## 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

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.

arXiv:1710.09761

## 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.

arXiv:1703.02489

## 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.

ArXiv:1703.02013

## 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

## 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)

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

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

Louk Rademaker, Zohar Nussinov, Leon Balents, Vladimir Dobrosavljevic

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

## APS March Meeting talk on glasses

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