Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCharge diffusion in the one-dimensional Hubbard model
177
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 $eta gtrsim 0.25$.
Based on tensor network simulations, we discuss the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice described by the extended Fermi-Hubbard model. Considering different initial states, namely noninteracting, metallic, insulating spin and charge density waves, we identify several types of sudden interaction quenches which lead to dynamical criticality. In different scenarios, clear connections between DQPTs and particular properties of the mean double occupation or charge imbalance can be established. Dynamical transitions resulting solely from high-frequency time-periodic modulation are also found, which are well described by a Floquet effective Hamiltonian. State-of-the-art cold-atom quantum simulators constitute ideal platforms to implement several reported DQPTs experimentally.
The phase diagram of the one-dimensional extended Hubbard model at half-filling is investigated by a weak coupling renormalization group method applicable beyond the usual continuum limit for the electron spectrum and coupling constants. We analyze the influence of irrelevant momentum dependent interactions on asymptotic properties of the correlation functions and the nature of dominant phases for the lattice model under study.
We propose a new combined approach of the exact diagonalization, the renormalization group and the Bethe ansatz for precise estimates of the charge gap $Delta$ in the one-dimensional extended Hubbard model with the onsite and the nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $Delta$ including the prefactor without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $Delta$ is exponentially small, beyond usual renormalization group methods and/or finite size scaling approaches. The detailed results of $Delta$ down to of order of $10^{-10}$ near the MIT are shown as contour lines on the $U$-$V$ plane.
We investigate the dynamical spin and charge structure factors and the one-particle spectral function of the one-dimensional extended Hubbard model at half band-filling using the dynamical density-matrix renormalization group method. The influence of the model parameters on these frequency- and momentum-resolved dynamical correlation functions is discussed in detail for the Mott-insulating regime. We find quantitative agreement between our numerical results and experiments for the optical conductivity, resonant inelastic X-ray scattering, neutron scattering, and angle-resolved photoemission spectroscopy in the quasi-one-dimensional Mott insulator SrCuO$_2$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
