Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userExceptional points in the one-dimensional Hubbard model
88
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
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.
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.
Using time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest neighbor repulsion, U and V, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit non-monotonic dependence on V. For small and intermediate values of V, both velocities increase with V. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by V. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit, and an effective model in the strong-coupling regime.
We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of $eta gtrsim 0.25$.
We study the interplay of disorder and correlation in the one-dimensional hole-doped Hubbard-model with disorder (Anderson-Hubbard model) by using the density-matrix renormalization group method. Concentrating on the doped-hole density profile, we find in a large $U/t$ regime that the clean system exhibits a simple fluid-like behavior whereas finite disorders create locally Mott regions which expand their area with increasing the disorder strength contrary to the ordinary sense. We propose that such an anomalous Mott phase formation assisted by disorder is observable in atomic Fermi gases by setup of the box shape trap.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
