Entanglement scaling of excited states in large one-dimensional many-body localized systems

We study the properties of excited states in one-dimensional many-body localized (MBL) systems using a matrix product state algorithm. First, the method is tested for a large disordered non-interacting system, where for comparison we compute a quasi-exact reference solution via a Monte Carlo sampling of the single-particle levels. Thereafter, we present extensive data obtained for large interacting systems of L~100 sites and large bond dimensions chi~1700, which allows us to quantitatively analyze the scaling behavior of the entanglement S in the system. The MBL phase is characterized by a logarithmic growth (L)~log(L) over a large scale separating the regimes where volume and area laws hold. We check the validity of the eigenstate thermalization hypothesis. Our results are consistent with the existence of a mobility edge

Loschmidt-amplitude wave function spectroscopy and the physics of dynamically driven phase transitions

We introduce the Loschmidt amplitude as a powerful tool to perform spectroscopy of generic many-body wave functions and use it to interrogate the wave function obtained after ramping the transverse field quantum Ising model through its quantum critical point. Previous results are confirmed and a more complete understanding of the population of defects and of the effects of magnon-magnon interaction or finite-size corrections is obtained. The influence of quantum coherence is clarified

Spectral properties of one-dimensional Fermi systems after an interaction quench

We show that the single-particle spectral properties of gapless one-dimensional Fermi systems in the Luttinger liquid state reached at intermediate times after an abrupt quench of the two-particle interaction are highly indicative of the unusual nonequilibrium nature of this state. The line shapes of the momentum integrated and resolved spectral functions strongly differ from their ground state as well as finite temperature equilibrium counterparts. Using an energy resolution improved version of radio-frequency spectroscopy of quasi one-dimensional cold Fermi gases it should be possible to experimentally identify this nonequilibrium state by its pronounced spectral signatures.Comment: 5 pages, 3 figure

Thermal conductivity of the one-dimensional Fermi-Hubbard model

We study the thermal conductivity of the one-dimensional Fermi-Hubbard model at finite temperature using a density matrix renormalization group approach. The integrability of this model gives rise to ballistic thermal transport. We calculate the temperature dependence of the thermal Drude weight at half filling for various interactions and moreover, we compute its filling dependence at infinite temperature. The finite-frequency contributions originating from the fact that the energy current is not a conserved quantity are investigated as well. We report evidence that breaking the integrability through a nearest-neighbor interaction leads to vanishing Drude weights and diffusive energy transport. Moreover, we demonstrate that energy spreads ballistically in local quenches with initially inhomogeneous energy density profiles in the integrable case. We discuss the relevance of our results for thermalization in ultra-cold quantum gas experiments and for transport measurements with quasi-one dimensional materials

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

Magnetic ordering tendencies in hexagonal-boron-nitride–bilayer-graphene moiré structures

When hexagonal boron nitride (hBN) and graphene are aligned at zero or a small twist angle, a moiré structure is formed due to the small lattice constant mismatch between the two structures. In this paper, we analyze magnetic ordering tendencies, driven by on-site Coulomb interactions, of encapsulated bilayer graphene (BG) forming a moiré structure with one (hBN-BG) or both hBN layers (hBN-BG-hBN), using the random phase approximation. The calculations are performed in a fully atomistic Hubbard model that takes into account all π electrons of the carbon atoms in one moiré unit cell. We analyze the charge neutral case and find that the dominant magnetic ordering instability is uniformly antiferromagnetic. Furthermore, at low temperatures, the critical Hubbard interaction Uc required to induce magnetic order is slightly larger in those systems where the moiré structure has caused a band gap opening in the noninteracting picture, although the difference is less than 6%. Mean-field calculations are employed to estimate how such an interaction-induced magnetic order may change the observable single-particle gap sizes

Review of recent developments of the functional renormalization group for systems out of equilibrium

We recapitulate recent developments of the functional renormalization group (FRG) approach to the steady state of systems out of thermal equilibrium. In particular, we discuss second-order truncation schemes which account for the frequency-dependence of the two particle vertex and which incorporate inelastic processes. Our focus is on two different types of one-dimensional fermion chains: (i) infinite, open systems which feature a translation symmetry, and (ii) finite systems coupled to left and right reservoirs. In addition to giving a detailed and unified review of the technical derivation of the FRG schemes, we briefly summarize some of the key physical results. In particular, we compute the non-equilibrium phase diagram and analyze the fate of the Berezinskii–Kosterlitz–Thouless transition in the infinite, open system

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

Technical note Biological treatment of industrial wastewater containing formaldehyde and formic acid

The biological treatment of wastewater from an aminoplastic resin-producing industry was studied in a pre-denitrification system. This study reports results on the removal of organic matter and nitrogen compounds from wastewater which contained high levels of formaldehyde and formic acid. The formaldehyde concentration in the feed varied between 2 087.0 and 2 200.0 mg/ℓ, the mean removal being 99.9%. The mean efficiency of formic acid removal was 99.7%, and its concentration in the feed ranged between 1 384.6 and 1 513.9 mg/ℓ. The total organic carbon (TOC) values in the feed varied from 1 423.0 to 1 599.5 mg/ℓ, corresponding to an organic loading rate of about 0.20 kg TOC/m3·d. High TOC removal was achieved, around 92.0%. With regard to nitrogen compounds, the total Kjeldahl nitrogen (TKN) concentration in the feed ranged between 467.8 and 492.3 mg/ℓ. The applied nitrogen loading rate was around 0.06 kg TKN/m3·d, and the mean percentage of TKN removal was 76.7%. Water SA Vol 32(1)pp:115-11