Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Role of the Exchange Interaction in the One-Dimensional $n$-Component Hubbard Model
106
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The commensurate $p/q$-filled $n$-component Hubbard chain was investigated by bosonization and high-precision density-matrix renormalization-group analysis. It was found that depending on the relation between the number of components $n$, and the filling parameter $q$, the system shows metallic or insulating behavior, and for special fillings bond-ordered (dimerized, trimerized, tetramerized etc.) ground state develops in the insulating phase. A mean-field analysis shows that this bond ordering is a direct consequence of the spin-exchange interaction, which plays a crucial role in the one-parameter Hubbard model -- not only for infinite Coulomb repulsion, but for intermediate values as well.
rate research
Read More
We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time evolution of these nonequilibrium states, by using numerical forward-propagation approaches to chains as long as 20 sites. For a class of typical states, we find excellent agreement with linear-response theory and unveil the existence of remarkably clean charge diffusion in the regime of strong particle-particle interactions. Moreover, we demonstrate that this diffusive behavior does not depend on certain details of our initial conditions, i.e., it occurs for five different realizations with random and nonrandom internal degrees of freedom, single and double occupation of the central site, and displacement of spin-up and spin-down particles.
Non-Hermitian phenomena offer a novel approach to analyze and interpret spectra in the presence of interactions. Using the density-matrix renormalization group (DMRG), we demonstrate the existence of exceptional points for the one-particle Greens function of the 1D alternating Hubbard chain with chiral symmetry, with a corresponding Fermi arc at zero frequency in the spectrum. They result from the non-Hermiticity of the effective Hamiltonian describing the Greens function and only appear at finite temperature. They are robust and can be topologically characterized by the zeroth Chern number. This effect illustrates a case where temperature has a strong effect in 1D beyond the simple broadening of spectral features. Finally, we demonstrate that exceptional points appear even in the two-particle Greens function (charge structure factor) where an effective Hamiltonian is difficult to establish, but move away from zero frequency due to a distinct symmetry constraint.
The one-dimensional repulsive SU$(n)$ Hubbard model is investigated analytically by bosonization approach and numerically using the density-matrix renormalization-group (DMRG) method for $n=3,4$, and 5 for commensurate fillings $f=p/q$ where $p$ and $q$ are relatively prime. It is shown that the behavior of the system is drastically different depending on whether $q>n$, $q=n$, or $q<n$. When $q>n$, the umklapp processes are irrelevant, the model is equivalent to an $n$-component Luttinger liquid with central charge $c=n$. When $q=n$, the charge and spin modes are decoupled, the umklapp processes open a charge gap for finite $U>0$, whereas the spin modes remain gapless and the central charge $c=n-1$. The translational symmetry is not broken in the ground state for any $n$. On the other hand, when $q<n$, the charge and spin modes are coupled, the umklapp processes open gaps in all excitation branches, and a spatially nonuniform ground state develops. Bond-ordered dimerized, trimerized or tetramerized phases are found depending on the filling.
A detailed study of the one-dimensional ionic Hubbard model with interaction $U$ is presented. We focus on the band insulating (BI) phase and the spontaneously dimerized insulating (SDI) phase which appears on increasing $U$. By a recently introduced continuous unitary transformation [Krull et al. Phys. Rev. B {bf 86}, 125113 (2012)] we are able to describe the system even close to the phase transition from BI to SDI although the bare perturbative series diverges before the transition is reached. First, the dispersion of single fermionic quasiparticles is determined in the full Brillouin zone. Second, we describe the binding phenomena between two fermionic quasiparticles leading to an $S=0$ and to an $S=1$ exciton. The latter corresponds to the lowest spin excitation and defines the spin gap which remains finite through the transition from BI to SDI. The former becomes soft at the transition indicating that the SDI corresponds to a condensate of these $S=0$ excitons. This view is confirmed by a BCS mean field theory for the SDI phase.
We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy $n_b=5$, we calculate the phase boundaries between the Mott insulator and the `superfluid phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the `superfluid phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the `superfluid phase the spectral weight is concentrated around zero momentum.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
