Publications

Order by: publication date number of citations

• Correlation functions and characteristic lengthscales in flat band superconductors

  Maxime Thumin, Georges Bouzerar

  SciPost Phys. 18, 025 (2025) · published 21 January 2025 | Toggle abstract · pdf

  The possibility of an unconventional form of high temperature superconductivity in flat band (FB) material does not cease to challenge our understanding of the physics in correlated systems. Here, we calculate the normal and anomalous one-particle correlation functions in various one and two dimensional FB systems and systematically extract the characteristic lengthscales. When the Fermi energy is located in the FB, it is found that the coherence length ($\xi$) is of the order of the lattice spacing and weakly sensitive to the strength of the electron-electron interaction. Recently, it has been argued that in FB compounds $\xi$ could be decomposed into a conventional part of BCS type ($\xi_{BCS}$) and a geometric contribution which characterises the FB eigenstates, the quantum metric ($\langle g \rangle$). However, by calculating the coherence length in two possible ways, our calculations show that $\xi ≠ \sqrt{\langle g \rangle.}$ This may suggest that the link between QM and coherence length is more complex, and leaves us with the open question: what is the appropriate definition of the coherence length in flat-band systems?

  5 citations

• 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.

  5 citations

• Free fermions beyond Jordan and Wigner

  Paul Fendley, Balazs Pozsgay

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

  5 citations

• Josephson junctions of topological nodal superconductors

  Ranjani Seshadri, Maxim Khodas, Dganit Meidan

  SciPost Phys. 12, 197 (2022) · published 23 June 2022 | Toggle abstract · pdf

  Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal superconductivity is associated with an energy-phase relation that depends on the momentum transverse to the current direction, with a $4\pi$ periodicity in between pairs of nodal points. We interpret this response as a result of a series of quantum phase transitions, driven by the transverse momentum, which separate a topological trivial phase and two distinct topologically non-trivial phases characterized by different winding invariants. This analysis sheds light on the stability of the Majorana flat bands to symmetry-breaking perturbations.

  5 citations

• Entanglement gap, corners, and symmetry breaking

  Vincenzo Alba

  SciPost Phys. 10, 056 (2021) · published 8 March 2021 | Toggle abstract · pdf

  We investigate the finite-size scaling of the lowest entanglement gap $\delta\xi$ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as $\delta\xi=\Omega/\sqrt{L\ln(L)}$. This is in contrast with the purely logarithmic behaviour as $\delta\xi=\pi^2/\ln(L)$ at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant $\Omega$, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to $\Omega$, at least for the case of a square corner.

  5 citations

• Stability of topological purity under random local unitaries

  Salvatore F. E. Oliviero, Lorenzo Leone, You Zhou, Alioscia Hamma

  SciPost Phys. 12, 096 (2022) · published 17 March 2022 | Toggle abstract · pdf

  In this work, we provide an analytical proof of the robustness of a form of topological entanglement under a model of random local perturbations. We define the notion of topological purity and show that, in the context of quantum double models, this quantity does detect topological order and is robust under the action of a random shallow quantum circuit.

  5 citations

• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation

  Miguel Alvarado, Alfredo Levy Yeyati

  SciPost Phys. 13, 009 (2022) · published 25 July 2022 | Toggle abstract · pdf

  Since the breakthrough of twistronics a plethora of topological phenomena in correlated systems has appeared. These devices can be typically analyzed in terms of lattice models using Green's function techniques. In this work we introduce a general method to obtain the boundary Green's function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. We illustrate our formalism analyzing the edge features of a Chern insulator, the Kitaev square lattice model for a topological superconductor and the Checkerboard lattice hosting topological flat bands. The efficiency and accuracy of the method is demonstrated by comparison to standard recursive Green's function calculations and direct diagonalizations.

  5 citations

• Phase diagram of the $\mathbb{Z}_3$-Fock parafermion chain with pair hopping

  Iman Mahyaeh, Jurriaan Wouters, Dirk Schuricht

  SciPost Phys. Core 3, 011 (2020) · published 12 November 2020 | Toggle abstract · pdf

  We study a tight binding model of $\mathbb{Z}_3$-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge $c=2$, and two gapless phases with central charge $c=1$. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.

  5 citations

• A splash in a one-dimensional cold gas

  Subhadip Chakraborti, Abhishek Dhar, P. L. Krapivsky

  SciPost Phys. 13, 074 (2022) · published 29 September 2022 | Toggle abstract · pdf

  We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, $m$ and $M$. The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by self-similar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations.

  5 citations

• Separability and entanglement of resonating valence-bond states

  Gilles Parez, Clément Berthiere, William Witczak-Krempa

  SciPost Phys. 15, 066 (2023) · published 21 August 2023 | Toggle abstract · pdf

  We investigate separability and entanglement of Rokhsar-Kivelson (RK) states and resonating valence-bond (RVB) states. These states play a prominent role in condensed matter physics, as they can describe quantum spin liquids and quantum critical states of matter, depending on their underlying lattices. For dimer RK states on arbitrary tileable graphs, we prove the exact separability of the reduced density matrix of $k$ disconnected subsystems, implying the absence of bipartite and multipartite entanglement between the subsystems. For more general RK states with local constraints, we argue separability in the thermodynamic limit, and show that any local RK state has zero logarithmic negativity, even if the density matrix is not exactly separable. In the case of adjacent subsystems, we find an exact expression for the logarithmic negativity in terms of partition functions of the underlying statistical model. For RVB states, we show separability for disconnected subsystems up to exponentially small terms in the distance $d$ between the subsystems, and that the logarithmic negativity is exponentially suppressed with $d$. We argue that separability does hold in the scaling limit, even for arbitrarily small ratio $d/L$, where $L$ is the characteristic size of the subsystems. Our results hold for arbitrary lattices, and encompass a large class of RK and RVB states, which include certain gapped quantum spin liquids and gapless quantum critical systems.

  5 citations