# Highlights

Publication Highlights

### Disorder-Free Localization in an Interacting 2D Lattice Gauge Theory

Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. This result is all the more surprising since the conventional many-body localization is conjectured to be unstable in two dimensions; hence the gauge invariance represents an alternative robust localization mechanism surviving in higher dimensions in the presence of interactions. Specifically, we demonstrate nonergodic behavior in the quantum link model by obtaining a bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition. We study the quantum dynamics in this system by introducing the method of “variational classical networks,” an efficient and perturbatively controlled representation of the wave function in terms of a network of classical spins akin to artificial neural networks. We identify a distinguishing dynamical signature by studying the propagation of line defects, yielding different light cone structures in the localized and ergodic phases, respectively. The methods we introduce in this work can be applied to any lattice gauge theory with finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.

P. Karpov et al., Phys. Rev. Lett. 126, 130401 (2021).
Publication Highlights

### Anatomy of $\mathbb{Z}_2$ fluxes in anyon Fermi liquids and Bose condensates

We study in detail the properties of $\pi$-fluxes embedded in a state with a finite density of anyons that form either a Fermi liquid or a Bose-Einstein condensate. By employing a recently developed exact lattice bosonization in 2D, we demonstrate that such $\pi$-flux remains a fully deconfined quasi-particle with a finite energy cost in a Fermi liquid of emergent fermions coupled to a $\mathbb{Z}_2$ gauge field. This $\pi$-flux is accompanied by a screening cloud of fermions, which in the case of a Fermi gas with a parabolic dispersion binds exactly 1/8 of a fermionic hole. In addition there is a long-ranged power-law oscillatory disturbance of the liquid surrounding the $\pi$-flux akin to Friedel oscillations. These results carry over directly to the $\pi$-flux excitations in orthogonal metals. In sharp contrast, when the $\pi$-flux is surrounded by a Bose-Einstein condensate of particles coupled to a $\mathbb{Z}_2$ gauge field, it binds a superfluid half-vortex, becoming a marginally confined excitation with a logarithmic energy cost divergence.

O. Pozo et al., Phys. Rev. B 103, 035145 (2021)
Publication Highlights

### Random Multipolar Driving: Tunably Slow Heating through Spectral Engineering

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For $n\geq 1$, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent $2n+1$. A simple theory based on Fermi’s golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the $n\to \infty$ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.

H. Zhao et al., Phys. Rev. Lett. 126, 040601 (2021).
Publication Highlights

### Possible Inversion Symmetry Breaking in the $S=1/2$ Pyrochlore Heisenberg Magnet

We address the ground-state properties of the long-standing and much-studied three-dimensional quantum spin liquid candidate, the $S=1/2$ pyrochlore Heisenberg antiferromagnet. By using SU(2) density-matrix renormalization group (DMRG), we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground-state energy, $E_0/N_{sites}=-0.490(6)$, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.

I. Hagymási et al., Phys. Rev. Lett. 126, 117204 (2021)
News

### MPI-PKS kicks off the year with 3 new research groups

A warm welcome to three new research group leaders at the institute! Pierre Haas joins us from the University of Oxford and heads the research group "Self-Organization of Multicellular Systems". The group is based jointly at the Center for Systems Biology Dresden, the MPI-PKS and the MPI-CBG and will focus on the mechanics of cells and tissues. In particular, Pierre's group is interested in deriving the continuum theories that represent the rich mechanical behavior of tissues during development and thus allow understanding how robust development is compatible with mechanical constraints and biological variability. While the research of the group is theoretical, it will work in close collaboration with experimental groups at the MPI-CBG and beyond. Matt Eiles originally joined MPI-PKS from Purdue University and was a Distinguished PKS Postdoctoral Fellow until December, now heading the new group "Correlations and Transport in Rydberg Matter" associated with the Finite Systems Division. Via the study of Rydberg matter the group aims to answer fundamental questions about atomic structure, low-energy collisions and scattering, and the behavior of ultracold gases, while also raising new questions related to localization, transport, highly correlated systems, quantum chaos, semiclassical dynamics, and quantum simulation. A strong relationship with ongoing experimental work and the flexibility of Rydberg atoms to shed insight into new theoretical inquiries motivate their research. Marko Popovic comes to Dresden from the EPFL Lausanne and establishes the research group "Order and Disorder in Driven Systems" associated with the Biological Physics Division. The group will investigate mechanical and rheological properties of out-of-equilbrium systems, with an emphasis on development of biological tissues and the role of structural disorder. Furthermore, emergence of order in biological systems and its relation to tissue mechanical properties will be of particular interest. Welcome to the institute and have a great start!
Publication Highlights

