arXiv subjects

Ari M. Turner

Publications and source records attributed to Ari M. Turner.

At least 19 recordsLinked to original sources

arXiv2026

Fixed points of Boolean networks with sparse connections

We study fixed points of cellular automata with $N$ sites on random sparse graphs. In the large $N$ limit such models are known to exhibit phase transitions, from a ``frozen'' phase, where at most a finite number of sites fluctuate at long times, to a ``fluctuating'' phase where a finite fraction of sites fluctuate. We consider several models, calculating the first and second moments of the number of fixed points, and find that these moments remain finite in the large $N$ limit, except at the transitions where they become singular. The singularities can take several forms, including divergence of the mean or variance of the number of fixed points, on one or both sides of the transition. The type of singularity is related to properties of the mean field dynamics or dynamics of the distance between copies of the system. In configuration space, we find that fixed points are organized into clusters, each consisting of sets of fixed points that agree with one another except for on a finite number of sites. In the frozen phase there is only one cluster, while in the fluctuating phase there may be multiple clusters. If there are multiple clusters, the distance between fixed points in different clusters is extensive. We show that the differences within the clusters correspond to local changes near short cycles in the directed graph of connections whose influence is eventually limited. In the frozen phase, we calculate the full distribution of the number of fixed points.

cond-mat.stat-mech↗

arXiv2025

Microscopic theory of Chern polarization via crystalline defect charge

The modern theory of polarization does not apply in its original form to systems with non-trivial band topology. Chern insulators are one such example. Defining polarization for them is complicated because they are insulating in the bulk but exhibit metallic edge states. Wannier functions formed a key ingredient of the original modern theory of polarization, but it has been considered that these cannot be applied to Chern insulators since they are no longer exponentially localized and the Wannier center, obtained from the Zak phase, is no longer gauge invariant. In this article, we provide an unambiguous definition of absolute polarization for a Chern insulator in terms of the Zak phase. We obtain our expression by studying the non-quantized fractional charge bound to lattice dislocations. Our expression can be computed directly from bulk quantities and makes no assumption on the edge state filling. It is fully consistent with previous results on the quantized charge bound to dislocations in the presence of crystalline symmetry. At the same time, our result is more general since it also applies to Chern insulators which do not have crystalline symmetries other than translations.

cond-mat.str-el↗

arXiv2024

Extinctions as a vestige of instability: the geometry of stability and feasibility

Species coexistence is a complex, multifaceted problem. At an equilibrium, coexistence requires two conditions: stability under small perturbations; and feasibility, meaning all species abundances are positive. Which of these two conditions is more restrictive has been debated for many years, with many works focusing on statistical arguments for systems with many species. Within the framework of the Lotka-Volterra equations, we examine the geometry of the region of coexistence in the space of interaction strengths, for symmetric competitive interactions and any finite number of species. We consider what happens when starting at a point within the coexistence region, and changing the interaction strengths continuously until one of the two conditions breaks. We find that coexistence generically breaks through the loss of feasibility, as the abundance of one species reaches zero. An exception to this rule - where stability breaks before feasibility - happens only at isolated points, or more generally on a lower dimensional subset of the boundary. The reason behind this is that as a stability boundary is approached, some of the abundances generally diverge towards minus infinity, and so go extinct at some earlier point, breaking the feasibility condition first. These results define a new sense in which feasibility is a more restrictive condition than stability, and show that these two requirements are closely interrelated. We then show how our results affect the changes in the set of coexisting species when interaction strengths are changed: a system of coexisting species loses a species by its abundance continuously going to zero, and this new fixed point is unique. As parameters are further changed, multiple alternative equilibria may be found. Finally, we discuss the extent to which our results apply to asymmetric interactions.

