities are demonstrated by comparison with the predictions of Luttinger liquid theory combined with Bethe ansatz solutions and other numerical methods. We find a complex behavior for quantum wires coupled to interacting leads when the sign of the interaction (repulsive/attractive) differs in the wire and leads. The renormalization of the conductance given by the Luttinger parameter in purely fermionic systems is shown to remain valid in the Luttinger liquid phase of the Holstein model with phononic degrees of freedom.
We investigate a ladder system with two inequivalent legs, namely, a Hubbard chain and a one-dimensional electron gas. Analytical approximations, the density-matrix renormalization group method, and continuous-time quantum Monte Carlo simulations are used to determine ground-state properties, gaps, and spectral functions of this system at half-filling. Evidence for the existence of four different phases as a function of the Hubbard interaction and the rung hopping is presented. First, a Luttinger liquid exists at very weak interchain hopping. Second, a Kondo-Mott insulator with spin and charge gaps induced by an effective rung exchange coupling is found at moderate interchain hopping or strong Hubbard interaction. Third, a spin-gapped paramagnetic Mott insulator with incommensurate excitations and pairing of doped charges is observed at intermediate values of the rung hopping and the interaction. Fourth, the usual correlated band insulator is recovered for large rung hopping. We show that the wave numbers of the lowest single-particle excitations are different in each insulating phase. In particular, the three gapped phases exhibit markedly different spectral functions. We discuss the relevance of asymmetric two-leg ladder systems as models for atomic wires deposited on a substrate.
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.