The phase diagram of the two-dimensional Hubbard model poses one of the most interesting conundrums in contemporary condensed matter physics. While describing essential aspects of high-temperature superconductors, it remains a paradigmatic model embodying the complexity of the ‘strong correlation problem’. In this talk, I demonstrate how our recent advances in tensor network methods allow us to perform controlled and accurate simulations ranging from the high-temperature incoherent limit down to essentially the ground state regime on finite cylinders. Focusing on the hole-doped square lattice at strong coupling, we discover a novel phase characterized by commensurate short-range antiferromagnetic correlations and a small nodal charge gap at temperatures above the half-filled stripe phase extending to zero temperature. These features bear a strong resemblance to the pseudogap regime of cuprate superconductors. Furthermore, our results on the frustrated triangular lattice Hubbard model at half-filling reveal a strong competition between several orders in the insulating regime. This includes various forms of magnetic orderings as well as chiral correlations, associated with a putative chiral spin liquid, which are stabilized at different temperatures due to order-by-disorder phenomena. These advances open up new avenues in understanding the emergence of superconductivity in doped and frustrated antiferromagnets.
Symmetry is a key concept in physics. Some symmetries exist however only in the classical world and can not be realized in the quantum theory. When this happens we speak of a (quantum) anomaly. The most prominent examples are the triangle anomalies arising the quantum field theory of chiral fermions. In particle physics they explain the short lifetime of the neutral pion, give rise to consistency conditions on gauge theories and allow powerful insight into the low energy dynamics. Over the last decade it has bee realized that anomalies also give rise to dissipationless transport phenomena in hot and dense relativistic matter. I will review this anomalous transport theory and then discuss how it can be applied to the electronics of Weyl semimetals, nuclear physics and quantum optics.
Quantum anomalies are a central feature of quantum field theories. The most notorious examples of such phenomena are the chiral anomalies, which show upon quantization of chiral massless fermions. In general, quantum field theories depict three types of chiral anomalies: Abelian, non-Abelian, and gravitational. In the past decade, with the discovery of Weyl semimetals, chiral anomalies have become pertinent in the realm of condensed matter physics. Since then, negative longitudinal magnetoresistance, bearing the signature of Abelian anomaly, has been observed in several Weyl materials and some of them also show an indirect signature of mixed gauge-gravity anomaly in thermal transport. Recent developments have allowed us to go beyond the original paradigm of linearly dispersing chiral fermions, as nowadays gapless chiral systems with finite band curvatures can be found in various solid-state compounds. In this talk, I will discuss a representative class of such systems, the multi-Weyl semimetals. The effective field theory for multi-Weyl semimetals will be constructed revealing the presence, for the first time in a condensed matter system, of non-Abelian anomalies. The imprint of the anomaly in the transport properties will also be discussed.
Minkowski functionals and tensors are comprehensive measures of random spatial structures [1,2]. In fact, they characterize all additive geometric information, as proven rigorously in integral geometry. Thus, they offer robust and versatile insights into the intricate interplay of geometry and physics in complex structures and have been have been successfully applied to a broad spectrum of physical systems, from galaxy distributions to nuclear matter and from cellular materials to nanostructured surfaces. This talk provides an overview of the definition, properties, and some recent applications of Minkowski functionals and tensors [3-5].  Schröder-Turk et al. Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures. Adv. Mater. 23, 2535–2553 (2011).  Klatt, Schröder-Turk, Mecke. Mean-intercept anisotropy analysis of porous media. II. Conceptual shortcomings of the MIL tensor definition and Minkowski tensors as an alternative. Med. Phys. 44, 3663–3675 (2017).  Klatt, Mecke. Detecting structured sources in noisy images via Minkowski maps. EPL 128, 60001 (2019).  Spengler et al. Strength of bacterial adhesion on nanostructured surfaces quantified by substrate morphometry. Nanoscale 11, 19713–19722 (2019).  Klatt et al. Universal hidden order in amorphous cellular geometries. Nature Communications 10, 811 (2019).
Will a large economy be stable? Building on Sir Robert May’s original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in which inputs for production are not easily substitutable, as in several real-world supply chains. We argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong, or when substitutability of their production inputs is reduced. At marginal stability and for large heterogeneities, we find that the distribution of firm sizes develops a power-law tail, as observed empirically. Crises can be triggered by small idiosyncratic shocks, which lead to “avalanches” of defaults characterized by a power-law distribution of total output losses. This scenario would naturally explain the well-known “small shocks, large business cycles” puzzle, as anticipated long ago by Bak, Chen, Scheinkman, and Woodford.