Transport properties of the one-dimensional Hubbard model at finite temperature

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is two-fold: First, we compute both the charge and the spin current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity sigma(omega) in presence of small integrability-breaking next-nearest neighbor interactions (the extended Hubbard model). The DC conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a testbed for our numerics, we compute sigma(omega) for the integrable XXZ spin chain in its gapped phase

Renormalization group flows in one-dimensional lattice models: impurity scaling, umklapp scattering and the orthogonality catastrophe

We show that to understand the orthogonality catastrophe in the half-filled lattice model of spinless fermions with repulsive nearest neighbor interaction and a local impurity in its Luttinger liquid phase one has to take into account (i) the impurity scaling, (ii) unusual finite size $L$ corrections of the form $\ln(L)/L$, as well as (iii) the renormalization group flow of the umklapp scattering. The latter defines a length scale $L_u$ which becomes exceedingly large the closer the system is to its transition into the charge-density wave phase. Beyond this transition umklapp scattering is relevant in the renormalization group sense. Field theory can only be employed for length scales larger than $L_u$. For small to intermediate two-particle interactions, for which the regime $L > L_u$ can be accessed, and taking into account the finite size corrections resulting from (i) and (ii) we provide strong evidence that the impurity backscattering contribution to the orthogonality exponent is asymptotically given by $1/16$. While further increasing the two-particle interaction leads to a faster renormalization group flow of the impurity towards the cut chain fixed point, the increased bare amplitude of the umklapp scattering renders it virtually impossible to confirm the expected asymptotic value of $1/16$ given the accessible system sizes. We employ the density matrix renormalization group.Comment: 12 pages, 9 figure

The antiferromagnetic phase of the Floquet-driven Hubbard model

A saddle point plus fluctuations analysis of the periodically driven half-filled two-dimensional Hubbard model is performed. For drive frequencies below the equilibrium gap, we find discontinuous transitions to time-dependent solutions. A highly excited, generically non-thermal distribution of magnons occurs even for drive frequencies far above the gap. Above a critical drive amplitude, the low-energy magnon distribution diverges as the frequency tends to zero and antiferromagnetism is destroyed, revealing the generic importance of collective mode excitations arising from a non-equilibrium drive

Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases

The field of quantum simulations in ultra-cold atomic gases has been remarkably successful. In principle it allows for an exact treatment of a variety of highly relevant lattice models and their emergent phases of matter. But so far there is a lack in the theoretical literature concerning the systematic study of the effects of the trap potential as well as the finite size of the systems, as numerical studies of such non periodic, correlated fermionic lattices models are numerically demanding beyond one dimension. We use the recently introduced real-space truncated unity functional renormalization group to study these boundary and trap effects with a focus on their impact on the superconducting phase of the $2$D Hubbard model. We find that in the experiments not only lower temperatures need to be reached compared to current capabilities, but also system size and trap potential shape play a crucial role to simulate emergent phases of matter.Comment: 21 pages, 9 Figure

Characterization of absorbent polymers for the removal of volatile hydrophobic pollutants from air

An emerging innovation for the treatment of polluted air consists in using a liquid–solid biphasic system, in which the sequestering phase contains inert polymer beads. The different polymers tested here for this purpose were; Hytrel® G3548L, Hytrel® G4078W, styrene butadiene copolymer, 28% and 31%, silicone rubber, PEBAX® 2533, and rubber tires. The selection of the most effective polymer(s) first requires a determination of the uptake of the pollutants by the solid phase in terms of key polymer properties such as partition coefficient, diffusion coefficient and biodegradability. RESULTS: A significant difference was found in the uptake levels of α-pinene from the gas phase for the different polymers tested. Based on partition coefficient measurements, relatively non-polar polymers such as Kraton® tend to uptake α-pinene better than polar ones, such as Hytrel®. A reduction in the partition coefficient of α-pinene into polymers in the presence of water has also been observed. It was also proven that the tested polymers are not biodegradable. CONCLUSIONS: The uptake of α-pinene by the different polymers tested was determined and it was shown that such polymers could be used for air pollution control. Furthermore, their non-biodegradability justifies their use as absorbents. This paper provides a new opportunity to work with biofilters (BFs)/biotrickling filters (BTFs) using polymers as a sequestering phase

Superconductivity of repulsive spinless fermions with sublattice potentials

We explore unconventional superconductivity of repulsive spinless fermions on square and honeycomb lattices with staggered sublattice potentials. The two lattices can exhibit staggered d-wave and f-wave pairing respectively at low doping stemming from an effective two-valley band structure. At higher doping, in particular the square lattice displays a much richer phase diagram including topological p+ip superconductivity which is induced by a qualitatively different mechanism compared to the d-wave pairing. We illuminate this from several complementary perspectives: we analytically perform sublattice projection to analyze the effective continuum low-energy description and we numerically calculate the binding energies for pair and larger bound states for few-body doping near half filling. Furthermore, for finite doping, we present phase diagrams based on extensive FRG and and DMRG calculations