q-bio.PE↗

arXiv2024

Motion from Measurement: The Role of Symmetry of Quantum Measurements

In quantum mechanics, measurements are dynamical processes and thus they should be capable of inducing currents. The symmetries of the Hamiltonian and measurement operator provide an organizing principle for understanding the conditions for such currents to emerge. The central role is played by the inversion and time-reversal symmetries. We classify the distinct behaviors that emerge from single and repeated measurements, with and without coupling to a dissipative bath. While the breaking of inversion symmetry alone is sufficient to generate currents through measurements, the breaking of time-reversal symmetry by the measurement operator leads to a dramatic increase in the magnitude of the currents. We consider the dependence on the measurement rate and find that the current is non-monotonic. Furthermore, nondegenerate measurements can lead to current loops within the steady state even in the Zeno limit.

quant-ph↗

arXiv2024

Unvortex Lattice and Topological Defects in Rigidly Rotating Multicomponent Superfluids

By examining rotating ferromagnetic spinor condensates through the perspective of large spin, we identify a novel type of topological point defects in the magnetization texture. These defects are not predicted by conventional homotopy analysis but rather by the Riemann-Hurwitz formula. The magnetization texture in the system is described by an equal-area mapping from the plane to the sphere of magnetization, forming a lattice of uniformly charged Skyrmions. This lattice contains doubly-quantized (winding number = 2) point defects arranged on the sphere in a tetrahedral configuration. The fluid found to be rotating rigidly, except at the point defects, where the vorticity vanishes. This vorticity structure describes an unconventional "unvortex" lattice, which contrasts with the well-known vortex lattice in scalar rotating superfluids, where vorticity is concentrated exclusively within defect points. Numerical results are presented, confirming these predictions and demonstrating their persistence in smaller-spin condensates.

cond-mat.quant-gas↗

arXiv2024

Optimally Localized Wannier Functions for 2D Chern Insulators

The construction of optimally localized Wannier functions (and Wannier functions in general) for a Chern insulator has been considered to be impossible owing to the fact that the second moment of such functions is generally infinite. In this manuscript, we propose a solution to this problem in the case of a single band. We accomplish this by drawing an analogy between the minimization of the variance and the minimization of the electrostatic energy of a periodic array of point charges in a smooth neutralizing background. In doing so, we obtain a natural regularization of the diverging variance and this leads to an analytical solution to the minimization problem. We demonstrate our results numerically for a particular model system. Furthermore, we show how the optimally localized Wannier functions provide a natural way of evaluating the electric polarization for a Chern insulator.

cond-mat.mtrl-sci↗

arXiv2024

Homotopy of periodic two by two matrices

We describe the homotopy classes of 2 by 2 periodic simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in three dimensions. The matrices represent gapped Bloch Hamiltonians in 1D with a two-dimensional Hilbert space per unit cell.

math-ph↗

arXiv2023

Generalized Lotka-Volterra equations with random, non-reciprocal interactions: the typical number of equilibria

We compute the typical number of equilibria of the Generalized Lotka-Volterra equations describing species-rich ecosystems with random, non-reciprocal interactions using the replicated Kac-Rice method. We characterize the multiple-equilibria phase by determining the average abundance and similaritybetween equilibria as a function of their diversity (i.e. of the number of coexisting species) and of the variability of the interactions. We show that linearly unstable equilibria are dominant, and that the typical number of equilibria differs with respect to the average number.

cond-mat.dis-nn↗

arXiv2022

Long-range influence of a pump on a critical fluid

A pump coupled to a conserved density generates long-range modulations, resulting from the non-equilibrium nature of the dynamics. We study how these modulations are modified at the critical point where the system exhibits intrinsic long-range correlations. To do so, we consider a pump in a diffusive fluid, which is known to generate a density profile in the form of an electric dipole potential and a current in the form of a dipolar field above the critical point. We demonstrate that while the current retains its form at the critical point, the density profile changes drastically. At criticality, in $d<4$ dimensions, the deviation of the density from the average is given by ${\rm sgn}(\cos(θ))|\cos(θ)/r^{(d-1)}|^{1/δ}$ at large distance $r$ from the pump and angle $θ$ with respect to the pump's orientation. At short distances, there is a crossover to a $\cos(θ)/r^{d-3+η}$ profile. Here $δ$ and $η$ are Ising critical exponents. The effect of the local pump on the domain wall structure below the critical point is also considered.

