Dynamics and transport at the threshold of many-body localization

Physics Reports Elsevier 862 (2020) 1-62

S Ashok Parameswaran, S Gopalakrishnan

Many-body localization (MBL) describes a class of systems that do not approach thermal equilibrium under their intrinsic dynamics; MBL and conventional thermalizing systems form distinct dynamical phases of matter, separated by a phase transition at which equilibrium statistical mechanics breaks down. True many-body localization is known to occur only under certain stringent conditions for perfectly isolated one-dimensional systems, with Hamiltonians that have strictly short-range interactions and lack any continuous non-Abelian symmetries. However, in practice, even systems that are not strictly MBL can be nearly MBL, with equilibration rates that are far slower than their other intrinsic timescales; thus, anomalously slow relaxation occurs in a much broader class of systems than strict localization. In this review we address transport and dynamics in such nearly-MBL systems from a unified perspective. Our discussion covers various classes of such systems: (i) disordered and quasiperiodic systems on the thermal side of the MBL-thermal transition; (ii) systems that are strongly disordered, but obstructed from localizing because of symmetry, interaction range, or dimensionality; (iii) multiple-component systems, in which some components would in isolation be MBL but others are not; and finally (iv) driven systems whose dynamics lead to exponentially slow rates of heating to infinite temperature. A theme common to many of these problems is that they can be understood in terms of approximately localized degrees of freedom coupled to a heat bath (or baths) consisting of thermal degrees of freedom; however, this putative bath is itself nontrivial, being either small or very slowly relaxing. We discuss anomalous transport, diverging relaxation times, and other signatures of the proximity to MBL in these systems. We also survey recent theoretical and numerical methods that have been applied to study dynamics on either side of the MBL transition.

Cooperatively enhanced reactivity and "stabilitaxis" of dissociating oligomeric proteins.

Proceedings of the National Academy of Sciences of the United States of America 117 (2020) 11894-11900

J Agudo-Canalejo, P Illien, R Golestanian

Many functional units in biology, such as enzymes or molecular motors, are composed of several subunits that can reversibly assemble and disassemble. This includes oligomeric proteins composed of several smaller monomers, as well as protein complexes assembled from a few proteins. By studying the generic spatial transport properties of such proteins, we investigate here whether their ability to reversibly associate and dissociate may confer on them a functional advantage with respect to nondissociating proteins. In uniform environments with position-independent association-dissociation, we find that enhanced diffusion in the monomeric state coupled to reassociation into the functional oligomeric form leads to enhanced reactivity with localized targets. In nonuniform environments with position-dependent association-dissociation, caused by, for example, spatial gradients of an inhibiting chemical, we find that dissociating proteins generically tend to accumulate in regions where they are most stable, a process that we term "stabilitaxis."

“Not- A”, representation symmetry-protected topological, and Potts phases in an S3 -invariant chain

Physical Review B: Condensed Matter and Materials Physics American Physical Society 101 (2020) 235108

E O’Brien, E Vernier, P Fendley

We analyze in depth an S 3 -invariant nearest-neighbor quantum chain in the region of a U ( 1 ) -invariant self-dual multicritical point. We find four distinct proximate gapped phases. One has three-state Potts order, corresponding to topological order in a parafermionic formulation. Another has “representation” symmetry-protected topological (RSPT) order, while its dual exhibits an unusual “not- A ” order, where the spins prefer to align in two of the three directions. Within each of the four phases, we find a frustration-free point with exact ground state(s). The exact ground states in the not- A phase are product states, each an equal-amplitude sum over all states where one of the three spin states on each site is absent. Their dual, the RSPT ground state, is a matrix product state similar to that of Affleck-Kennedy-Lieb-Tasaki. A field-theory analysis shows that all transition lines are in the universality class of the critical three-state Potts model. They provide a lattice realization of a flow from a free-boson field theory to the Potts conformal field theory.

Active inter-cellular forces in collective cell motility.

Journal of the Royal Society, Interface 17 (2020) 20200312-20200312

G Zhang, R Mueller, A Doostmohammadi, JM Yeomans

The collective behaviour of confluent cell sheets is strongly influenced both by polar forces, arising through cytoskeletal propulsion, and by active inter-cellular forces, which are mediated by interactions across cell-cell junctions. We use a phase-field model to explore the interplay between these two contributions and compare the dynamics of a cell sheet when the polarity of the cells aligns to (i) their main axis of elongation, (ii) their velocity and (iii) when the polarity direction executes a persistent random walk. In all three cases, we observe a sharp transition from a jammed state (where cell rearrangements are strongly suppressed) to a liquid state (where the cells can move freely relative to each other) when either the polar or the inter-cellular forces are increased. In addition, for case (ii) only, we observe an additional dynamical state, flocking (solid or liquid), where the majority of the cells move in the same direction. The flocking state is seen for strong polar forces, but is destroyed as the strength of the inter-cellular activity is increased.

