## Hofstadter subband ferromagnetism in twisted bilayer graphene

Together with the Yu Saito and Andrea Young (UC Santa Barbara) we wrote a paper about symmetry broken states in the presence of large magnetic fields in twisted bilayer graphene.

## Many-body localization and delocalization from the perspective of Integrals of Motion

Title: Many-body localization and delocalization from the perspective of Integrals of Motion
Louk Rademaker, Miguel Ortuno, Andres M. Somoza

Abstract: We study many-body localization (MBL) and delocalization from the perspective of integrals of motion (IOMs). MBL can be understood phenomenologically through the existence of macroscopically many localized IOMs. However, IOMs exist for all many-body systems, and non-localized IOMs determine properties on the ergodic side of the MBL transition too. Here we explore their properties using our method of displacement transformations. We show how different quantities can be calculated using the IOMs as an expansion in the number of operators. For all values of disorder the typical IOMs are localized, suggesting the importance of rare fluctuations in understanding the delocalization transition.

arXiv:1610.06238

## Absence of Marginal Stability in Self-Generated Coulomb Glasses

Title: Absence of Marginal Stability in Self-Generated Coulomb Glasses

Abstract: We investigate the structure of metastable states in self-generated Coulomb glasses. In dramatic contrast to disordered electron glasses, we find that these states lack marginal stability. Such absence of marginal stability is reflected by the suppression of the single-particle density of states into an exponentially soft gap of the form $g(\epsilon) \sim |\epsilon|^{-3/2} e^{-V / \xi |\epsilon|}$.
To analytically explain this behavior, we extend the stability criterion of Efros and Shklovskii to incorporate local charge correlations, in quantitative agreement with our numerical findings.
Our work suggests the existence of a new class of self-generated glasses dominated by strong geometric frustration.

arXiv:1605.01822

## Quantum Critical Matter and Phase Transitions in Rare-Earths and Actinides

Today I finished a review paper, together with John Mydosh from Leiden University, about quantum criticality in heavy fermion materials. It will be published (after editing and such) in the Handbook of Chemistry and Physics of Rare Earths and Actinides. Unfortunately, the Elsevier policies do not allow me to put it on arXiv, only on my personal webpage.

Download here our raw manuscript of the review paper ‘Quantum Critical Matter and Phase Transitions in Rare-Earths and Actinides’

Abstract: In this Chapter we discuss quantum critically, the notion that properties of a material are governed by the existence of a phase transition at zero temperature. The point where a second-order (continuous) phase transition takes places is known as a quantum critical point (QCP). Materials that exhibit a quantum critical points can be tuned through their quantum phase transition by, for example, pressure, chemical doping or disorder, frustration, and magnetic field. The study of quantum phase transitions (QPT) was initially theoretically driven, showing that high- temperature properties of a material with a QPT are directly influenced by the properties of the QCP itself. We start this Chapter by discussing the predictions of quantum critical and Hertz- Millis theory. Experimentally, we will mainly limit ourselves to f-electron based materials: the rare-earths Li(Ho,Y)F4, Ce(Cu,Au)6, YbRh2Si2, the Cerium series Ce(Co, Rh; Ir)In5 and one actinide based material, URu2Si2. These ‘heavy fermion’ metals (4f or 5f) represent prototype materials of quantum critical matter, and we will critically review their experimental signatures and their evolving theoretical descriptions. We conclude with other manifestations of quantum phase transitions beyond the rare-earths and actinides.

## Publication: Influence of long-range interactions on charge ordering phenomena on a square lattice

Abstract: Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice with fixed particle density, we have identified several interesting phases, such as a generalization of Wigner crystals at low particle densities and stripe phases at densities between ρ=1/3 and 1/2. These stripes act as domain walls in the checkerboard phase present at half-filling. The phases are characterized at zero temperatures using numerical simulations, and mean field theory is used to construct a finite temperature phase diagram.
ReferenceLouk Rademaker, Yohanes Pramudya, Jan Zaanen, and Vladimir Dobrosavljević, Phys. Rev. E 88, 032121 (2013)