cond-mat.stat-mech↗

arXiv2022

Gapping fragile topological bands by interactions

We consider the stability of fragile topological bands protected by space-time inversion symmetry in the presence of strong electron-electron interactions. At the single-particle level, the topological nature of the bands prevents the opening of a gap between them. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaking any symmetry or mixing degrees of freedom from remote bands. Furthermore, the resulting ground state is not topologically ordered. Thus, a fragile topological band structure does not present an obstruction to forming a "featureless insulator" ground state. Our construction relies on the formation of fermionic bound states of two electrons and one hole, known as "trions". The trions form a band whose coupling to the electronic band enables the gap opening. This result may be relevant to the gapped state indicated by recent experiments in magic angle twisted bilayer graphene at charge neutrality.

cond-mat.str-el↗

arXiv2021

Local and collective transitions in sparsely-interacting ecological communities

Interactions in natural communities can be highly heterogeneous, with any given species interacting appreciably with only some of the others, a situation commonly represented by sparse interaction networks. We study the consequences of sparse competitive interactions, in a theoretical model of a community assembled from a species pool. We find that communities can be in a number of different regimes, depending on the interaction strength. When interactions are strong, the network of coexisting species breaks up into small subgraphs, while for weaker interactions these graphs are larger and more complex, eventually encompassing all species. This process is driven by emergence of new allowed subgraphs as interaction strength decreases, leading to sharp changes in diversity and other community properties, and at weaker interactions to two distinct collective transitions: a percolation transition, and a transition between having a unique equilibrium and having multiple alternative equilibria. Understanding community structure is thus made up of two parts: first, finding which subgraphs are allowed at a given interaction strength, and secondly, a discrete problem of matching these structures over the entire community. In a shift from the focus of many previous theories, these different regimes can be traversed by modifying the interaction strength alone, without need for heterogeneity in either interaction strengths or the number of competitors per species.

q-bio.PE↗

arXiv2020

Origin and localization of topological band gaps in gyroscopic metamaterials

Networks of interacting gyroscopes have proven to be versatile structures for understanding and harnessing finite-frequency topological excitations. Spinning components give rise to band gaps and topologically protected wave transport along the system's boundaries, whether the gyroscopes are arranged in a lattice or in an amorphous configuration. Here, we examine the irrelevance of periodic order for generating topological gaps. Starting from the symplectic dynamics of our model metamaterial, we present a general method for predicting whether a gap exists and for approximating the Chern number using only local features of a network, bypassing the costly diagonalization of the system's dynamical matrix. We then study how strong disorder interacts with band topology in gyroscopic metamaterials and find that amorphous gyroscopic Chern insulators exhibit similar critical behavior to periodic lattices. Our experiments and simulations additionally reveal a topological Anderson insulation transition, wherein disorder drives a trivial phase into a topological one.

cond-mat.mes-hall↗

arXiv2020

Neutron scattering off Weyl semimetals

We present how to detect type-$1$ Weyl nodes in a material by inelastic neutron scattering. Such an experiment first of all allows one to determine the dispersion of the Weyl fermions. We extend the reasoning to produce a quantitative test of the Weyl equation taking into account realistic anisotropic properties. These anisotropies are mostly contained in the form of the emergent magnetic moment of the excitations, which determines how they couple to the neutron. Although there are many material parameters, we find several quantitative predictions that are universal and demonstrate that the excitations are described by solutions to the Weyl equation. The realistic, anisotropic coupling between electrons and neutrons implies that even fully unpolarized neutrons can reveal the spin-momentum locking of the Weyl fermions because the neutrons will couple to some components of the Weyl fermion pseudospin more strongly. On the other hand, in an experiment with polarized neutrons, the scattered neutron beam remains fully polarized in a direction that varies as a function of momentum transfer (within the range of validity of the Weyl equation). This allows measurement of the chirality of Weyl fermions for inversion symmetric nodes. Furthermore, we estimate that the scattering rate may be large enough for such experiments to be practical; in particular, the magnetic moment may be larger than the ordinary Bohr magneton, compensating for a small density of states.