Twisted bilayer graphene in a parallel magnetic field

Physical review B: Condensed matter and materials physics American Physical Society 101 (2020) 205116

YH Kwan, S Ashok Parameswaran, S Sondhi

We study the effect of an in-plane magnetic field on the non-interacting dispersion of twisted bilayer graphene. Our analysis is rooted in the chirally symmetric continuum model, whose zero-field band structure hosts exactly flat bands and large energy gaps at the magic angles. At the first magic angle, the central bands respond to a parallel field by forming a quadratic band crossing point (QBCP) at the moire Brillouin zone center. Over a large ´ range of fields, the dispersion is invariant with an overall scale set by the magnetic field strength. For deviations from the magic angle and for realistic interlayer couplings, the motion and merging of the Dirac points lying near charge neutrality are discussed in the context of the symmetries, and we show that small magnetic fields are able to induce a qualitative change in the energy spectrum. We conclude with a discussion on the possible ramifications of our study to the interacting ground states of twisted bilayer graphene systems.

Exact Phoretic Interaction of Two Chemically Active Particles.

Physical review letters 124 (2020) 168003-

B Nasouri, R Golestanian

We study the nonequilibrium interaction of two isotropic chemically active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed point-a phenomenon that cannot be captured under the far-field approximation. We find that, due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that the near-field effects originate from a self-generated neighbor-reflected chemical gradient, similar to interactions of a self-propelling phoretic particle and a flat substrate.

Mesoscale modelling of polymer aggregate digestion

Current Research in Food Science Elsevier BV 3 (2020) 122-133

JK Novev, A Doostmohammadi, A Zöttl, JM Yeomans

Yang-Baxter integrable Lindblad equations

SciPost Physics SciPost (2020)

FHL Essler, AA Ziolkowska

We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. Employing Bethe Ansatz techniques we show that the late-time dynamics of some of these models is diffusive.

Quantum oscillations probe the Fermi surface topology of the nodal-line semimetal CaAgAs

Physical Review Research American Physical Society 2 (2020) 012055(R)

YH Kwan, P Reiss, Y Han, M Bristow, D Prabhakaran, D Graf, A McCollam, S Ashok Parameswaran, AI Coldea

Nodal semimetals are a unique platform to explore topological signatures of the unusual band structure that can manifest by accumulating a nontrivial phase in quantum oscillations. Here we report a study of the de Haas–van Alphen oscillations of the candidate topological nodal line semimetal CaAgAs using torque measurements in magnetic fields up to 45 T. Our results are compared with calculations for a toroidal Fermi surface originating from the nodal ring. We find evidence of a nontrivial π phase shift only in one of the oscillatory frequencies. We interpret this as a Berry phase arising from the semiclassical electronic Landau orbit which links with the nodal ring when the magnetic field lies in the mirror (ab) plane. Furthermore, additional Berry phase accumulates while rotating the magnetic field for the second orbit in the same orientation which does not link with the nodal ring. These effects are expected in CaAgAs due to the lack of inversion symmetry. Our study experimentally demonstrates that CaAgAs is an ideal platform for exploring the physics of nodal line semimetals and our approach can be extended to other materials in which trivial and nontrivial oscillations are present.

Quantum Hall network models as Floquet topological insulators

Phys. Rev. Lett. 125 (2020) 086601-086601

AC Potter, J Chalker, V Gurarie

Network models for equilibrium integer quantum Hall (IQH) transitions are described by unitary scattering matrices, that can also be viewed as representing non-equilibrium Floquet systems. The resulting Floquet bands have zero Chern number, and are instead characterized by a chiral Floquet (CF) winding number. This begs the question: How can a model without Chern number describe IQH systems? We resolve this apparent paradox by showing that non-zero Chern number is recovered from the network model via the energy dependence of network model scattering parameters. This relationship shows that, despite their topologically distinct origins, IQH and CF topology-changing transitions share identical universal scaling properties.

