Publications

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Discounted Mean-Field Game model of a dense static crowd with variable information crossed by an intruder

Matteo Butano, Cécile Appert-Rolland, Denis Ullmo

SciPost Phys. 16, 104 (2024) · published 12 April 2024 | · pdf

It was demonstrated in [Bonnemain et al., Phys. Rev. E 107, 024612 (2023)] that the anticipation pattern displayed by a dense crowd crossed by an intruder can be successfully described by a minimal Mean-Field Games model. However, experiments show that changes in the pedestrian knowledge significantly modify the dynamics of the crowd. Here, we show that the addition of a single parameter, the discount factor $\gamma$, which gives a lower weight to events distant in time, is sufficient to observe the whole variety of behaviors observed in the experiments. We present a comparison between the discounted MFG and the experimental data, also providing new analytic results and insight about how the introduction of $\gamma$ modifies the model.
Exact instanton transseries for quantum mechanics

Alexander van Spaendonck, Marcel Vonk

SciPost Phys. 16, 103 (2024) · published 12 April 2024 | · pdf

We calculate the instanton corrections to energy spectra of one-dimensional quantum mechanical oscillators to all orders and unify them in a closed form transseries description. Using alien calculus, we clarify the resurgent structure of these transseries and demonstrate two approaches in which the Stokes constants can be derived. As a result, we formulate a minimal one-parameter transseries for the natural nonperturbative extension to the perturbative energy, which captures the Stokes phenomenon in a single stroke. We derive these results in three models: quantum oscillators with cubic, symmetric double well and cosine potentials. In the latter two examples, we find that the resulting full transseries for the energy has a more convoluted structure that we can factorise in terms of a minimal and a median transseries. For the cosine potential we briefly discuss this more complicated transseries structure in conjunction with topology and the concept of the resurgence triangle.
Free fermions beyond Jordan and Wigner

Paul Fendley, Balazs Pozsgay

SciPost Phys. 16, 102 (2024) · published 10 April 2024 | · pdf

The Jordan-Wigner transformation is frequently utilised to rewrite quantum spin chains in terms of fermionic operators. When the resulting Hamiltonian is bilinear in these fermions, i.e. the fermions are free, the exact spectrum follows from the eigenvalues of a matrix whose size grows only linearly with the volume of the system. However, several Hamiltonians that do not admit a Jordan-Wigner transformation to fermion bilinears still have the same type of free-fermion spectra. The spectra of such "free fermions in disguise" models can be found exactly by an intricate but explicit construction of the raising and lowering operators. We generalise the methods further to find a family of such spin chains. We compute the exact spectrum, and generalise an elegant graph-theory construction. We also explain how this family admits an N=2 lattice supersymmetry.
Global LHC constraints on electroweak-inos with SModelS v2.3

Mohammad Mahdi Altakach, Sabine Kraml, Andre Lessa, Sahana Narasimha, Timothée Pascal, Théo Reymermier, Wolfgang Waltenberger

SciPost Phys. 16, 101 (2024) · published 10 April 2024 | · pdf

Electroweak-inos, superpartners of the electroweak gauge and Higgs bosons, play a special role in supersymmetric theories. Their intricate mixing into chargino and neutralino mass eigenstates leads to a rich phenomenology, which makes it difficult to derive generic limits from LHC data. In this paper, we present a global analysis of LHC constraints for promptly decaying electroweak-inos in the context of the minimal supersymmetric standard model, exploiting the SMODELS software package. Combining up to 16 ATLAS and CMS searches for which electroweak-ino efficiency maps are available in SMODELS, we study which combinations maximise the sensitivity in different regions of the parameter space, how fluctuations in the data in individual analyses influence the global likelihood, and what is the resulting exclusion power of the combination compared to the analysis-by-analysis approach.
Symmetries and anomalies of Kitaev spin-S models: Identifying symmetry-enforced exotic quantum matter

Ruizhi Liu, Ho Tat Lam, Han Ma, Liujun Zou

SciPost Phys. 16, 100 (2024) · published 9 April 2024 | · pdf

We analyze the internal symmetries and their anomalies in the Kitaev spin-$S$ models. Importantly, these models have a lattice version of a $\mathbb{Z}_2$ 1-form symmetry, denoted by $\mathbb{Z}_2^{[1]}$. There is also an ordinary 0-form $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T$ symmetry, where $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}$ are $\pi$ spin rotations around two orthogonal axes, and $\mathbb{Z}_2^T$ is the time reversal symmetry. The anomalies associated with the full $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T×\mathbb{Z}_2^{[1]}$ symmetry are classified by $\mathbb{Z}_2^{17}$. We find that for $S∈\mathbb{Z}$ the model is anomaly-free, while for $S∈\mathbb{Z}+\frac{1}{2}$ there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries. The consequences of these symmetries and anomalies apply to not only the Kitaev spin-$S$ models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries. If these local perturbations are weak, generically these consequences still apply even if the perturbations break the 1-form symmetry. A notable consequence is that there should generically be a deconfined fermionic excitation carrying no fractional quantum number under the $\mathbb{Z}_2^{(x)}×\mathbb{Z}_2^{(y)}×\mathbb{Z}_2^T$ symmetry if $S∈\mathbb{Z}+\frac{1}{2}$, which implies symmetry-enforced exotic quantum matter. We also discuss the consequences for $S∈\mathbb{Z}$.
On correlation functions for the open XXZ chain with non-longitudinal boundary fields: The case with a constraint

