Publications

Order by: publication date number of citations

• Mode-shell correspondence, a unifying phase space theory in topological physics - Part I: Chiral number of zero-modes

  Lucien Jezequel, Pierre Delplace

  SciPost Phys. 17, 060 (2024) · published 23 August 2024 | Toggle abstract · pdf

  We propose a theory, that we call the mode-shell correspondence, which relates the topological zero-modes localised in phase space to a shell invariant defined on the surface forming a shell enclosing these zero-modes. We show that the mode-shell formalism provides a general framework unifying important results of topological physics, such as the bulk-edge correspondence, higher-order topological insulators, but also the Atiyah-Singer and the Callias index theories. In this paper, we discuss the already rich phenomenology of chiral symmetric Hamiltonians where the topological quantity is the chiral number of zero-dimensional zero-energy modes. We explain how, in a lot of cases, the shell-invariant has a semi-classical limit expressed as a generalised winding number on the shell, which makes it accessible to analytical computations.

• Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

  Alexander Nikolaenko, Ya-Hui Zhang

  SciPost Phys. 17, 034 (2024) · published 5 August 2024 | Toggle abstract · pdf

  Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling $J_K$ at fixed doping x. At large positive $J_K$, we confirm the expected conventional Luttinger liquid phase with $2k_F=\frac{1+x}{2}$ (in units of $2\pi$), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the $J_K ≤ 0$ side, our simulation finds the existence of a fractional Luttinger liquid (LL$\star$) phase with $2k_F=\frac{x}{2}$, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL$\star$) phase in higher dimensions. The LL$\star$ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive $J_K$. Then we mainly focus on the "critical regime" between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of $J_K$, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around $0.035 J$) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent $z=+$. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

• The Hoyle Family: break-up measurements to probe α-condensation in light nuclei

  Robin Smith, Jack Bishop, Joel Hirst, Tzany Kokalova, Carl Wheldon

  SciPost Phys. Proc. 3, 030 (2020) · published 26 February 2020 | Toggle abstract · pdf

  The 12C Hoyle state is a candidate for α-condensation, due to its large volume and α-cluster structure. This paper discusses precision break-up measurements and how they can elucidate α-condensate structures. Two experiments are discussed in detail, firstly concerning the break-up of 12C and then the decays of heavier nuclei. With more theoretical input, and increasingly complex detector setups, precision break-up measurements can, in principle, provide insight into the structures of states in α-conjugate nuclei. At present, such searches have not delivered evidence for α-condensation in 12C or 16O.

• On the Virasoro fusion kernel at $c=25$

  Sylvain Ribault, Ioannis Tsiares

  SciPost Phys. 17, 058 (2024) · published 22 August 2024 | Toggle abstract · pdf

  We find a formula for the Virasoro fusion kernel at $c=25$, in terms of the connection coefficients of the Painlevé VI differential equation. Our formula agrees numerically with previously known integral representations of the kernel. The derivation of our formula relies on a duality $c\to 26-c$ that is obeyed by the shift equations for the fusion and modular kernels. We conjecture that for $c<1$ the fusion and modular kernels are not smooth functions, but distributions.

• The role of atomic interactions in cavity-induced continuous time crystals

  Christian Høj Johansen, Johannes Lang, Francesco Piazza

  SciPost Phys. 17, 089 (2024) · published 24 September 2024 | Toggle abstract · pdf

  We consider continuous time-crystalline phases in dissipative many-body systems of atoms in cavities, focusing on the role of short-range interatomic interactions. First, we show that the latter can alter the nature of the time crystal by changing the type of the underlying critical bifurcation. Second, we characterize the heating mechanism and dynamics resulting from the short-range interactions and demonstrate that they make the time crystal inherently metastable. We argue this is generic for the broader class of dissipative time crystals in atom-cavity systems whenever the cavity loss rate is comparable to the atomic recoil energy. We observe that such a scenario for heating has several similarities to the one proposed for preheating in the early universe, where the oscillating coherent inflation field decays into a cascade of exponentially growing fluctuations. By extending approaches for dissipative dynamical systems to our many-body problem, we obtain analytical predictions for the parameters describing the phase transition and the heating rate inside the time-crystalline phase. We underpin and extend the analytical predictions of the heating rates with numerical simulations, which also show that the metastable regime exists when the inherent stochastic nature is taken into account.

