Twisted bilayer graphene, Kitaev quenches and spontaneous symmetry breaking

The month november was quite successful publication-wise, as four of my publications have been accepted.

Quenching the Kitaev honeycomb model
Starting from an antiferromagnet, let it evolve with Kitaev’s spin liquid honeycomb model. I developed the technique to study what happens next, a combination of Majorana Loschmidt echo’s and gauge field Monte Carlo. A prethermal regime appears, characterized by magnetization oscillations that can be described by the toric code. Accepted by SciPost.

An Introduction to Spontaneous Symmetry Breaking
Together with Aron Beekman and Jasper van Wezel, I wrote a lecture notes on the basics of spontaneous symmetry breaking. Aimed at graduate students, it is a modern overview containing both the classics (Mermin-Wagner theorem, Nambu-Goldstone modes) as well as modern notions (tower of states, type A/B symmetry breaking, topology). Accepted by SciPost Lecture Notes.

Exact ground state of the Lieb-Mattis Hamiltonian as a superposition of Néel states
The Lieb-Mattis Hamiltonian was originally used to show that the ground state of the Heisenberg antiferromagnet is a symmetric singlet state. How then, one might wonder, does the symmetry broken antiferromagnetic state arise? Well, read my published work in Physical Review Research. 

Charge smoothening and band flattening due to Hartree corrections in twisted bilayer graphene
Together with Paula Mellado I calculated the Hartree corrections in twisted bilayer graphene when doping away from charge neutrality. Surprisingly, the charge transfer we observe between AB/BA and AA regions of the Moiré unit cell makes the flat bands even flatter. Published in Physical Review B.

Quantum Anomalous Hall effect in Twisted Bilayer Graphene

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.

To read:
Serlin et al., Intrinsic quantized anomalous Hall effect in a moiré heterostructure,

Unconventional Many-Body Localization in Long-Range Quantum Spin Glasses

At the Conference on “Complex Quantum Systems out of Equilibrium” in Murcia, Spain I presented my latest work with Dmitry Abanin on the relation between MBL and spin glasses. This work has been published on the arXiv now as well. The full presentation slides can be downloaded here (PDF).

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.

The nu=-2 state in Twisted Bilayer Graphene: A Bad Insulator?

At the “Mottness, Poor Conductors, and Strange Metals” Workshop at the Tsung-Dao Lee Institute, Shanghai, China I presented my work and some new speculations on twisted bilayer graphene. The full presentation can be downloaded here (PDF).

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

Quenching the Kitaev honeycomb model

This work was presented first in a seminar at the University of Toronto on 18 October 2017. The slides of this presentation can be downloaded here (pptx, 13 MB).

Title: Quenching the Kitaev honeycomb model

Author: Louk Rademaker


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.


Quantum Thermalization and the Expansion of Atomic Clouds

I also presented this work in the form of a poster at the SPICE workshop ’Non-equilibrium Quantum Matter’, Mainz, Germany, from 30 May to 2 June 2017. The poster can be downloaded here (pdf, 1.3 MB).

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.



Phonon linewidth due to electron-phonon interactions with strong forward scattering in FeSe thin films on oxide substrates

Title: Phonon linewidth due to electron-phonon interactions with strong forward scattering in FeSe thin films on oxide substrates

Authors: Yan Wang, Louk Rademaker, Elbio Dagotto, Steven Johnston

Abstract: The discovery of an enhanced superconducting transition temperature Tc in monolayers of FeSe grown on several oxide substrates has opened a new route to high-Tc superconductivity through interface engineering. One proposal for the origin of the observed enhancement is an electron-phonon (e-ph) interaction across the interface that peaked at small momentum transfers. In this paper, we examine the implications of such a coupling on the phononic properties of the system. We show that a strong forward scattering leads to a sizable broadening of phonon lineshape, which may result in charge instabilities at long-wavelengths. However, we further find that the inclusion of Coulombic screening significantly reduces the phonon broadening. Our results show that one might not expect anomalously broad phonon linewidths in the FeSe interface systems, despite the fact that the e-ph interaction has a strong peak in the forward scattering (small q) direction.


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.


MBL-to-Ergodic Transition from the perspective of Integrals of Motion

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.

A sneak peek: the accuracy of our method increases order by order and with increasing disorder. Download the full presentation as a pptx file (4.5 MB)