### The aging of protein droplets

Many proteins form small droplets that separate out of the cell’s cytoplasm, just like oil de-mixes from water. Since their discovery, these liquid-like protein droplets have been identified in myriad important biological phenomena ranging from embryonic development over neuro-degeneration to DNA regulation. For instance, the localization of protein droplets in a specific location during early development of a worm is believed to determine which cells will become the sexual organs of the adult worm. In another example, protein condensation into droplets under cell stress is associated with the growth of fibers related to neurodegeneration as seen in ALS (Amyotrophic lateral sclerosis) disease.
Observations have shown that the material properties of these protein condensates change with time. However, an appropriate measurement and description of the material properties and their evolution over time was missing so far. Researchers from the MPI of Molecular Cell Biology and Genetics (MPI-CBG) and the MPI for the Physics of Complex Systems (MPI-PKS), together with their colleagues from the TU Dresden, EMBL Heidelberg and the IMBA Vienna have now filled this gap. In their study, recently published in Science, the scientists show that protein droplets exhibit aging behavior in which they change slowly from liquid-like behavior to a more solid-like state.
Louise Jawerth, postdoc in the Frank Jülicher and Tony Hyman groups and first author of the publication, explains, “In order to carefully measure and characterize the time-dependent material properties we first developed a new optical trap technique (Jawerth et al physical review letters 2018 121 (25), 258101)”. The former ELBE postdoctoral fellow at the CSBD continues, ”We then found that droplet aging shows a strongly increasing viscosity, which leads to more solid-like behaviour. Our study suggests that the time-dependent material properties arise from unspecific mechanisms such as jamming of molecules.”
Frank Jülicher, director at the MPI-PKS and member of the CSBD and the “Physics of Life” (PoL) Cluster of Excellence at the TU Dresden, adds, “Similar aging has been seen in other materials with time-dependent properties such as traditional glass, plastics, rubbers, or common household items like toothpaste or mayonnaise. By establishing a connection to glass forming systems, we open a new window in which we can utilize a wealth of understanding of these other systems to understand protein droplets.”
The second supervisor of the study, Anthony Hyman, director at the MPI-CBG and member of the CSBD, summarizes, “The analogy to traditional glasses also suggests that the unspecific interactions resulting in a solid-like state require less energy to dissolve than, for instance, in comparison to a gel comprised of very strong bonds. Furthermore, it may be used in cells as novel stress sensors. Further study on aging in protein droplets may help to answer fundamental biological questions, for example in embryonic development or DNA transcription, and to better understand neurodegenerative diseases. Vice versa, it may also lead to insights into glass-like aging more generally, which is considered one of the big unsolved questions in condensed matter physics.”

L. Jawerth et al., Science 370, 1317 (2020)
Publication Highlights

### Many-Body Delocalization via Emergent Symmetry

Many-body localization (MBL) provides a mechanism to avoid thermalization in many-body quantum systems. Here, we show that an emergent symmetry can protect a state from MBL. Specifically, we propose a $Z_2$ symmetric model with nonlocal interactions, which has an analytically known, SU(2) invariant, critical ground state. At large disorder strength, all states at finite energy density are in a glassy MBL phase, while the lowest energy states are not. These do, however, localize when a perturbation destroys the emergent SU(2) symmetry. The model also provides an example of MBL in the presence of nonlocal, disordered interactions that are more structured than a power law. Finally, we show how the protected state can be moved into the bulk of the spectrum.

N. S. Srivatsa et al., Phys. Rev. Lett. 125, 240401 (2020).
Awards and Honors

### Carlsberg Foundation Young Researcher Fellowship for Anne E. B. Nielsen

Anne E. B. Nielsen receives 670 thousand euro from the Carlsberg Foundation to search for and investigate new types of non-thermal behaviors in strongly correlated quantum many-body systems. The Carlsberg Foundation Young Researcher Fellowships are three-year grants that allow the grantee to establish an independent research group working on a research topic within natural science, social science, or the humanities.
Publication Highlights

### Protein condensates as aging Maxwell fluids

Cells organize their biochemistry by forming liquid-like condensates of biomolecules that can act as tiny reactors to localize chemical reactions. Researchers from the Physics of Complex Systems together with with colleagues of the MPI of molecular cell biology and genetics in Dresden investigate the physical nature and material properties of protein condensates using microrheology techniques. They find that many protein condensates increase their viscosity with time and slow their dynamics, while always remaining soft and liquid-like. This is suggestive of glassy behaviors and could have important implications for cellular dynamics.

Jawerth et al. Science 370, 1317 (2020)