# Publications

## Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene

Physical Review Letters American Physical Society **126** (2021) 137601

We uncover topological features of neutral particle-hole pair excitations of correlated quantum anomalous Hall (QAH) insulators whose approximately flat conduction and valence bands have equal and opposite nonzero Chern number. Using an exactly solvable model we show that the underlying band topology affects both the center-of-mass and relative motion of particle-hole bound states. This leads to the formation of topological exciton bands whose features are robust to nonuniformity of both the dispersion and the Berry curvature. We apply these ideas to recently reported broken-symmetry spontaneous QAH insulators in substrate aligned magic-angle twisted bilayer graphene.

## Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory

PRX Quantum American Physical Society **2** (2021) 10352

A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPTs) and also to entanglement transitions in random tensor networks. Many of our results are for “all-to-all” quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field-theory descriptions for spatially local systems of any finite dimensionality. To build intuition, we first solve the simplest “minimal cut” toy model for entanglement dynamics in all-to-all circuits, finding scaling forms and exponents within this approximation. We then show that certain all-to-all measurement circuits allow exact results by exploiting local treelike structure in the circuit geometry. For this reason, we make a detour to give general universal results for entanglement phase transitions in a class of random tree tensor networks with bond dimension 2, making a connection with the classical theory of directed polymers on a tree. We then compare these results with numerics in all-to-all circuits, both for the MPT and for the simpler “forced-measurement phase transition” (FMPT). We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information that is propagated between the initial and final time. We demonstrate signatures of the two phases that can be understood from simple models. Finally we propose Landau-Ginsburg-Wilson-like field theories for the measurement phase transition, the forced-measurement phase transition, and for entanglement transitions in random tensor networks. This analysis shows a surprising difference between the measurement phase transition and the other cases. We discuss variants of the measurement problem with additional structure (for example free-fermion structure), and questions for the future.

## Memory effects, arches and polar defect ordering at the cross-over from wet to dry active nematics.

Soft matter (2021)

We use analytic arguments and numerical solutions of the continuum, active nematohydrodynamic equations to study how friction alters the behaviour of active nematics. Concentrating on the case where there is nematic ordering in the passive limit, we show that, as the friction is increased, memory effects become more prominent and +1/2 topological defects leave increasingly persistent trails in the director field as they pass. The trails are preferential sites for defect formation and they tend to impose polar order on any new +1/2 defects. In the absence of noise and for high friction, it becomes very difficult to create defects, but trails formed by any defects present at the beginning of the simulations persist and organise into parallel arch-like patterns in the director field. We show aligned arches of equal width are approximate steady state solutions of the equations of motion which co-exist with the nematic state. We compare our results to other models in the literature, in particular dry systems with no hydrodynamics, where trails, arches and polar defect ordering have also been observed.

## Author Correction: Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers.

Nature materials (2021)

## Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers

Nature Materials Nature Research (2021)

Actomyosin machinery endows cells with contractility at a single-cell level. However, within a monolayer, cells can be contractile or extensile based on the direction of pushing or pulling forces exerted by their neighbours or on the substrate. It has been shown that a monolayer of fibroblasts behaves as a contractile system while epithelial or neural progentior monolayers behave as an extensile system. Through a combination of cell culture experiments and in silico modelling, we reveal the mechanism behind this switch in extensile to contractile as the weakening of intercellular contacts. This switch promotes the build-up of tension at the cell-substrate interface through an increase in actin stress fibres and traction forces. This is accompanied by mechanotransductive changes in vinculin and YAP activation. We further show that contractile and extensile differences in cell activity sort cells in mixtures, uncovering a generic mechanism for pattern formation during cell competition, and morphogenesis.

## Magnetic Microswimmers Exhibit Bose-Einstein-like Condensation.

Physical review letters **126** (2021) 078001-

We study an active matter system comprised of magnetic microswimmers confined in a microfluidic channel and show that it exhibits a new type of self-organized behavior. Combining analytical techniques and Brownian dynamics simulations, we demonstrate how the interplay of nonequilibrium activity, external driving, and magnetic interactions leads to the condensation of swimmers at the center of the channel via a nonequilibrium phase transition that is formally akin to Bose-Einstein condensation. We find that the effective dynamics of the microswimmers can be mapped onto a diffusivity-edge problem, and use the mapping to build a generalized thermodynamic framework, which is verified by a parameter-free comparison with our simulations. Our work reveals how driven active matter has the potential to generate exotic classical nonequilibrium phases of matter with traits that are analogous to those observed in quantum systems.

## Distinguishing localization from chaos: challenges in finite-size systems

Annals of Physics Elsevier **427** (2021) 168415

We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we discuss a recent study (Šuntajs et al., 2020) of the behaviour of the Thouless energy and level repulsion in disordered spin chains, and its implications for the question of whether MBL is a true phase of matter.