cond-mat.mes-hall↗

arXiv2016

Statistics of fractionalized excitations through threshold spectroscopy

We show that the anyonic statistics of fractionalized excitations display characteristic signatures in threshold spectroscopic measurements. Drawing motivation from topologically ordered phases such as gapped quantum spin liquids and fractional chern insulators which possess fractionalized excitations, we consider gapped systems with abelian anyonic excitations. The low energy onset of associated correlation functions near the threshold show universal behaviour depending on the statistics of the anyons. This explains some recent theoretical results in spin systems and also provides a route towards detecting statistics in experiments such as neutron scattering and tunneling spectroscopy.

cond-mat.str-el↗

arXiv2015

Topological mechanics of gyroscopic metamaterials

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial -- comprised of coupled gyroscopes on a lattice -- that breaks time-reversal symmetry. The vibrational spectrum of these novel structures displays a sonic gap populated by topologically protected edge modes which propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We envision applications of these edges modes to the design of loss-free, one-way, acoustic waveguides and demonstrate this functionality in experiment.

cond-mat.soft↗

arXiv2014

Berry phase induced dimerization in one-dimensional quadrupolar systems

We investigate the effect of the Berry phase on quadrupoles that occur for example in the low-energy description of spin models. Specifically we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many years about this model is whether it has a non-dimerized fluctuating nematic phase. The dimerization has recently been proposed to be related to Berry phases of the quantum fluctuations. We use an effective low-energy description to calculate the scaling of the dimerization according to this theory, and then verify the predictions using large scale density-matrix renormalization group (DMRG) simulations, giving good evidence that the state is dimerized all the way up to its transition into the ferromagnetic phase. We furthermore discuss the multiplet structure found in the entanglement spectrum of the ground state wave functions.

cond-mat.str-el↗

arXiv2013

Featureless and non-fractionalized Mott insulators on the honeycomb lattice at 1/2 site filling

Within the Landau paradigm, phases of matter are distinguished by spontaneous symmetry breaking. Implicit here is the assumption that a completely symmetric state exists: a paramagnet. At zero temperature such quantum featureless insulators may be forbidden, triggering either conventional order or topological order with fractionalized excitations. Such is the case for interacting particles when the particle number per unit cell, f, is not an integer. But, can lattice symmetries forbid featureless insulators even at integer f? An especially relevant case is the honeycomb (graphene) lattice --- where free spinless fermions at f=1 (the two sites per unit cell mean f=1 is half filling per site) are always metallic. Here we present wave functions for bosons, and a related spin-singlet wave function for spinful electrons, on the f=1 honeycomb, and demonstrate via quantum to classical mappings that they do form featureless Mott insulators. The construction generalizes to symmorphic lattices at integer f in any dimension. Our results explicitly demonstrate that in this case, despite the absence of a non-interacting insulator at the same filling, lack of order at zero temperature does not imply fractionalization.

cond-mat.str-el↗

arXiv2013

Topological phases in gapped edges of fractionalized systems

Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions. We introduce a classification scheme for the phases that can occur in parafermionic chains. We find that the parafermions support both topological symmetry fractionalized phases as well as phases in which the parafermions condense. In the presence of additional symmetries, the phases form a non-Abelian group. As a concrete example of the classification, we consider the effective edge model for a $ν= 1/3$ fractional topological insulator for which we calculate the entanglement spectra numerically and show that all possible predicted phases can be realized.

cond-mat.str-el↗