From Gapped Excitons to Gapless Triplons in One Dimension

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.Comment: 18 pages, 10 figure

Antiferromagnetic Chern insulator with large charge gap in heavy transition-metal compounds

Despite the discovery of multiple intrinsic magnetic topological insulators in recent years the observation of Chern insulators is still restricted to very low temperatures due to the negligible charge gaps. Here, we uncover the potential of heavy transition-metal compounds for realizing a collinear antiferromagnetic Chern insulator (AFCI) with a charge gap as large as 300 meV. Our analysis relies on the Kane-Mele-Kondo model with a ferromagnetic Hund coupling $J_{\rm H}$ between the spins of itinerant electrons and the localized spins of size $S$. We show that a spin-orbit coupling $\lambda_{\rm SO} \gtrsim 0.03t$, where $t$ is the nearest-neighbor hopping element, is already large enough to stabilize an AFCI provided the alternating sublattice potential $\delta$ is in the range $\delta \approx SJ_{\rm H}$. We establish a remarkable increase in the charge gap upon increasing $\lambda_{\rm SO}$ in the AFCI phase. Using our results we explain the collinear AFCI recently found in monolayers of CrO and MoO with charge gaps of 1 and $50$ meV, respectively. In addition, we propose bilayers of heavy transition-metal oxides of perovskite structure as candidates to realize a room-temperature AFCI if grown along the $[111]$ direction and subjected to a perpendicular electric field.Comment: 10 pages, 6 figure

A simplified approach to the magnetic blue shift of Mott gaps

The antiferromagnetic ordering in Mott insulators upon lowering the temperature is accompanied by a transfer of the single-particle spectral weight to lower energies and a shift of the Mott gap to higher energies (magnetic blue shift, MBS). The MBS is governed by the double exchange and the exchange mechanisms. Both mechanisms enhance the MBS upon increasing the number of orbitals. We provide an expansion for the MBS in terms of hopping and exchange coupling of a prototype Hubbard-Kondo-Heisenberg model and discuss how the results can be generalized for application to realistic Mott or charge-transfer insulator materials. This allows estimating the MBS of the charge gap in real materials in an extremely simple way avoiding extensive theoretical calculations. The approach is exemplarily applied to $\alpha$-MnTe, NiO, and BiFeO$_3$ and an MBS of about $130$ meV, $360$ meV, and $157$ meV is found, respectively. The values are compared with the previous theoretical calculations and the available experimental data. Our ready-to-use formula for the MBS simplifies the future studies searching for materials with a strong coupling between the antiferromagnetic ordering and the charge excitations, which is paramount to realize a coupled spin-charge coherent dynamics at a femtosecond time scale.Comment: 16 pages, 13 figure

Antiferromagnetic Chern insulator in centrosymmetric systems

An antiferromagnetic Chern insulator (AFCI) can exist if the effect of the time-reversal transformation on the electronic state cannot be compensated by a space group operation. The AFCI state with collinear magnetic order is already realized in noncentrosymmetric honeycomb structures through the Kane-Mele-Hubbard model. In this paper, we demonstrate the existence of the collinear AFCI in a square lattice model which preserves the inversion symmetry. Our study relies on the time-reversal-invariant Harper-Hofstadter-Hubbard model extended by a next-nearest-neighbor hopping term including spin-orbit coupling and a checkerboard potential. We show that an easy $z$-axis AFCI appears between the band insulator at weak and the easy $xy$-plane AF Mott insulator at strong Hubbard repulsion provided the checkerboard potential is large enough. The close similarity between our results and the results obtained for the noncentrosymmetric Kane-Mele-Hubbard model suggests the AFCI as a generic consequence of spin-orbit coupling and strong electronic correlation which exists beyond a specific model or lattice structure. An AFCI with the electronic and the magnetic properties originating from the same strongly interacting electrons is promising candidate for a strong magnetic blue shift of the charge gap below the N\'eel temperature and for realizing the quantum anomalous Hall effect at higher temperatures so that applications for data processing become possible.Comment: 14 pages, 9 figure

