Publications

Order by: publication date number of 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.

  10 citations

• Enhancement of stability of metastable states in the presence of Lévy noise

  Alexander A. Dubkov, Claudio Guarcello, Bernardo Spagnolo

  SciPost Phys. 18, 006 (2025) · published 8 January 2025 | Toggle abstract · pdf

  The barrier-crossing event for superdiffusion characterized by symmetric Lévy flights is analyzed. Starting from the fractional Fokker-Planck equation, we derive an integro-differential equation along with the necessary conditions to calculate the mean residence time of a particle within a fixed interval. We consider an arbitrary smooth potential profile, particularly metastable, with a sink and Lévy noise characterized by both an arbitrary index $\alpha$ and arbitrary noise intensity parameter. For the specific case of Lévy flights with an index $\alpha = 1$ and a cubic metastable potential, a closed expression for the mean residence time is obtained in quadratures. The analytical results reveal an enhancement of the mean residence time in the metastable state due to the influence of Lévy noise.

  10 citations

• Topological Frustration can modify the nature of a Quantum Phase Transition

  Vanja Marić, Gianpaolo Torre, Fabio Franchini, Salvatore Marco Giampaolo

  SciPost Phys. 12, 075 (2022) · published 24 February 2022 | Toggle abstract · pdf

  Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a system's phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.

  9 citations

• Generating dense packings of hard spheres by soft interaction design

  Thibaud Maimbourg, Mauro Sellitto, Guilhem Semerjian, Francesco Zamponi

  SciPost Phys. 4, 039 (2018) · published 26 June 2018 | Toggle abstract · pdf

  Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize a lower bound on packing density. Our results suggest that exponentially many (in the number of particles) distinct disordered sphere packings can be effectively constructed by this method, up to a packing fraction close to $7\, d\, 2^{-d}$. The latter is determined by solving the inverse problem of maximizing the dynamical glass transition over the space of the interaction potentials. Our method crucially exploits a recent exact formulation of the thermodynamics and the dynamics of simple liquids in infinite dimension.

  9 citations

• Classical Casimir free energy for two Drude spheres of arbitrary radii: A plane-wave approach

  Tanja Schoger, Gert-Ludwig Ingold

  SciPost Phys. Core 4, 011 (2021) · published 4 May 2021 | Toggle abstract · pdf

  We derive an exact analytic expression for the high-temperature limit of the Casimir interaction between two Drude spheres of arbitrary radii. Specifically, we determine the Casimir free energy by using the scattering approach in the plane-wave basis. Within a round-trip expansion, we are led to consider the combinatorics of certain partitions of the round trips. The relation between the Casimir free energy and the capacitance matrix of two spheres is discussed. Previously known results for the special cases of a sphere-plane geometry as well as two spheres of equal radii are recovered. An asymptotic expansion for small distances between the two spheres is determined and analytical expressions for the coefficients are given.

  9 citations

• Automatic contraction of unstructured tensor networks

  Adam S. Jermyn

  SciPost Phys. 8, 005 (2020) · published 15 January 2020 | Toggle abstract · pdf

  The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.

  9 citations

• Impurities in systems of noninteracting trapped fermions

  David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Gregory Schehr

  SciPost Phys. 10, 082 (2021) · published 14 April 2021 | Toggle abstract · pdf

  We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when the impurity is placed near the edge of the trap in the region where the unperturbed system is described by the Airy gas. Our method also allows us to compute the effective potential felt by the impurity both in the bulk and at the edge. In the bulk this effective potential is shown to be a universal function only of the local Fermi wave vector, or equivalently of the local fermion density. When the impurity is placed near the edge of the Fermi gas, the effective potential can be expressed in terms of Airy functions. For an attractive impurity placed far outside the support of the fermion density, we show that an interesting transition occurs where a single fermion is pulled out of the Fermi sea and forms a bound state with the impurity. This is a quantum analogue of the well-known Baik-Ben Arous-P\'ech\'e (BBP) transition, known in the theory of spiked random matrices. The density at the location of the impurity plays the role of an order parameter. We also consider the case of two impurities in the bulk and compute exactly the effective force between them mediated by the background Fermi gas.