Partial equilibration of the anti-Pfaffian edge due to Majorana Disorder

Physical Review Letters American Physical Society 124 (2020) 126801

S Simon, B Rosenow

We consider electrical and thermal equilibration of the edge modes of the Anti-Pfaffian quantum Hall state at ν = 5/2 due to tunneling of the Majorana edge mode to trapped Majorana zero modes in the bulk. Such tunneling breaks translational invariance and allows scattering between Majorana and other edge modes in such a way that there is a parametric difference between the length scales for equilibration of charge and heat transport between integer and Bose mode on the one hand, and for thermal equilibration of the Majorana edge mode on the other hand. We discuss a parameter regime in which this mechanism could explain the recent observation of quantized heat transport [Banerjee et all, Nature 559, 7713 (2018)].

Active matter in a viscoelastic environment

Physical Review Fluids American Physical Society 5 (2020) 023102

E Plan, J Yeomans, A Doostmohammadi

Active matter systems such as eukaryotic cells and bacteria continuously transform chemical energy to motion. Hence living systems exert active stresses on the complex environments in which they reside. One recurring aspect of this complexity is the viscoelasticity of the medium surrounding living systems: bacteria secrete their own viscoelastic extracellular matrix, and cells constantly deform, proliferate, and self-propel within viscoelastic networks of collagen. It is therefore imperative to understand how active matter modifies, and gets modified by, viscoelastic fluids. Here, we present a two-phase model of active nematic matter that dynamically interacts with a passive viscoelastic polymeric phase and perform numerical simulations in two dimensions to illustrate its applicability. Motivated by recent experiments we first study the suppression of cell division by a viscoelastic medium surrounding the cell. We further show that the self-propulsion of a model keratocyte cell is modified by the polymer relaxation of the surrounding viscoelastic fluid in a non-uniform manner and find that increasing polymer viscosity effectively suppresses the cell motility. Lastly, we explore the hampering impact of the viscoelastic medium on the generic hydrodynamic instabilities of active nematics by simulating the dynamics of an active stripe within a polymeric fluid. The model presented here can provide a framework for investigating more complex dynamics such as the interaction of multicellular growing systems with viscoelastic environments.

Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions

in Fractional Quantum Hall Effects: New Developments, World Scientific (2020)


Measurement-induced steering of quantum systems

Phys. Rev. Research 2 (2020) 033347-033347

S Roy, J Chalker, I Gornyi, Y Gefen

We set out a general protocol for steering the state of a quantum system from an arbitrary initial state towards a chosen target state by coupling it to auxiliary quantum degrees of freedom. The protocol requires multiple repetitions of an elementary step: during each step the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term 'detector qubits') that have been prepared in a specified initial state. The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes. The steering harnesses back-action of the detector qubits on the system, arising from entanglement generated during the coupled evolution. We establish principles for the design of the system-detector coupling that ensure steering of a desired form. We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state). We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering. Our protocols are amenable to implementations using present-day technology. Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.

Polar jets of swimming bacteria condensed by a patterned liquid crystal

Nature Physics Nature Research 16 (2020) 481–487-

T Turiv, R Koizumi, K Thijssen, J Yeomans, A Doostmohammadi

Active matter exhibits remarkable collective behaviour in which flows, continuously generated by active particles, are intertwined with the orientational order of these particles. The relationship remains poorly understood as the activity and order are difficult to control independently. Here we demonstrate important facets of this interplay by exploring the dynamics of swimming bacteria in a liquid crystalline environment with predesigned periodic splay and bend in molecular orientation. The bacteria are expelled from the bend regions and condense into polar jets that propagate and transport cargo unidirectionally along the splay regions. The bacterial jets remain stable even when the local concentration exceeds the threshold of bending instability in a non-patterned system. Collective polar propulsion and the different roles of bend and splay are explained by an advection–diffusion model and by numerical simulations that treat the system as a two-phase active nematic. The ability of prepatterned liquid crystalline medium to streamline the chaotic movements of swimming bacteria into polar jets that can carry cargo along a predesigned trajectory opens the door for potential applications in microscale delivery and soft microrobotics.

"Not-A", representation symmetry-protected topological, and Potts phases in an S-3-invariant chain

PHYSICAL REVIEW B 101 (2020) ARTN 235108

E O'Brien, E Vernier, P Fendley

Large classes of quantum scarred Hamiltonians from matrix product states

PHYSICAL REVIEW B 102 (2020) ARTN 085120

S Moudgalya, E O'Brien, BA Bernevig, P Fendley, N Regnault

Degenerate states, emergent dynamics and fluid mixing by magnetic rotors.