Giuliano Niccoli, Véronique Terras

SciPost Phys. 16, 099 (2024) · published 9 April 2024 | · pdf

This paper is a continuation of [J. Phys. A: Math. Theor. 55, 405203 (2022)], in which a set of matrix elements of local operators was computed for the XXZ spin-1/2 open chain with a particular case of unparallel boundary fields. Here, we extend these results to the more general case in which both fields are non-longitudinal and related by one constraint, allowing for a partial description of the spectrum by usual Bethe equations. More precisely, the complete spectrum and eigenstates can be characterized within the Separation of Variables (SoV) framework. One uses here the fact that, under the constraint, a part of this SoV spectrum can be described via solutions of a usual, homogeneous, TQ-equation, with corresponding transfer matrix eigenstates coinciding with generalized Bethe states. We explain how to generically compute the action of a basis of local operators on such kind of states, and this under the most general boundary condition on the last site of the chain. As a result, we can compute the matrix elements of some of these basis elements in any eigenstate described by the homogenous TQ-equation. Assuming, following a conjecture of Nepomechie and Ravanini, that the ground state itself can be described in this framework, we obtain multiple integral representations for these matrix elements in the half-infinite chain limit, generalizing those previously obtained in the case of longitudinal boundary fields and in the case of the special boundary conditions considered in [J. Phys. A: Math. Theor. 55, 405203 (2022)].
Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries

Sahand Seifnashri

SciPost Phys. 16, 098 (2024) · published 9 April 2024 | · pdf

We study 't Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the "anomaly cocycle" using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group $H^3(G,U(1)) × H^2(G,U(1))$. The first factor captures the anomaly in the internal symmetry group $G$, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving $G$ and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly.
Mechanically-driven stem cell separation in tissues caused by proliferating daughter cells

Johannes C. Krämer, Edouard Hannezo, Gerhard Gompper, Jens Elgeti

SciPost Phys. 16, 097 (2024) · published 8 April 2024 | · pdf

The homeostasis of epithelial tissue relies on a balance between the self-renewal of stem cell populations, cellular differentiation, and loss. Although this balance needs to be tightly regulated to avoid pathologies, such as tumor growth, the regulatory mechanisms, both cell-intrinsic and collective, which ensure tissue steady-state are still poorly understood. Here, we develop a computational model that incorporates basic assumptions of stem cell renewal into distinct populations and mechanical interactions between cells. We find that the model generates unexpected dynamic features: stem cells repel each other in the bulk tissue and are thus found rather isolated, as in a number of in vivo contexts. By mapping the system onto a gas of passive Brownian particles with effective repulsive interactions, that arise from the generated flows of differentiated cells, we show that we can quantitatively describe such stem cell distribution in tissues. The interaction potential between a pair of stem cells decays exponentially with a characteristic length that spans several cell sizes, corresponding to the volume of cells generated per stem cell division. Our findings may help understanding the dynamics of normal and cancerous epithelial tissues.
Vertical and lateral manipulation of single Cs atoms on the semiconductor InAs(111)A

Rian A. M. Ligthart, Cristophe Coinon, Ludovic Desplanque, Xavier Wallart, Ingmar Swart

SciPost Phys. 16, 096 (2024) · published 5 April 2024 | · pdf

The tip of the scanning tunneling microscope can be used to position atoms and molecules on surfaces with atomic scale precision. Here, we report the controlled vertical and lateral manipulation of single Cs atoms on the InAs(111)A surface. The Cs adatom adsorbs on the In-vacancy site of the InAs(111)A—(2x2) surface reconstruction. Lateral manipulation is possible in all directions over the surface, not just along high-symmetry directions. Both pushing and pulling modes were observed in the height profile of the tip. We assembled two artificial structures, demonstrating the reliability of the manipulation procedures. Structures remained intact to a temperature of at least 44 K.
Inferring effective couplings with restricted Boltzmann machines

Aurélien Decelle, Cyril Furtlehner, Alfonso De Jesús Navas Gómez, Beatriz Seoane

SciPost Phys. 16, 095 (2024) · published 5 April 2024 | · pdf

Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a neural network. We address here the challenge of understanding the physical interpretation of such models. In this study, we propose a simple solution by implementing a direct mapping between the Restricted Boltzmann Machine and an effective Ising spin Hamiltonian. This mapping includes interactions of all possible orders, going beyond the conventional pairwise interactions typically considered in the inverse Ising (or Boltzmann Machine) approach, and allowing the description of complex datasets. Earlier works attempted to achieve this goal, but the proposed mappings were inaccurate for inference applications, did not properly treat the complexity of the problem, or did not provide precise prescriptions for practical application. To validate our method, we performed several controlled inverse numerical experiments in which we trained the RBMs using equilibrium samples of predefined models with local external fields, 2-body and 3-body interactions in different sparse topologies. The results demonstrate the effectiveness of our proposed approach in learning the correct interaction network and pave the way for its application in modeling interesting binary variable datasets. We also evaluate the quality of the inferred model based on different training methods.

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