At the University of Geneva a group of enthusiastic graduate students have instigated a seminar series devoted to ‘relevant techniques in many-body physics’: the “ToolBoX“. I had the honor of providing the first set of lectures on density functional theory, for which I prepared some notes with exercises.. Download it here below!
At our weekly “Flat Club” in Geneva I presented on Friday 11 October the latest experiments from Andrea Young’s group, who observed the quantum anomalous Hall effect in twisted bilayer graphene. Download my slides here (PDF).
Title: Quantum Anomalous Hall effect in Twisted Bilayer Graphene
Abstract: A recent experiment brings together many topics discussed in earlier Flat Club meetings: namely the observation of a Quantum Anomalous Hall effect in magic angle twisted bilayer graphene aligned with hBN. In order to understand these results, we will discuss first the concept of a Chern insulator, its response in a magnetic field, and the role of ferromagnetism. Next, we will discuss how the alignment of hBN with twisted graphene opens up the possibility of creating a ferromagnetic Chern insulator. We will end with the experiments by the Young group who observed a QAH with a quantized rho_xy within 0.1% of h/e^2.
Title: Unconventional Many-Body Localization in Long-Range Quantum Spin Glasses
Abstract: Spin glasses are a well-studied class of classical systems where random interactions lead to spin freezing at low temperatures. On the other hand, many-body localization is a quantum phe- nomenon where randomness and interactions lead to localization characterized by, amongst others, area law entanglement entropy and local integrals of motion. We show that a third, intermediate, state can emerge in a long-range one-dimensional spin glass under the applica- tion of a transverse field. At small applied fields and low temperatures the spin glass order remains, as characterized by the Edwards-Anderson order parameter. However, interacting low-energy spin resonances at large distances create unconventional long-range entanglement in eigenstates. The quench dynamics therefore display a wide variety in possible results: while some spins remain frozen, others ‘thaw’. The ”quantum spin glass” is therefore neither ergodic, nor many-body localized.
Title: The nu = -2 state in Twisted Bilayer Graphene: a bad Mott insulator?
Abstract: Twisted bilayer graphene near the ‘magic angle’ has shown a wealth of interesting states: superconductivity, ferromagnetism, correlated insulator states and a linear resistivity ‘strange metal’. I will focus on the state at carrier density nu = -2 relative to charge neutrality. At this filling the resistivity is minimal at around 4 K, above which there is reported linear resistivity and below which it is insulating. Using unbiased real-space Hartree-Fock calculations, we show that the nu = -2 state undergoes a charge transfer between “ring” and “center” orbitals leading to an even further flattening of the bands. Including a Hubbard interaction will then lead to a Mott insulator. However, unlike ‘strong’ Mott insulators like the cuprate parent compounds, this Mott state can easily be destroyed by temperature or magnetic field. I will discuss possible mechanisms for this ‘bad insulator’ behavior, including its relation to the multi-channel Kondo effect
Abstract: I studied the non-equilibrium response of an initial Néel state under time evolution with the Kitaev honeycomb model. This time evolution can be computed using a random sampling over all relevant flux configurations. With isotropic interactions the system quickly equilibrates into a steady state valence bond solid. Anisotropy induces an exponentially long prethermal regime whose dynamics are governed by an effective toric code. Signatures of topology are absent, however, due to the high energy density nature of the initial state.
Title: Quantum Thermalization and the Expansion of Atomic Clouds
Authors: Louk Rademaker, Jan Zaanen
Abstract: The ultimate consequence of quantum many-body physics is that even the air we breathe is governed by strictly unitary time evolution. The reason that we perceive it nonetheless as a completely classical high temperature gas is due to the incapacity of our measurement machines to keep track of the dense many-body entanglement of the gas molecules. The question thus arises whether there are instances where the quantum time evolution of a macroscopic system is qualitatively different from the equivalent classical system? Here we study this question through the expansion of noninteracting atomic clouds. While in many cases the full quantum dynamics is indeed indistinguishable from classical ballistic motion, we do find a notable exception. The subtle quantum correlations in a Bose gas approaching the condensation temperature appear to affect the expansion of the cloud, as if the system has turned into a diffusive collision-full classical system.
At the 16th International Conference on Transport in Interacting Disordered Systems (TIDS16) in Granada, Spain I presented my work done with Miguel Ortuño and Andres Somoza on many-body localization (MBL). Specifically, these are the first large-system results using our method of displacement transformations to find the MBL integrals of motion.
At the APS March Meeting 2016 in Baltimore I was giving an invited talk, with the title ‘New theoretical tools for quantum glasses, with and without quenched disorder’ (that’s talk F13.01). Now the APS allowed me to upload the slides and everything on their website, so if you missed the talk, please find the info here: https://absuploads.aps.org/presentation.cfm?pid=11532