Publications

Order by: publication date number of citations

• Properties of fermionic systems with the path-integral ground state method

  Sebastian Ujevic, Vinicius Zampronio, Bruno R. de Abreu, Silvio A. Vitiello

  SciPost Phys. Core 6, 031 (2023) · published 20 April 2023 | Toggle abstract · pdf

  We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure $^4$He systems demonstrate most of the features of the method. Complementarily, for pure $^3$He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate $^3$He-$^4$He mixtures, demonstrating the method's robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature $T = 0$ without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the $^3$He kinetic energy in the mixture.

  1 citation

• Majorana bound states in encapsulated bilayer graphene

  Fernando Peñaranda, Ramón Aguado, Elsa Prada, Pablo San-Jose

  SciPost Phys. 14, 075 (2023) · published 18 April 2023 | Toggle abstract · pdf

  The search for robust topological superconductivity and Majorana bound states continues, exploring both one-dimensional (1D) systems such as semiconducting nanowires and two-dimensional (2D) platforms. In this work we study a 2D approach based on graphene bilayers encapsulated in transition metal dichalcogenides that, unlike previous proposals involving the Quantum Hall regime in graphene, requires weaker magnetic fields and does not rely on interactions. The encapsulation induces strong spin-orbit coupling on the graphene bilayer, which opens a sizeable gap and stabilizes fragile pairs of helical edge states. We show that, when subject to an in-plane Zeeman field, armchair edges can be transformed into p-wave one-dimensional topological superconductors by contacting them laterally with conventional superconductors. We demonstrate the emergence of Majorana bound states (MBSs) at the sample corners of crystallographically perfect flakes, belonging either to the D or the BDI symmetry classes depending on parameters. We compute the phase diagram, the resilience of MBSs against imperfections, and their manifestation as a 4$\pi$-periodic effect in Josephson junction geometries, all suggesting the existence of a topological phase within experimental reach.

  4 citations

• Optimal compression of quantum many-body time evolution operators into brickwall circuits

  Maurits S. J. Tepaske, Dominik Hahn, David J. Luitz

  SciPost Phys. 14, 073 (2023) · published 17 April 2023 | Toggle abstract · pdf

  Near term quantum computers suffer from a degree of decoherence which is prohibitive for high fidelity simulations with deep circuits. An economical use of circuit depth is therefore paramount. For digital quantum simulation of quantum many-body systems, real time evolution is typically achieved by a Trotter decomposition of the time evolution operator into circuits consisting only of two qubit gates. To match the geometry of the physical system and the CNOT connectivity of the quantum processor, additional SWAP gates are needed. We show that optimal fidelity, beyond what is achievable by simple Trotter decompositions for a fixed gate count, can be obtained by compiling the evolution operator into optimal brickwall circuits for the $S=1/2$ quantum Heisenberg model on chains and ladders, when mapped to one dimensional quantum processors without the need of additional SWAP gates.

  6 citations

• Extracting electronic many-body correlations from local measurements with artificial neural networks

  Faluke Aikebaier, Teemu Ojanen, Jose L. Lado

  SciPost Phys. Core 6, 030 (2023) · published 17 April 2023 | Toggle abstract · pdf

  The characterization of many-body correlations provides a powerful tool for analyzing correlated quantum materials. However, experimental extraction of quantum entanglement in correlated electronic systems remains an open problem in practice. In particular, the correlation entropy quantifies the strength of quantum correlations in interacting electronic systems, yet it requires measuring all the single-particle correlators of a macroscopic sample. To circumvent this bottleneck, we introduce a strategy to obtain the correlation entropy of electronic systems solely from a set of local measurements. We show that, by combining local particle-particle and density-density correlations with a neural-network algorithm, the correlation entropy can be predicted accurately. Specifically, we show that for a generalized interacting fermionic model, our algorithm yields an accurate prediction of the correlation entropy from a set of noisy local correlators. Our work shows that the correlation entropy in interacting electron systems can be reconstructed from local measurements, providing a starting point to experimentally extract many-body correlations with local probes.