## Bacteria solve the problem of crowding by moving slowly

Nature Physics Springer Nature **17** (2020) 205-210

Bacteria commonly live attached to surfaces in dense collectives containing billions of cells1. While it is known that motility allows these groups to expand en masse into new territory2,3,4,5, how bacteria collectively move across surfaces under such tightly packed conditions remains poorly understood. Here we combine experiments, cell tracking and individual-based modelling to study the pathogen Pseudomonas aeruginosa as it collectively migrates across surfaces using grappling-hook-like pili3,6,7. We show that the fast-moving cells of a hyperpilated mutant are overtaken and outcompeted by the slower-moving wild type at high cell densities. Using theory developed to study liquid crystals8,9,10,11,12,13, we demonstrate that this effect is mediated by the physics of topological defects, points where cells with different orientations meet one another. Our analyses reveal that when defects with topological charge +1/2 collide with one another, the fast-moving mutant cells rotate to point vertically and become trapped. By moving more slowly, wild-type cells avoid this trapping mechanism and generate collective behaviour that results in faster migration. In this way, the physics of liquid crystals explains how slow bacteria can outcompete faster cells in the race for new territory.

## Minimum Dissipation Theorem for Microswimmers

Physical Review Letters **126** (2021)

© 2021 authors. We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at a low Reynolds number. We show that, for any swimmer, the minimum dissipation at a given velocity can be expressed in terms of the resistance tensors of two passive bodies of the same shape with a no-slip and perfect-slip boundary. To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body. Using this theorem, we propose an alternative definition of the energetic efficiency of microswimmers that, unlike the commonly used Lighthill efficiency, can never exceed unity. We validate the theory by calculating the efficiency limits of spheroidal swimmers.

## Roadmap on emerging concepts in the physical biology of bacterial biofilms: from surface sensing to community formation.

Physical biology (2021)

Bacterial biofilms are communities of bacteria that exist as aggregates that can adhere to surfaces or be free-standing. This complex, social mode of cellular organization is fundamental to the physiology of microbes and often exhibits surprising behaviour. Bacterial biofilms are more than the sum of their parts: Single cell behaviour has a complex relation to collective community behaviour, in a manner perhaps cognate to the complex relation between atomic physics and condensed matter physics. Biofilm microbiology is a relatively young field by biology standards, but it has already attracted intense attention from physicists. Sometimes, this attention takes the form of seeing biofilms as inspiration for new physics. In this roadmap, we highlight the work of those who have taken the opposite strategy: We highlight work of physicists and physical scientists who use physics to engage fundamental concepts in bacterial biofilm microbiology, including adhesion, sensing, motility, signalling, memory, energy flow, community formation and cooperativity. These contributions are juxtaposed with microbiologists who have made recent important discoveries on bacterial biofilms using state-of-the-art physical methods. The contributions to this roadmap exemplify how well physics and biology can be combined to achieve a new synthesis, rather than just a division of labour.

## Local measures enable COVID-19 containment with fewer restrictions due to cooperative effects

EClinicalMedicine (2021)

© 2020 The Authors Background: Many countries worldwide are faced with the choice between the (re)surgence of COVID-19 and endangering the economic and mental well-being of their citizens. While infection numbers are monitored and measures adjusted, a systematic strategy for balancing contact restrictions and socioeconomic life in the absence of a vaccine is currently lacking. Methods: In a mathematical model, we determine the efficacy of regional containment strategies, where contact restrictions are triggered locally in individual regions upon crossing critical infection number thresholds. Our stochastic meta-population model distinguishes between contacts within a region and cross-regional contacts. We use current data on the spread of COVID-19 in Germany, Italy, England, New York State and Florida, including the effects of their individual national lockdowns, and county population sizes obtained from census data to define individual regions. As a performance measure, we determine the number of days citizens will experience contact restrictions over the next 5 years (‘restriction time’) and compare it to an equivalent national lockdown strategy. To extract crucial parameters, we vary the proportion of cross-regional contacts (between 0% and 100%), the thresholds for initiating local measures (between 5 and 20 active infections per 100,000 inhabitants) as well as their duration after infection numbers have returned below the threshold (between 7 and 28 days). We compare performance across the five different countries and test how further subdivision of large counties into independently controlled regions of up to 100,000 or 200,000 inhabitants affects the results. Findings: Our numerical simulations show a substantially reduced restriction time for regional containment, if the effective reproduction number of SARS-CoV-2 without restrictions, R0, is only slightly larger than 1 and the proportion of cross-regional contacts (the so-called leakiness) is low. In Germany, specifically, for R0=1.14, a leakiness of 1% is sufficiently low to reduce the mean restriction time from 468 days (s.d. 3 days) for the national containment strategy to 43 days (s.d. 3 days across simulations) for the regional strategy, when local measures are initiated at 10 infections per 100,000 inhabitants in the past 7 days. For R0=1.28, the allowed leakiness for minimal restriction time reduces to approximately 0.3%. The dependence of the restriction time on the leakiness is threshold-like only for regional containment, due to cooperative effects. It rises to levels similar to the national containment strategy for a leakiness > 10% (517 days national vs. 486 days regional for leakiness 32% and R0=1.14). We find a strong correlation between the population size of each region and the experienced restriction time. For countries with large counties, this can result in only a mild reduction in restriction time for regional containment, which can only be partly compensated by lower thresholds for initiating local measures and increasing their duration. In contrast, further subdividing large counties into smaller units can ensure a strong reduction of the restriction time for the regional strategy. Interpretation: The leakiness, i.e. the proportion of cross-regional contacts, and the regional structure itself were crucial parameters for the performance of the regional strategy. Therefore, regional strategies could offer an adaptive way to contain the epidemic with fewer overall restrictions, if cross-regional infections can be kept below the critical level, which could be achieved without affecting local socioeconomic freedom. Maintaining general hygiene and contact tracing, testing should be intensified to ensure regional measures can be initiated at low infection thresholds, preventing the spread of the disease to other regions before local elimination. While such tight control could lead to more restrictions in the short run, restrictions necessary for long-term containment could be reduced by up to a factor of 10. Our open-source simulation code is freely available and can be readily adapted to other countries. Funding: This work was supported by the Max Planck Society.

