# Publications

## Twist-induced crossover from two-dimensional to three-dimensional turbulence in active nematics.

Physical review. E **98** (2018) 010601-

While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-two-dimensional (quasi-2D) to three-dimensional (3D) chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines spanning the height of the channel and exhibiting effectively 2D active turbulence. Upon increasing channel height, we find a crossover to 3D chaotic flows due to the contortion of disclinations above a critical activity. Above this critical activity highly contorted disclination lines and disclination loops are formed. We further show that these contortions are engendered by twist perturbations producing a sharp change in the curvature of disclinations.

## Solution of a Minimal Model for Many-Body Quantum Chaos

PHYSICAL REVIEW X **8** (2018) ARTN 041019

## Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4

PHYSICAL REVIEW X **8** (2018) ARTN 031028

## Phoresis and Enhanced Diffusion Compete in Enzyme Chemotaxis.

Nano letters **18** (2018) 2711-2717

Chemotaxis of enzymes in response to gradients in the concentration of their substrate has been widely reported in recent experiments, but a basic understanding of the process is still lacking. Here, we develop a microscopic theory for chemotaxis that is valid for enzymes and other small molecules. Our theory includes both nonspecific interactions between enzyme and substrate as well as complex formation through specific binding between the enzyme and the substrate. We find that two distinct mechanisms contribute to enzyme chemotaxis: a diffusiophoretic mechanism due to the nonspecific interactions and a new type of mechanism due to binding-induced changes in the diffusion coefficient of the enzyme. The latter chemotactic mechanism points toward lower substrate concentration if the substrate enhances enzyme diffusion and toward higher substrate concentration if the substrate inhibits enzyme diffusion. For a typical enzyme, attractive phoresis and binding-induced enhanced diffusion will compete against each other. We find that phoresis dominates above a critical substrate concentration, whereas binding-induced enhanced diffusion dominates for low substrate concentration. Our results resolve an apparent contradiction regarding the direction of urease chemotaxis observed in experiments and, in general, clarify the relation between the enhanced diffusion and the chemotaxis of enzymes. Finally, we show that the competition between the two distinct chemotactic mechanisms may be used to engineer nanomachines that move toward or away from regions with a specific substrate concentration.

## Enhanced Diffusion and Chemotaxis at the Nanoscale.

Accounts of chemical research **51** (2018) 2365-2372

Enzymes have been recently proposed to have mechanical activity associated with their chemical activity. In a number of recent studies, it has been reported that enzymes undergo enhanced diffusion in the presence of their corresponding substrate when this substrate is uniformly distributed in solution. Moreover, if the concentration of the substrate is nonuniform, enzymes and other small molecules have been reported to show chemotaxis (biased stochastic movement in the direction of the substrate gradient), typically toward higher concentrations of this substrate, with a few exceptions. The underlying physical mechanisms responsible for enhanced diffusion and chemotaxis at the nanoscale, however, are still not well understood. Understanding these processes is important both for fundamental biological research, for example, in the context of spatial organization of enzymes in metabolic pathways (metabolon formation), as well as for engineering applications, such as in the design of new vehicles for targeted drug delivery. In this Account, we will review the available experimental observations of both enhanced diffusion and chemotaxis, and we will discuss critically the different theories that have been proposed to explain the two. We first focus on enhanced diffusion, beginning with an overview of the experimental results. We then discuss the two main types of mechanisms that have been proposed, namely, active mechanisms relying on the catalytic step of the enzymatic reaction and equilibrium mechanisms, which consider the reversible binding and unbinding of the substrate to the enzyme. We put particular emphasis on an equilibrium model recently introduced by us, which describes how the diffusion of dumbbell-like modular enzymes can be enhanced in the presence of substrate thanks to a binding-induced reduction of the internal fluctuations of the enzyme. We then turn to chemotaxis, beginning with an overview of the experimental evidence for the chemotaxis of enzymes and small molecules, followed by a description of a number of shortcomings and pitfalls in the thermodynamic and phenomenological models for chemotaxis introduced in those and other works in the literature. We then discuss a microscopic model for chemotaxis including both noncontact interactions and specific binding between enzyme and substrate recently developed by us, which overcomes many of these shortcomings and is consistent with the experimental observations of chemotaxis. Finally, we show that the results of this model may be used to engineer chemically active macromolecules that are directed in space via patterning of the concentrations of their substrates.