  6 citations

• Engineering a pure Dirac regime in ZrTe$_5$

  Jorge I. Facio, Elisabetta Nocerino, Ion Cosma Fulga, Rafal Wawrzynczak, Joanna Brown, Genda Gu, Qiang Li, Martin Mansson, Yasmine Sassa, Oleh Ivashko, Martin v. Zimmermann, Felix Mende, Johannes Gooth, Stanislaw Galeski, Jeroen van den Brink, Tobias Meng

  SciPost Phys. 14, 066 (2023) · published 11 April 2023 | Toggle abstract · pdf

  Real-world topological semimetals typically exhibit Dirac and Weyl nodes that coexist with trivial Fermi pockets. This tends to mask the physics of the relativistic quasiparticles. Using the example of ZrTe$_5$, we show that strain provides a powerful tool for in-situ tuning of the band structure such that all trivial pockets are pushed far away from the Fermi energy, but only for a certain range of Van der Waals gaps. Our results naturally reconcile contradicting reports on the presence or absence of additional pockets in ZrTe$_5$, and provide a clear map of where to find a pure three-dimensional Dirac semimetallic phase in the structural parameter space of the material.

  2 citations

• Pychastic: Precise Brownian dynamics using Taylor-Itō integrators in Python

  Radost Waszkiewicz, Maciej Bartczak, Kamil Kolasa, Maciej Lisicki

  SciPost Phys. Codebases 11 (2023) · published 3 April 2023 | Toggle abstract · pdf

  In the last decade, Python-powered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the Itō calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated Taylor-Itō integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on $S^2$ and $SO(3)$. The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lower-level programming languages, but with a much simpler end-user interface.

  2 citations

• Codebase release 0.2 for Pychastic

  Radost Waszkiewicz, Maciej Bartczak, Kamil Kolasa, Maciej Lisicki

  SciPost Phys. Codebases 11-r0.2 (2023) · published 3 April 2023 | Toggle abstract · src

  In the last decade, Python-powered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the Itō calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated Taylor-Itō integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on $S^2$ and $SO(3)$. The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lower-level programming languages, but with a much simpler end-user interface.

  1 citation

• Vortex states in a PbTiO$_3$ ferroelectric cylinder

  Svitlana Kondovych, Maksim Pavlenko, Yurii Tikhonov, Anna Razumnaya, Igor Lukyanchuk

  SciPost Phys. 14, 056 (2023) · published 30 March 2023 | Toggle abstract · pdf

  The past decade's discovery of topological excitations in nanoscale ferroelectrics has turned the prevailing view that the polar ground state in these materials is uniform. However, the systematic understanding of the topological polar structures in ferroelectrics is still on track. Here we study stable vortex-like textures of polarization in the nanocylinders of ferroelectric PbTiO$_3$, arising due to the competition of the elastic and electrostatic interactions. Using the phase-field numerical modeling and analytical calculations, we show that the orientation of the vortex core with respect to the cylinder axis is tuned by the geometrical parameters and temperature of the system.

  3 citations

• A path integral ground state Monte Carlo algorithm for entanglement of lattice bosons

  Emanuel Casiano-Diaz, C. M. Herdman, Adrian Del Maestro

  SciPost Phys. 14, 054 (2023) · published 29 March 2023 | Toggle abstract · pdf

  A ground state path integral quantum Monte Carlo algorithm is introduced that allows for the study of entanglement in lattice bosons at zero temperature. The Rényi entanglement entropy between spatial subregions is explored across the phase diagram of the one dimensional Bose-Hubbard model for systems consisting of up to $L=256$ sites at unit-filling without any restrictions on site occupancy, far beyond the reach of exact diagonalization. The favorable scaling of the algorithm is demonstrated through a further measurement of the Rényi entanglement entropy at the two dimensional superfluid-insulator critical point for large system sizes, confirming the existence of the expected entanglement boundary law in the ground state. The Rényi estimator is extended to measure the symmetry resolved entanglement that is operationally accessible as a resource for experimentally relevant lattice gases with fixed total particle number.

  1 citation

• Structural classification of boron nitride twisted bilayers and ab initio investigation of their stacking-dependent electronic structure

  Sylvain Latil, Hakim Amara, Lorenzo Sponza

  SciPost Phys. 14, 053 (2023) · published 29 March 2023 | Toggle abstract · pdf

  Since the discovery of superconductive twisted bilayer graphene which initiated the field of twistronics, moiré systems have not ceased to exhibit fascinating properties. We demonstrate that in boron nitride twisted bilayers, for a given moiré periodicity, there are five different stackings which preserve the monolayer hexagonal symmetry (i.e. the invariance upon rotations of 120°) and not only two as always discussed in literature. We introduce some definitions and a nomenclature that identify unambiguously the twist angle and the stacking sequence of any hexagonal bilayer with order-3 rotation symmetry. Moreover, we employ density functional theory to study the evolution of the band structure as a function of the twist angle for each of the five stacking sequences of boron nitride bilayers. We show that the gap is indirect at any angle and in any stacking, and identify features that are conserved within the same stacking sequence irrespective of the angle of twist.

  1 citation