  9 citations

• Entanglement evolution after a global quench across a conformal defect

  Luca Capizzi, Viktor Eisler

  SciPost Phys. 14, 070 (2023) · published 13 April 2023 | Toggle abstract · pdf

  We study the evolution of entanglement after a global quench in a one-dimensional quantum system with a localized impurity. For systems described by a conformal field theory, the entanglement entropy between the two regions separated by the defect grows linearly in time. Introducing the notion of boundary twist fields, we show how the slope of this growth can be related to the effective central charge that emerges in the study of ground-state entropy in the presence of the defect. On the other hand, we also consider a particular lattice realization of the quench in a free-fermion chain with a conformal defect. Starting from a gapped initial state, we obtain the slope via a quasiparticle ansatz and observe small discrepancies between the field theory and lattice results, which persist even in the limit of a vanishing gap.

  9 citations

• Spatial structure of unstable normal modes in a glass-forming liquid

  Masanari Shimada, Daniele Coslovich, Hideyuki Mizuno, Atsushi Ikeda

  SciPost Phys. 10, 001 (2021) · published 4 January 2021 | Toggle abstract · pdf

  The phenomenology of glass-forming liquids is often described in terms of their underlying, high-dimensional potential energy surface. In particular, the statistics of stationary points sampled as a function of temperature provides useful insight into the thermodynamics and dynamics of the system. To make contact with the real space physics, however, analysis of the spatial structure of the normal modes is required. In this work, we numerically study the potential energy surface of a glass-forming ternary mixture. Starting from liquid configurations equilibrated over a broad range of temperatures using a swap Monte Carlo method, we locate the nearby stationary points and investigate the spatial architecture and the energetics of the associated unstable modes. Through this spatially-resolved analysis, originally developed to study local minima, we corroborate recent evidence that the nature of the unstable modes changes from delocalized to localized around the mode-coupling temperature. We find that the displacement amplitudes of the delocalized modes have a slowly decaying far field, whereas the localized modes consist of a core with large displacements and a rapidly decaying far field. The fractal dimension of unstable modes around the mobility edge is equal to 1, consistent with the scaling of the participation ratio. Finally, we find that around and below the mode-coupling temperature the unstable modes are localized around structural defects, characterized by a disordered local structure markedly different from the liquid's locally favored structure. These defects are similar to those associated to quasi-localized vibrations in local minima and are good candidates to predict the emergence of localized excitations at low temperature.

  9 citations

• Special transition and extraordinary phase on the surface of a two-dimensional quantum Heisenberg antiferromagnet

  Chengxiang Ding, Wenjing Zhu, Wenan Guo, Long Zhang

  SciPost Phys. 15, 012 (2023) · published 18 July 2023 | Toggle abstract · pdf

  Continuous phase transitions exhibit richer critical phenomena on the surface than in the bulk, because distinct surface universality classes can be realized at the same bulk critical point by tuning the surface interactions. The exploration of surface critical behavior provides a window looking into higher-dimensional boundary conformal field theories. In this work, we study the surface critical behavior of a two-dimensional (2D) quantum critical Heisenberg model by tuning the surface coupling strength, and discover a direct special transition on the surface from the ordinary phase into an extraordinary phase. The extraordinary phase has a long-range antiferromagnetic order on the surface, in sharp contrast to the logarithmic decaying spin correlations in the 3D classical O(3) model. The special transition point has a new set of critical exponents, $y_{s}=0.86(4)$ and $\eta_{\parallel}=-0.33(1)$, which are distinct from the special transition of the classical O(3) model and indicate a new surface universality class of the 3D O(3) Wilson-Fisher theory.

  9 citations