Soft matter 16 (2020) 6484-6492

T Kawai, D Matsunaga, F Meng, JM Yeomans, R Golestanian

We investigate the collective motion of magnetic rotors suspended in a viscous fluid under a uniform rotating magnetic field. The rotors are positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For a 3 × 3 array of magnets, we observe three characteristic dynamical patterns as the external field strength is varied: a synchronized pattern, an oscillating pattern, and a chessboard pattern. The relative stability of these depends on the competition between the energy due to the external magnetic field and the energy of the magnetic dipole-dipole interactions among the rotors. We argue that the chessboard pattern can be understood as an alternation in the stability of two degenerate states, characterized by striped and spin-ice configurations, as the applied magnetic field rotates. For larger arrays, we observe propagation of slip waves that are similar to metachronal waves. The rotor arrays have potential as microfluidic devices that can mix fluids and create vortices of different sizes.

SerraNA: a program to determine nucleic acids elasticity from simulation data


V Velasco-Berrelleza, M Burman, J Shepherd, M Leake, R Golestanian, A Noy

Abstract The resistance of DNA to stretch, twist and bend is broadly well estimated by experiments and is important for gene regulation and chromosome packing. However, their sequence-dependence and how bulk elastic constants emerge from local fluctuations is less understood. Here, we present SerraNA , which is an open software that calculates elastic parameters of double-stranded nucleic acids from dinucleotide length up to the whole molecule using ensembles from numerical simulations. The program reveals that global bendability emerge from local periodic bending angles in phase with the DNA helicoidal shape. We also apply SerraNA to the whole set of 136 tetra-bp combinations and we observe a high degree of sequence-dependence for all elastic parameters with differences over 200%. Tetramers with TA and CA base-pair steps are especially flexible, while tetramers containing AA and AT tend to be the most rigid. Our results thus suggest AT-rich motifs generate extreme mechanical properties depending of the exact sequence ordering, which seems critical for creating strong global bendability on longer sequences when phased properly. SerraNA is a tool to be applied in the next generation of interdisciplinary investigations to further understand what determines the elasticity of DNA. <jats:sec id="s6"> Graphical TOC Entry <jats:fig id="ufig1" position="float" orientation="portrait" fig-type="figure"><jats:graphic xmlns:xlink="" xlink:href="004945v2_ufig1" position="float" orientation="portrait" />

Social Cooperativity of Bacteria during Reversible Surface Attachment in Young Biofilms: a Quantitative Comparison of Pseudomonas aeruginosa PA14 and PAO1.

mBio 11 (2020)

CK Lee, J Vachier, J de Anda, K Zhao, AE Baker, RR Bennett, CR Armbruster, KA Lewis, RL Tarnopol, CJ Lomba, DA Hogan, MR Parsek, GA O'Toole, R Golestanian, GCL Wong

What are bacteria doing during "reversible attachment," the period of transient surface attachment when they initially engage a surface, besides attaching themselves to the surface? Can an attaching cell help any other cell attach? If so, does it help all cells or employ a more selective strategy to help either nearby cells (spatial neighbors) or its progeny (temporal neighbors)? Using community tracking methods at the single-cell resolution, we suggest answers to these questions based on how reversible attachment progresses during surface sensing for Pseudomonas aeruginosa strains PAO1 and PA14. Although PAO1 and PA14 exhibit similar trends of surface cell population increase, they show unanticipated differences when cells are considered at the lineage level and interpreted using the quantitative framework of an exactly solvable stochastic model. Reversible attachment comprises two regimes of behavior, processive and nonprocessive, corresponding to whether cells of the lineage stay on the surface long enough to divide, or not, before detaching. Stark differences between PAO1 and PA14 in the processive regime of reversible attachment suggest the existence of two surface colonization strategies. PAO1 lineages commit quickly to a surface compared to PA14 lineages, with early c-di-GMP-mediated exopolysaccharide (EPS) production that can facilitate the attachment of neighbors. PA14 lineages modulate their motility via cyclic AMP (cAMP) and retain memory of the surface so that their progeny are primed for improved subsequent surface attachment. Based on the findings of previous studies, we propose that the differences between PAO1 and PA14 are potentially rooted in downstream differences between Wsp-based and Pil-Chp-based surface-sensing systems, respectively.IMPORTANCE The initial pivotal phase of bacterial biofilm formation known as reversible attachment, where cells undergo a period of transient surface attachment, is at once universal and poorly understood. What is more, although we know that reversible attachment culminates ultimately in irreversible attachment, it is not clear how reversible attachment progresses phenotypically, as bacterial surface-sensing circuits fundamentally alter cellular behavior. We analyze diverse observed bacterial behavior one family at a time (defined as a full lineage of cells related to one another by division) using a unifying stochastic model and show that our findings lead to insights on the time evolution of reversible attachment and the social cooperative dimension of surface attachment in PAO1 and PA14 strains.