We study the one-dimensional two-orbital Hubbard model with general local interactions including a pair-hopping term. The model might be realized in one-dimensional transition-metal nanowires. Phase diagrams at $T=0$ are obtained by numerical integration of renormalization group equations and bosonization. Particular attention is paid to the effects of orbital degeneracy (or near degeneracy), interactions favoring locally high-spin configurations, and velocity differences. Dynamical symmetry enlargement and duality approaches are employed to determine ground states and to understand quantum phase transitions between them. An important result is that the pair-hopping term and associated orbital symmetry can lead to new insulating states. The ground state for the spin-polarized case is also discussed.
We study the one-dimensional two-orbital Hubbard model with general local interactions including a pair-hopping term. The model might be realized in one-dimensional transition-metal nanowires. Phase diagrams at T=0 are obtained by numerical integration of renormalization group equations and bosonization. Particular attention is paid to the effects of orbital degeneracy (or near degeneracy), interactions favoring locally high-spin configurations, and velocity differences. Dynamical symmetry enlargement and duality approaches are employed to determine ground states and to understand quantum phase transitions between them. An important result is that the pair-hopping term and associated orbital symmetry can lead to new insulating states. The ground state for the spin-polarized case is also discussed.
The Hubbard model is a simple but profound theoretical tool for understanding the physics underlying strongly correlated systems. This phenomenology includes, but is not limited to, metal-insulating transitions, charge and spin order (charge density/spin density waves), superconducting phases, non-Fermi liquid physics, among others. Examining one dimensional physical models described by the Hubbard Hamiltonian can teach us much about the related physics of higher dimensional systems. Applying advanced numerical computational techniques such as density matrix numerical renormalization group (DMRG) to one-dimensional manypbody model Hamiltonians allows for the calculation of ground state energies and dynamical spectral functions with extremely high precision and accuracy. This thesis explores the application of DMRG numerical techniques to one-dimensional physical systems described by Hamiltonians beyond the conventional Hubbard model, and the nuanced physical effects observed for these systems across various regimes and phases. A Wannier Hubbard chain composed of non-orthogonal overlapping atomic orbitals was transformed to an orthogonal atomic basis using a non-unitary Lowdin transformation. The calculation of energies, dynamical spectral functions and the photoemission spectrum for this Wannier Hubbard chain revealed phases not previously observed for Hubbard chains at half-filling. Additional analysis and calculations were performed for a CuO chain described by the Luther-Emery Hamiltonian that epitomizes charge-transfer physics. The motivation for studying this CuO chain was previous literature on transition metal oxides (TMOs) and the mapping of multiband Hamiltonians to single band models in certain energy regimes. Finally, we performed computational analysis for a spin-3/2 generalized Hubbard chain. By spanning the full phase space of our spin-3/2 Hubbard chain in terms of chemical potential μ and external magnetic field h we observed non-typical Cooper pairing states and novel phases for different symmetries of our Hamiltonian.--Author's abstract
The low-energy physics of the one-dimensional pair hopping (PH) and attractive Hubbard models are expected to be similar. Based on numerical calculations on small chains, several authors have recently challenged this idea and predicted the existence of a phase transition at half filling and finite positive coupling for the pair-hopping model. We reexamine the controversy by making systematic comparisons between numerical results obtained for the PH and attractive Hubbard models. To do so, we have calculated the Luttinger parameters (spin and charge velocities, stiffnesses, etc.) of the two models using both the density matrix renormalization-group method for large systems and Lancz\'os calculations with twisted boundary conditions for smaller systems. Although most of our results confirm that both models are very similar we have found some important differences in the spin properties for the small sizes considered by previous numerical studies (6-12 sites). However, we show that these differences disappear at larger sizes (14-42 sites) when sufficiently accurate eigenstates are considered. Accordingly, our results strongly suggest that the ground-state phase transition previously found for small systems is a finite size artifact. Interpreting our results within the framework of the Luttinger liquid theory, we discuss the origin of the apparent contradiction between the predictions of the perturbative renormalization-group approach and numerical calculations at small sizes.
The one-band two-dimensional Hubbard Hamiltonian is analyzed using a real-space renormalization-group block method. The renormalization-group method, previously applied to the one-dimensional case has been extended to two dimensions. It is also shown how to avoid the proliferation of new terms during the process if the shape of the blocks and the symmetries of the kept states are chosen conveniently. We characterize the ground state by its energy per site, the gap of charge excitations, the double occupancy, and the effective hopping. The system shows an insulating behavior in the case of half filling for all nonzero interaction parameter, U, if the hopping is isotropic (ty=tx); that is to say, the gap opens for all positive U, as in the one-dimensional case. If the hopping anisotropy, \ensuremath{\alpha}=ty/tx, is different from the unity and zero the ground state is a conductor up to a critical value (U/t)c1, which depends on \ensuremath{\alpha}. We have analyzed in the same way another filling, n=7/9. The system behaves as a conductor, paramagnetic up to a value (U/t)c2\ensuremath{\sim}2 and weakly ferromagnetic for higher values of U.
By the bosonization and renormalization-group schemes, a half-filled Hubbard chain with density-dependent hopping is investigated at weak coupling. The model involved has an electron–hole symmetry and an SO(4) symmetry. The phase diagram consists of three different phases divided by a charge transition at on-site repulsion U = U c and a spin transition at U = U s , with U s = − U c = 16 π ( t c − 1 ) , including a Mott insulator with the SDW correlation, a dimerized insulator with the BCDW correlation, and a Luttinger metal with the coexisting TS and BSDW correlations. The effective three-body repulsion ( t c − 1 > 0 ) and attraction ( t c − 1 < 0 ) induce the dimerized and metallic phases, respectively. • We study a 1D Hubbard model with symmetric density-dependent hopping analytically. • We provide a theoretical scheme of realization of the BCDW and TS instabilities. • The results supplement further understanding of quantum properties of 1D correlated systems.
We investigate three different types of quantum phase transition occurring in quasi one-dimensional systems theoretically and numerically. First, we study the band-insulator to Mott-insulator transition occurring in charge-transfer complexes, for which the half-filled one-dimensional ionic Hubbard model is considered to be the prototype model. The study is carried out by first deriving an effective spin-one model, and then studying the model numerically using the density matrix renormalization group. We perform a careful finite-size scaling analysis of the mass gaps, order-parameters, and relative susceptibility. We confirm the existence of two quantum critical points. Analysis of the critical exponents confirms that the band-insulator-to-spontaneously-dimerized phase transition belong to the 2D Ising class. The spontaneously dimerized phase undergoes a phase transition to the Mott-insulator which is an infinite-order. Second, we investigate the Mott metal-insulator transition for the half-filled Hubbard model with both nearest-neighbor t and next-nearest-neighbor t′ hopping terms. We study the model using the bosonization approach and density matrix renormalization group simulations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We present results of density matrix renormalization group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving the spin and the charge degrees of freedom. Finally, we investigate quantum phase transitions phases in low-dimensional fermionic and spin models that go from uniform to spatially inhomogeneous, i.e., dimerized, trimerized, or incommensurate, phases. We propose a new approach based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.
We study the real-time evolution of a charge-excited state in a one-dimensional eg-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the z direction, electrons hop between adjacent 3z2−r2 orbitals, while x2−y2 orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies 3z2−r2 orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between 3z2−r2 orbital and x2−y2 orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems.