Publications

Order by: publication date number of citations

• Parametrization and thermodynamic scaling of pair correlation functions for the fractional quantum Hall effect

  Jørgen Fulsebakke, Mikael Fremling, Niall Moran, Joost K. Slingerland

  SciPost Phys. 14, 149 (2023) · published 9 June 2023 | Toggle abstract · pdf

  The calculation of pair correlations and density profiles of quasiholes are routine steps in the study of proposed fractional quantum Hall states. Nevertheless, the field has not adopted a standard way to present the results of such calculations in an easily reproducible form. We develop a polynomial expansion that allows for easy quantitative comparison between different candidate wavefunctions, as well as reliable scaling of correlation and quasihole profiles to the thermodynamic limit. We start from the well-known expansion introduced by Girvin [PRB, 30 (1984)] (see also [Girvin, MacDonald and Platzman, PRB, 33 (1986)]), which is physically appealing but, as we demonstrate, numerically unstable. We orthogonalize their basis set to obtain a new basis of modified Jacobi polynomials, whose coefficients can be stably calculated. We then apply our expansion to extract pair correlation expansion coefficients and quasihole profiles in the thermodynamic limit for a wide range of fractional quantum Hall wavefunctions. These include the Laughlin series, composite fermion states with both reverse and direct flux attachment, the Moore-Read Pfaffian state, and BS hierarchy states. The expansion procedure works for both abelian and non-abelian quasiholes, even when the density at the core is not zero. We find that the expansion coefficients for all quantum Hall states considered can be fit remarkably well using a cosine oscillation with exponentially decaying amplitude. The frequency and the decay length are related in an intuitive, but not elementary way to the filling fraction. Different states at the same filling fraction can have distinct values for these parameters. Finally, we also use our scaled correlation functions to calculate estimates for the magneto-roton gaps of the various states.

  1 citation

• Exact one-particle density matrix for SU(N) fermionic matter-waves in the strong repulsive limit

  Andreas Osterloh, Juan Polo, Wayne J. Chetcuti, Luigi Amico

  SciPost Phys. 15, 006 (2023) · published 11 July 2023 | Toggle abstract · pdf

  We consider a gas of repulsive $N$-component fermions confined in a ring-shaped potential, subjected to an effective magnetic field. For large repulsion strengths, we work out a Bethe ansatz scheme to compute the two-point correlation matrix and then the one-particle density matrix. Our results hold in the mesoscopic regime of finite but sufficiently large number of particles and system size that are not accessible by numerics. We access the momentum distribution of the system and analyse its specific dependence of interaction, magnetic field and number of components $N$. In the context of cold atoms, the exact computation of the correlation matrix to determine the interference patterns that are produced by releasing cold atoms from ring traps is carried out.

  1 citation

• Transitions in Xenes between excitonic, topological and trivial insulator phases: Influence of screening, band dispersion and external electric field

  Olivia Pulci, Paola Gori, Davide Grassano, Marco D'Alessandro, Friedhelm Bechstedt

  SciPost Phys. 15, 025 (2023) · published 24 July 2023 | Toggle abstract · pdf

  Using a variational approach, the binding energies $E_b$ of the lowest bound excitons in Xenes under varying electric field are investigated. The internal exciton motion is described both by Dirac electron dispersion and in effective-mass approximation, while the screened electron-hole attraction is modeled by a Rytova-Keldysh potential with a 2D electronic polarizability $\alpha_{2D}$. The most important parameters as spin-orbit-induced gap $E_g$, Fermi velocity $v_F$ and $\alpha_{2D}$ are taken from ab initio density functional theory calculations. In addition, $\alpha_{2D}$ is approximated in two different ways. The relation of $E_b$ and $E_g$ is ruled by the screening. The existence of an excitonic insulator phase with $E_b>E_g$ sensitively depends on the chosen $\alpha_{2D}$. The values of $E_g$ and $\alpha_{2D}$ are strongly modified by a vertical external electric bias $U$, which defines a transition from the topological into a trivial insulator at $U=E_g/2$, with the exception of plumbene. Within the Dirac approximation, but also within the effective mass description of the kinetic energy, the treatment of screening dominates the appearance or non-appearance of an excitonic insulator phase. Gating does not change the results: the prediction done at zero electric field is confirmed when a vertical electric field is applied. Finally, Many-Body perturbation theory approaches based on the Green's function method, applied to stanene, confirm the absence of an excitonic insulator phase, thus validating our results obtained by ab initio modeling of $\alpha_{2D}$.

  1 citation

• Optimizing Floquet engineering for non-equilibrium steady states with gradient-based methods

  Alberto Castro, Shunsuke A. Sato

  SciPost Phys. 15, 029 (2023) · published 26 July 2023 | Toggle abstract · pdf

  Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment - as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the coherent states of isolated systems (or to the transient phase for states that are weakly coupled to the environment), it may sometimes be of more interest to consider the final steady states that are reached after decoherence and dissipation take place. In this work, we demonstrate how those final states can be optimally tuned with respect to a given predefined metric, such as for example the maximization of the temporal average value of some observable, by using multicolor periodic perturbations. We show a computational framework that can be used for that purpose, and exemplify the concept using a simple model for the nitrogen-vacancy center in diamond: the goal in this case is to find the driving periodic magnetic field that maximizes a time-averaged spin component. We show that, for example, this technique permits to prepare states whose spin values are forbidden in thermal equilibrium at any temperature.