MARBLER: An Open Platform for Standarized Evaluation of Multi-Robot Reinforcement Learning Algorithms

Multi-agent reinforcement learning (MARL) has enjoyed significant recent progress, thanks to deep learning. This is naturally starting to benefit multi-robot systems (MRS) in the form of multi-robot RL (MRRL). However, existing infrastructure to train and evaluate policies predominantly focus on challenges in coordinating virtual agents, and ignore characteristics important to robotic systems. Few platforms support realistic robot dynamics, and fewer still can evaluate Sim2Real performance of learned behavior. To address these issues, we contribute MARBLER: Multi-Agent RL Benchmark and Learning Environment for the Robotarium. MARBLER offers a robust and comprehensive evaluation platform for MRRL by marrying Georgia Tech's Robotarium (which enables rapid prototyping on physical MRS) and OpenAI's Gym framework (which facilitates standardized use of modern learning algorithms). MARBLER offers a highly controllable environment with realistic dynamics, including barrier certificate-based obstacle avoidance. It allows anyone across the world to train and deploy MRRL algorithms on a physical testbed with reproducibility. Further, we introduce five novel scenarios inspired by common challenges in MRS and provide support for new custom scenarios. Finally, we use MARBLER to evaluate popular MARL algorithms and provide insights into their suitability for MRRL. In summary, MARBLER can be a valuable tool to the MRS research community by facilitating comprehensive and standardized evaluation of learning algorithms on realistic simulations and physical hardware. Links to our open-source framework and the videos of real-world experiments can be found at https://shubhlohiya.github.io/MARBLER/.Comment: 7 pages, 3 figures, submitted to MRS 2023, for the associated website, see https://shubhlohiya.github.io/MARBLER

Magnetic blue shift of Mott gaps enhanced by double exchange

A substantial energy gap of charge excitations induced by strong correlations is the characteristic feature of Mott insulators. We study how the Mott gap is affected by long-range antiferromagnetic order. Our key finding is that the Mott gap is increased by the magnetic ordering: A magnetic blue shift (MBS) occurs. Thus the effect is proportional to the exchange coupling in the leading order in the Hubbard model. In systems with additional localized spins the double-exchange mechanism induces an additional contribution to the MBS which is proportional to the hopping in the leading order. The coupling between spin and charge degrees of freedom bears the potential to enable spin-to-charge conversion in Mott systems on extreme time scales determined by hopping and exchange only, since a spin-orbit-mediated transfer of angular momentum is not involved in the process. In view of spintronic and magnonic applications, it is highly promising to observe that several entire classes of compounds show exchange and double-exchange effects. Exemplarily, we show that the magnetic contribution to the band-gap blue shift observed in the optical conductivity of α-MnTe is correctly interpreted as the MBS of a Mott gap

Effect of high-pressure torsion on microstructure, mechanical properties and corrosion resistance of cast pure Mg

© 2018, The Author(s). High-pressure torsion (HPT) processing was applied to cast pure magnesium, and the effects of the deformation on the microstructure, hardness, tensile properties and corrosion resistance were evaluated. The microstructures of the processed samples were examined by electron backscatter diffraction, and the mechanical properties were determined by Vickers hardness and tensile testing. The corrosion resistance was studied using electrochemical impedance spectroscopy in a 3.5% NaCl solution. The results show that HPT processing effectively refines the grain size of Mg from millimeters in the cast structure to a few micrometers after processing and also creates a basal texture on the surface. It was found that one or five turns of HPT produced no significant difference in the grain size of the processed Mg and the hardness was a maximum after one turn due to recovery in some grains. Measurements showed that the yield strength of the cast Mg increased by about seven times whereas the corrosion resistance was not significantly affected by the HPT processing