• Topological linear response of hyperbolic Chern insulators

  Canon Sun, Anffany Chen, Tomáš Bzdušek, Joseph Maciejko

  SciPost Phys. 17, 124 (2024) · published 4 November 2024 | Toggle abstract · pdf

  We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) formula. By generalizing the Kubo formula to hyperbolic lattices, we show that the Hall conductivity is quantized to $-e^2C_{ij}/h$, where $C_{ij}$ is the first Chern number. Through a flux-threading argument, we provide an interpretation of the Chern number as a topological invariant in hyperbolic band theory. We demonstrate that, although it receives contributions from both Abelian and non-Abelian Bloch states, the Chern number can be calculated solely from Abelian states, resulting in a tremendous simplification of the topological band theory. Finally, we verify our results numerically by computing various Chern numbers in the hyperbolic Haldane model.

• Theory of universal diode effect in three-terminal Josephson junctions

  Jorge Huamani Correa, Michał P. Nowak

  SciPost Phys. 17, 037 (2024) · published 7 August 2024 | Toggle abstract · pdf

  We theoretically study the superconducting diode effect in a three-terminal Josephson junction. The diode effect in superconducting systems is typically related to the presence of a difference in the critical currents for currents flowing in the opposite direction. We show that in multi-terminal systems this effect occurs naturally without the need of the presence of any spin interactions and is a result of the presence of a relative shift between the Andreev bound states carrying the supercurrent. On an example of a three-terminal junction, we demonstrate that the non-reciprocal current in one of the superconducting contacts can be induced by proper phase biasing of the other contacts, provided that there are at least two Andreev bound states in the system and the symmetry of the system is broken. This result is confirmed in numerical models describing the junctions in both the short- and long-regime. By optimizing the geometry of the junction, we show that the efficiency of the realized superconducting diode exceeds 35%. We relate our predictions to recent experiments on multi-terminal junctions, in which non-reciprocal supercurrents were observed.

• Response functions and cross sections for inclusive neutrino scattering off $^2$H, $^3$H and $^3$He

  Alessandro Grassi, Jacek Golak, Roman Skibiński, Kacper Topolnicki, Henryk Witała, Hiroyuki Kamada, Laura Elisa Marcucci

  SciPost Phys. Proc. 3, 031 (2020) · published 26 February 2020 | Toggle abstract · pdf

  For several decades there has been an interest in studying neutrino scattering on light nuclei, with the hope of increasing knowledge about the theory of weak interactions and electroweak unification. A study of several neutrino induced reactions on light nuclei ($^2$H, $^3$H and $^3$He) is presented here. The cross section for these reactions is evaluated using the nuclear response functions, which holds the information about the nuclear interactions and structure. This approach has been tested for break-up reactions on the deuteron before and is now extended to three-nucleon break-up reactions.

• Calculation of asymptotic normalization coefficients in the complex-ranged Gaussian basis

  Dinmukhamed A. Sailaubek, Olga A. Rubtsova

  SciPost Phys. Proc. 3, 043 (2020) · published 27 February 2020 | Toggle abstract · pdf

  A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in approximation for a radial part of the bound state wave function from the origin up to the far asymptotic distances, which allows to extract ANCs rather accurately. The method is illustrated by calculations of single-particle ANCs for nuclei bound states in cases of non-local nucleon-nucleus interactions, in particular, phenomenological global potentials with the Perey-Buck's non-locality.

• Anisotropic Kondo line defect and ODE/IM correspondence

  Jingxiang Wu

  SciPost Phys. 15, 248 (2023) · published 20 December 2023 | Toggle abstract · pdf

  We study the anisotropic Kondo line defects in products of chiral SU(2) WZW models. We propose an ODE/IM correspondence for the anisotropic Kondo problems by considering the four-dimensional Chern Simons theory in the trigonometric case. We verify the claim both by explicit perturbative calculations in the ultraviolet and by exact WKB analysis in the infrared. In doing so, we derived the infrared dynamics of a large class of anisotropic line defects.