## Two-dimensional, blue phase tactoids

MOLECULAR PHYSICS **116** (2018) 2856-2863

## Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos

PHYSICAL REVIEW B **98** (2018) ARTN 144304

## Critical behavior of the extended Hubbard model with bond dimerization

PHYSICA B-CONDENSED MATTER **536** (2018) 474-478

## Operator Spreading in Random Unitary Circuits

PHYSICAL REVIEW X **8** (2018) ARTN 021014

## Projective phase measurements in one-dimensional Bose gases

SciPost Physics Stichting SciPost **5** (2018) 046

<jats:p>We consider time-of-flight measurements in split one-dimensional Bose gases. It is well known that the low-energy sector of such systems can be described in terms of two compact phase fields <jats:inline-formula><jats:alternatives><jats:tex-math>\hat{\phi}_{a,s}(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mover><mml:mi>ϕ</mml:mi><mml:mo accent="true">̂</mml:mo></mml:mover><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>. Building on existing results in the literature we discuss how a single projective measurement of the particle density after trap release is in a certain limit related to the eigenvalues of the vertex operator <jats:inline-formula><jats:alternatives><jats:tex-math>e^{i\hat{\phi}_a(x)}</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:msub><mml:mover><mml:mi>ϕ</mml:mi><mml:mo accent="true">̂</mml:mo></mml:mover><mml:mi>a</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:msup></mml:math></jats:alternatives></jats:inline-formula>. We emphasize the theoretical assumptions underlying the analysis of “single-shot” interference patterns and show that such measurements give direct access to multi-point correlation functions of <jats:inline-formula><jats:alternatives><jats:tex-math>e^{i\hat{\phi}_a(x)}</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:msub><mml:mover><mml:mi>ϕ</mml:mi><mml:mo accent="true">̂</mml:mo></mml:mover><mml:mi>a</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:msup></mml:math></jats:alternatives></jats:inline-formula> in a substantial parameter regime. For experimentally relevant situations, we derive an expression for the measured particle density after trap release in terms of convolutions of the eigenvalues of vertex operators involving both sectors of the two-component Luttinger liquid that describes the low-energy regime of the split condensate. This opens the door to accessing properties of the symmetric sector via an appropriate analysis of existing experimental data.</jats:p>

## Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy

SciPost Physics Stichting SciPost **5** (2018) 059

<jats:p>We consider the dimerized spin-1 XXZ chain with single-ion anisotropy D. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.</jats:p>

## Many-body localization, symmetry and topology.

Reports on progress in physics. Physical Society (Great Britain) **81** (2018) 082501-

We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder, prevents systems from equilibrating to a thermal state where the delicate quantum correlations necessary for topological order are often washed out. Instead, many-body localized systems can exhibit a type of eigenstate phase structure wherein their entire many-body spectrum is characterized by various types of quantum order, usually restricted to quantum ground states. After introducing many-body localization and explaining how it can protect quantum order, we then explore how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.

## Trial wave functions for a composite Fermi liquid on a torus

PHYSICAL REVIEW B **97** (2018) ARTN 035149

## Strong-disorder renormalization group for periodically driven systems

PHYSICAL REVIEW B **98** (2018) ARTN 174203

## Localization-protected order in spin chains with non-Abelian discrete symmetries

PHYSICAL REVIEW B **98** (2018) ARTN 064203

## Floquet quantum criticality.

Proceedings of the National Academy of Sciences of the United States of America **115** (2018) 9491-9496

We study transitions between distinct phases of one-dimensional periodically driven (Floquet) systems. We argue that these are generically controlled by infinite-randomness fixed points of a strong-disorder renormalization group procedure. Working in the fermionic representation of the prototypical Floquet Ising chain, we leverage infinite randomness physics to provide a simple description of Floquet (multi)criticality in terms of a distinct type of domain wall associated with time translational symmetry-breaking and the formation of "Floquet time crystals." We validate our analysis via numerical simulations of free-fermion models sufficient to capture the critical physics.

## Far-field theory for trajectories of magnetic ellipsoids in rectangular and circular channels

IMA JOURNAL OF APPLIED MATHEMATICS **83** (2018) 767-782

## Size constraints on a Majorana beam-splitter interferometer: Majorana coupling and surface-bulk scattering

PHYSICAL REVIEW B **97** (2018) ARTN 115424