  1 citation

• Codebase release 1.1 for LinReTraCe

  Matthias Pickem, Emanuele Maggio, Jan M. Tomczak

  SciPost Phys. Codebases 16-r1.1 (2023) · published 17 July 2023 | Toggle abstract · src

  We describe the "Linear Response Transport Centre" (LinReTraCe), a package for the simulation of transport properties of solids. LinReTraCe captures quantum (in)coherence effects beyond semi-classical Boltzmann techniques, while incurring similar numerical costs. The enabling algorithmic innovation is a semi-analytical evaluation of Kubo formulae for resistivities and the coefficients of Hall, Seebeck and Nernst. We detail the program's architecture, its interface and usage with electronic-structure packages such as WIEN2k, VASP, and Wannier90, as well as versatile tight-binding settings.

  1 citation

• Fluctuation based interpretable analysis scheme for quantum many-body snapshots

  Henning Schlömer, Annabelle Bohrdt

  SciPost Phys. 15, 099 (2023) · published 18 September 2023 | Toggle abstract · pdf

  Microscopically understanding and classifying phases of matter is at the heart of strongly-correlated quantum physics. With quantum simulations, genuine projective measurements (snapshots) of the many-body state can be taken, which include the full information of correlations in the system. The rise of deep neural networks has made it possible to routinely solve abstract processing and classification tasks of large datasets, which can act as a guiding hand for quantum data analysis. However, though proven to be successful in differentiating between different phases of matter, conventional neural networks mostly lack interpretability on a physical footing. Here, we combine confusion learning [Nat. Phys. 13, 435 (2017)] with correlation convolutional neural networks [Nat. Commun. 12, 3905 (2021)], which yields fully interpretable phase detection in terms of correlation functions. In particular, we study thermodynamic properties of the 2D Heisenberg model, whereby the trained network is shown to pick up qualitative changes in the snapshots above and below a characteristic temperature where magnetic correlations become significantly long-range. We identify the full counting statistics of nearest neighbor spin correlations as the most important quantity for the decision process of the neural network, which go beyond averages of local observables. With access to the fluctuations of second-order correlations — which indirectly include contributions from higher order, long-range correlations — the network is able to detect changes of the specific heat and spin susceptibility, the latter being in analogy to magnetic properties of the pseudogap phase in high-temperature superconductors [Phys. Rev. Lett. 62, 957 (1989)]. By combining the confusion learning scheme with transformer neural networks, our work opens new directions in interpretable quantum image processing being sensible to long-range order.

  1 citation

• Tensor network study of the Shastry-Sutherland model with weak interlayer coupling

  Patrick C. G. Vlaar, Philippe Corboz

  SciPost Phys. 15, 126 (2023) · published 2 October 2023 | Toggle abstract · pdf

  The layered material SrCu$_2$(BO$_3$)$_2$ has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu$_2$(BO$_3$)$_2$ under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around $J''/J\sim0.04-0.05$ than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu$_2$(BO$_3$)$_2$ to be around $J''/J\sim 0.027$ at ambient pressure.

  1 citation

• xSPDE3: Extensible software for stochastic ordinary and partial differential equations

  Simon Kiesewetter, Ria R. Joseph, Peter D. Drummond

  SciPost Phys. Codebases 17 (2023) · published 2 October 2023 | Toggle abstract · pdf

  The xSPDE toolbox treats stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and/or sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $\chi^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. All equations may have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector field component, and at either end of any interval.

  1 citation

• Codebase release 3.44 for xSPDE

  Simon Kiesewetter, Ria R. Joseph, Peter D. Drummond

  SciPost Phys. Codebases 17-r3.44 (2023) · published 2 October 2023 | Toggle abstract · src

  The xSPDE toolbox treats stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and/or sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $\chi^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. All equations may have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector field component, and at either end of any interval.

  1 citation

• Photon pumping, photodissociation and dissipation at interplay for the fluorescence of a molecule in a cavity

  Megha Gopalakrishna, Emil Viñas Boström, Claudio Verdozzi

  SciPost Phys. 15, 138 (2023) · published 5 October 2023 | Toggle abstract · pdf

  We introduce a model description of a diatomic molecule in an optical cavity, with pump and fluorescent fields, and electron and nuclear motion are treated on equal footing and exactly. The model accounts for several optical response temporal scenarios: A Mollow spectrum hindered by electron correlations, a competition of harmonic generation and molecular dissociation, a dependence of fluorescence on photon pumping rate and dissipation. It is thus a general and flexible template for insight into experiments where quantum photon confinement, leakage, nuclear motion and electronic correlations are at interplay.

  1 citation