Publications

Order by: publication date number of citations

• Constraints on the spectrum of field theories with non-integer $O(N)$ symmetry from quantum evanescence

  Weiguang Cao, Xiaochuan Lu, Tom Melia

  SciPost Phys. Core 7, 055 (2024) · published 14 August 2024 | Toggle abstract · pdf

  We identify constraints in the energy spectra of quantum theories that have a global $O(N)$ symmetry, where $N$ is treated as a continuous parameter. We point out that a class of evanescent states fall out of the spectrum at integer values of $N$ in pairs, via an annihilation mechanism. This forces the energies of the states in such a pair to approach equality as $N$ approaches a certain integer, with both states disappearing at precisely integer $N$ and the point of would-be degeneracy. These constraints occur between different irreducible representations of the analytic continuation of $O(N)$ and hold non-perturbatively. We give examples in the spectra of the critical $O(N)$ model.

  1 citation

• Dense Hopfield networks in the teacher-student setting

  Robin Thériault, Daniele Tantari

  SciPost Phys. 17, 040 (2024) · published 8 August 2024 | Toggle abstract · pdf

  Dense Hopfield networks with $p$-body interactions are known for their feature to prototype transition and adversarial robustness. However, theoretical studies have been mostly concerned with their storage capacity. We derive the phase diagram of pattern retrieval in the teacher-student setting of $p$-body networks, finding ferromagnetic phases reminiscent of the prototype and feature learning regimes. On the Nishimori line, we find the critical amount of data necessary for pattern retrieval, and we show that the corresponding ferromagnetic transition coincides with the paramagnetic to spin-glass transition of $p$-body networks with random memories. Outside of the Nishimori line, we find that the student can tolerate extensive noise when it has a larger $p$ than the teacher. We derive a formula for the adversarial robustness of such a student at zero temperature, corroborating the positive correlation between number of parameters and robustness in large neural networks. Our model also clarifies why the prototype phase of $p$-body networks is adversarially robust.

  1 citation

• Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions

  Pierre Le Doussal, Naftali R. Smith, Nathan Argaman

  SciPost Phys. 17, 038 (2024) · published 7 August 2024 | Toggle abstract · pdf

  We consider a system of $N$ spinless fermions, interacting with each other via a power-law interaction $\epsilon/r^n$, and trapped in an external harmonic potential $V(r) = r^2/2$, in $d=1,2,3$ dimensions. For any $0 < n < d+2$, we obtain the ground-state energy $E_N$ of the system perturbatively in $\epsilon$, $E_{N}=E_{N}^{(0)}+\epsilon E_{N}^{(1)}+O(\epsilon^{2})$. We calculate $E_{N}^{(1)}$ exactly, assuming that $N$ is such that the "outer shell" is filled. For the case of $n=1$ (corresponding to a Coulomb interaction for $d=3$), we extract the $N \gg 1$ behavior of $E_{N}^{(1)}$, focusing on the corrections to the exchange term with respect to the leading-order term that is predicted from the local density approximation applied to the Thomas-Fermi approximate density distribution. The leading correction contains a logarithmic divergence, and is of particular importance in the context of density functional theory. We also study the effect of the interactions on the fermions' spatial density. Finally, we find that our result for $E_{N}^{(1)}$ significantly simplifies in the case where $n$ is even.

  1 citation

• Long-range entanglement and topological excitations

  Gianpaolo Torre, Jovan Odavić, Pierre Fromholz, Salvatore Marco Giampaolo, Fabio Franchini

  SciPost Phys. Core 7, 050 (2024) · published 5 August 2024 | Toggle abstract · pdf

  Topological order comes in different forms, and its classification and detection is an important field of modern research. In this work, we show that the Disconnected Entanglement Entropy, a measure originally introduced to identify topological phases, is also able to unveil the long-range entanglement (LRE) carried by a single, fractionalized excitation. We show this by considering a quantum, delocalized domain wall excitation that can be introduced into a system by inducing geometric frustration in an antiferromagnetic spin chain. Furthermore, we show that the LRE of such systems is resilient against a quantum quench and the introduction of disorder, as it happens in traditional symmetry-protected topological phases. All these evidences establish the existence of a new phase induced by frustration with topological features despite not being of the usual type.

  4 citations

• Large deviations in the symmetric simple exclusion process with slow boundaries: A hydrodynamic perspective

  Soumyabrata Saha, Tridib Sadhu

  SciPost Phys. 17, 033 (2024) · published 5 August 2024 | Toggle abstract · pdf

  We revisit the one-dimensional model of the symmetric simple exclusion process slowly coupled with two unequal reservoirs at the boundaries. In its non-equilibrium stationary state, the large deviations functions of density and current have been recently derived using exact microscopic analysis by Derrida, Hirschberg and Sadhu in [J. Stat. Phys. 182, 15 (2021)]. We present an independent derivation using the hydrodynamic approach of the macroscopic fluctuation theory (MFT). The slow coupling introduces additional boundary terms in the MFT-Action, which modifies the spatial boundary conditions for the associated variational problem. For the density large deviations, we explicitly solve the corresponding Euler-Lagrange equations using a simple local transformation of the optimal fields. For the current large deviations, our solution is obtained using the additivity principle. In addition to recovering the expression of the large deviations functions, our solution describes the most probable path for these rare fluctuations.