## Exact axisymmetric interaction of phoretically active Janus particles

JOURNAL OF FLUID MECHANICS **905** (2020) ARTN A13

## Integrability of one-dimensional Lindbladians from operator-space fragmentation

Physical Review E American Physical Society **102** (2020) 062210

We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: (i) The space of operators splits into exponentially many (in system size) subspaces that are left invariant under the dissipative evolution; (ii) the time evolution of the density matrix on each invariant subspace is described by an integrable Hamiltonian. The prototypical example is the quantum version of the asymmetric simple exclusion process (ASEP) which we analyze in some detail. We show that in each invariant subspace the dynamics is described in terms of an integrable spin-1/2 XXZ Heisenberg chain with either open or twisted boundary conditions. We further demonstrate that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimensions.

## A systematic 1/c-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model

SciPost Physics SciPost **9** (2020) 82

We introduce a framework for calculating dynamical correlations in the Lieb-Liniger model in arbitrary energy eigenstates and for all space and time, that combines a Lehmann representation with a 1/c expansion. The nth term of the expansion is of order 1/cn and takes into account all [n/2] + 1 particle-hole excitations over the averaging eigenstate. Importantly, in contrast to a "bare" 1/c expansion it is uniform in space and time. The framework is based on a method for taking the thermodynamic limit of sums of form factors that exhibit non integrable singularities. We expect our framework to be applicable to any local operator. We determine the first three terms of this expansion and obtain an explicit expression for the density-density dynamical correlations and the dynamical structure factor at order 1/c2. We apply these to finite-temperature equilibrium states and non-equilibrium steady states after quantum quenches. We recover predictions of (nonlinear) Luttinger liquid theory and generalized hydrodynamics in the appropriate limits, and are able to compute sub-leading corrections to these.

## From anyons to Majoranas

Nature Review Physics Nature **2** (2020) 667-668

Anyons, particles that are neither bosons nor fermions, were predicted in the 1980s, but strong experimental evidence for the existence of the simplest type of anyons has only emerged this year. Further theoretical and experimental advances promise to nail the existence of more exotic types of anyons, such as Majorana fermions, which would make topological quantum computation possible.

## One-Step Generation of Core-Gap-Shell Microcapsules for Stimuli-Responsive Biomolecular Sensing

ADVANCED FUNCTIONAL MATERIALS **30** (2020) ARTN 2006019

## Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions

PHYSICAL REVIEW B **102** (2020) ARTN 201116

## Diffusion and steady state distributions of flexible chemotactic enzymes

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS **229** (2020) 2791-2806

## Contrasting lattice geometry dependent versus independent quantities: Ramifications for Berry curvature, energy gaps, and dynamics

Physical Review B: Condensed Matter and Materials Physics American Physical Society **102** (2020) 165148

In the tight-binding description of electronic, photonic, or cold atomic dynamics in a periodic lattice potential, particle motion is described in terms of hopping amplitudes and potentials on an abstract network of discrete sites corresponding to physical orbitals in the lattice. The physical attributes of the orbitals, including their locations in three-dimensional space, are independent pieces of information. In this paper we identify a notion of geometry-independence: any physical quantity or observable that depends only on the tight-binding parameters (and not on the explicit information about the orbital geometry) is said to be “geometry-independent.” The band structure itself, and for example the Chern numbers of the bands in a two-dimensional system, are geometryindependent, while the Bloch-band Berry curvature is geometry-dependent. Careful identification of geometry-dependent versus independent quantities can be used as a novel principle for constraining a variety of results. By extending the notion of geometry-independence to certain classes of interacting systems, where the many-body energy gap is evidently geometry-independent, we shed new light on a hypothesized relation between many-body energy gaps of fractional Chern insulators and the uniformity of Bloch band Berry curvature in the Brillouin zone. We furthermore explore the geometry-dependence of semiclassical wave packet dynamics, and use this principle to show how two different types of Hall response measurements may give markedly different results due to the fact that one is geometry-dependent, while the other is geometry-independent. Similar considerations apply for anomalous thermal Hall response, in both electronic and spin systems.

## Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model

PHYSICAL REVIEW X **10** (2020) ARTN 041009