  3 citations

• Analytic thermodynamic properties of the Lieb-Liniger gas

  Matthew L. Kerr, Giulia De Rosi, Karen V. Kheruntsyan

  SciPost Phys. Core 7, 047 (2024) · published 30 July 2024 | Toggle abstract · pdf

  We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact repulsive interactions. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics-thanks to its integrability and possible experimental realization using, e.g., ensembles of ultracold bosonic atoms confined to quasi-1D geometries. The thermodynamics of the uniform Lieb-Liniger gas can be obtained numerically using the exact thermal Bethe ansatz (TBA) method, first derived in 1969 by Yang and Yang. However, the TBA numerical calculations do not allow for the in-depth understanding of the underlying physical mechanisms that govern the thermodynamic behavior of the Lieb-Liniger gas at finite temperature. Our work is then motivated by the insights that emerge naturally from the transparency of closed-form analytic results, which are derived here in six different regimes of the gas and which exhibit an excellent agreement with the TBA numerics. Our findings can be further adopted for characterising the equilibrium properties of inhomogeneous (e.g., harmonically trapped) 1D Bose gases within the local density approximation and for the development of improved hydrodynamic theories, allowing for the calculation of breathing mode frequencies which depend on the underlying thermodynamic equation of state. Our analytic approaches can be applied to other systems including impurities in a quantum bath, liquid helium-4, and ultracold Bose gas mixtures.

  2 citations

• Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal

  Róbert Juhász, István A. Kovács

  SciPost Phys. Core 7, 044 (2024) · published 16 July 2024 | Toggle abstract · pdf

  Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical renormalization group results for the paradigmatic model, the contact process, in the combined presence of these factors in both one and two-dimensional systems. Our results confirm our analytic arguments stating that the density vanishes smoothly at the extinction threshold, in a way characteristic of infinite-order transitions. This extremely smooth vanishing of the global density entails an enhanced exposure of the population to extinction events. At the same time, a reverse order parameter, the local persistence displays a discontinuity characteristic of mixed-order transitions, as it approaches a non-universal critical value algebraically with an exponent $\beta_p'<1$.

• Stress correlations in near-crystalline packings

  Roshan Maharana, Kabir Ramola

  SciPost Phys. 17, 012 (2024) · published 15 July 2024 | Toggle abstract · pdf

  We derive exact results for stress correlations in near-crystalline systems in two and three dimensions. We study energy minimized configurations of particles interacting through Harmonic as well as Lennard-Jones potentials, for varying degrees of microscopic disorder and quenched forces on grains. Our findings demonstrate that the macroscopic elastic properties of such near-crystalline packings remain unchanged within a certain disorder threshold, yet they can be influenced by various factors, including packing density, pressure, and the strength of inter-particle interactions. We show that the stress correlations in such systems display anisotropic behavior at large lengthscales and are significantly influenced by the pre-stress of the system. The anisotropic nature of these correlations remains unaffected as we increase the strength of the disorder. Additionally, we derive the large lengthscale behavior for the change in the local stress components that shows a $1/r^d$ radial decay for the case of particle size disorder and a $1/r^{d-1}$ behavior for quenched forces introduced into a crystalline network. Finally, we verify our theoretical results numerically using energy-minimised static particle configurations.

• KPZ fluctuations in finite volume

  Sylvain Prolhac

  SciPost Phys. Lect. Notes 81 (2024) · published 12 June 2024 | Toggle abstract · pdf

  These lecture notes, adapted from the habilitation thesis of the author, survey in a first part various exact results obtained in the past few decades about KPZ fluctuations in one dimension, with a special focus on finite volume effects describing the relaxation to its stationary state of a finite system starting from a given initial condition. The second part is more specifically devoted to an approach allowing to express in a simple way the statistics of the current in the totally asymmetric simple exclusion process in terms of a contour integral on a compact Riemann surface, whose infinite genus limit leads to KPZ fluctuations in finite volume.

  4 citations

• The two critical temperatures conundrum in La$_{1.83}$Sr$_{0.17}$CuO$_4$

  Abhisek Samanta, Itay Mangel, Amit Keren, Daniel P. Arovas, Assa Auerbach

  SciPost Phys. 16, 148 (2024) · published 5 June 2024 | Toggle abstract · pdf

  The in-plane and out-of-plane superconducting stiffness of ${\rm La}^{\vphantom{\dagger}}_{1.83}{\rm Sr}^{\vphantom{\dagger}}_{0.17}{\rm CuO}^{\vphantom{\dagger}}_4$ rings appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by very small ratio $\alpha$ of inter-plane over intra-plane Josephson couplings. For three dimensional rings of millimeter dimensions, a crossover from layered three dimensional to quasi one dimensional behavior occurs at temperatures near the thermodynamic transition temperature ${T_{\rm c}}$, and the out-of-plane stiffness appears to vanish below ${T_{\rm c}}$ by a temperature shift of order $\alpha L_a/{\xi^{\parallel}}$, where $L_a/{\xi^{\parallel}}$ is the sample's width over coherence length. Including the effects of layer-correlated disorder, the measured temperature shifts can be fit by a value of $\alpha=4.1× 10^{-5}$, near ${T_{\rm c}}$, which is significantly lower than its previously measured value near zero temperature.