Publications

Order by: publication date number of citations

• Topological-insulator nanocylinders

  Michele Governale, Fabio Taddei

  SciPost Phys. Core 6, 032 (2023) · published 21 April 2023 | Toggle abstract · pdf

  Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy spectrum, the surface states and the dipole matrix elements for optical transitions with in-plane polarization of 3DTI nanocylinders of finite height $L$ and radius $R$. We first derive an effective 2D Hamiltonian by exploiting the cylindrical symmetry of the problem. We develop two approaches: the first one is an exact numerical tight-binding model obtained by discretising the Hamiltonian. The second one, which allows us to obtain analytical results, is an approximated model based on a large-$R$ expansion and on an effective boundary condition to account for the finite height of the nanocylinder. We find that the agreement between the two models, as far as eigenenergies and eigenfunctions are concerned, is excellent for the lowest absolute value of the longitudinal component of the angular momentum. Finally, we derive analytical expressions for the dipole matrix elements by first considering the lateral surface alone and the bases alone, and then for the whole nanocylinder. In particular, we focus on the two limiting cases of tall and squat nanocylinders. The latter case is compared with the numerical results finding a good agreement.

• 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

• 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.

  5 citations

• Stochastic representation of the quantum quartic oscillator

  Gennaro Tucci, Stefano De Nicola, Sascha Wald, Andrea Gambassi

  SciPost Phys. Core 6, 029 (2023) · published 14 April 2023 | Toggle abstract · pdf

  Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.

• Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios

  Emanuel-Cristian Boghiu, Flavien Hirsch, Pei-Sheng Lin, Marco Túlio Quintino, Joseph Bowles

  SciPost Phys. Core 6, 028 (2023) · published 11 April 2023 | Toggle abstract · pdf

  It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent entanglement certification. In this work we strengthen these results and explore new aspects of this phenomenon. First, we prove new results related to the activation of Bell nonlocality. We construct Bell inequalities tailored to the broadcast scenario, and show how broadcasting can lead to even stronger notions of Bell nonlocality activation. In particular, we exploit these ideas to show that bipartite states admitting a local hidden-variable model for general measurements can lead to genuine tripartite nonlocal correlations. We then study device-independent entanglement certification in the broadcast scenario, and show through semidefinite programming techniques that device-independent entanglement certification is possible for the two-qubit Werner state in essentially the entire range of entanglement. Finally, we extend the concept of EPR steering to the broadcast scenario, and present novel examples of activation of the two-qubit isotropic state. Our results pave the way for broadcast-based device-independent and semi-device-independent protocols.

  1 citation

• Photoemission "experiments" on holographic lattices

  Filip Herček, Vladan Gecin, Mihailo Čubrović

  SciPost Phys. Core 6, 027 (2023) · published 6 April 2023 | Toggle abstract · pdf

  We construct a 2D holographic ionic lattice with hyperscaling-violating infrared geometry and study single-electron spectral functions ("ARPES photoemission curves") on this background. The spectra typically show a three-peak structure, where the central peak undergoes a crossover from a sharp but not Fermi-liquid-like quasiparticle to a wide incoherent maximum, and the broad side peaks resemble the Hubbard bands. These findings are partially explained by a perturbative near-horizon analysis of the bulk Dirac equation. Comparing the holographic Green functions in imaginary frequency with the Green functions of the Hubbard model obtained from quantum Monte Carlo, we find that the holographic model provides a very good fit to the Hubbard Green function. However, the information loss when transposing the holographic Green functions to imaginary frequencies implies that a deeper connection to Hubbard-like models remains questionable.

  2 citations

• Replica method for eigenvalues of real Wishart product matrices

  Jacob A. Zavatone-Veth, Cengiz Pehlevan

  SciPost Phys. Core 6, 026 (2023) · published 5 April 2023 | Toggle abstract · pdf

  We show how the replica method can be used to compute the asymptotic eigenvalue spectrum of a real Wishart product matrix. For unstructured factors, this provides a compact, elementary derivation of a polynomial condition on the Stieltjes transform first proved by Müller [IEEE Trans. Inf. Theory. 48, 2086-2091 (2002)]. We then show how this computation can be extended to ensembles where the factors are drawn from matrix Gaussian distributions with general correlation structure. For both unstructured and structured ensembles, we derive polynomial conditions on the average values of the minimum and maximum eigenvalues, which in the unstructured case match the results obtained by Akemann, Ipsen, and Kieburg [Phys. Rev. E 88, 052118 (2013)] for the complex Wishart product ensemble.

  1 citation

• The resistance of quantum entanglement to temperature in the Kugel-Khomskii model

  Valerii E. Valiulin, Andrey V. Mikheyenkov, Nikolay M. Chtchelkatchev, Kliment I. Kugel

  SciPost Phys. Core 6, 025 (2023) · published 4 April 2023 | Toggle abstract · pdf

  The Kugel-Khomskii model with entangled spin and orbital degrees of freedom is a good testing ground for many important features in quantum information processing, such as robust gaps in the entanglement spectra. Here, we demonstrate that the entanglement can be also robust under effect of temperature within a wide range of parameters. It is shown, in particular, that the temperature dependence of entanglement often exhibits a nonmonotonic behavior. Namely, there turn out to be ranges of the model parameters, where entanglement is absent at zero temperature, but then, with an increase in temperature, it appears, passes through a maximum, and again vanishes.

• Uhlmann phase of coherent states and the Uhlmann-Berry correspondence

  Xin Wang, Xu-Yang Hou, Zheng Zhou, Hao Guo, and Chih-Chun Chien

  SciPost Phys. Core 6, 024 (2023) · published 31 March 2023 | Toggle abstract · pdf

  We first compare the geometric frameworks behind the Uhlmann and Berry phases in a fiber-bundle language and then evaluate the Uhlmann phases of bosonic and fermionic coherent states. The Uhlmann phases of both coherent states are shown to carry geometric information and decrease smoothly with temperature. Importantly, the Uhlmann phases approach the corresponding Berry phases as temperature decreases. Together with previous examples in the literature, we propose a correspondence between the Uhlmann and Berry phases in the zero-temperature limit as a general property except some special cases and present a conditional proof of the correspondence.

  2 citations

• Generalized Lindblad master equation for measurement-induced phase transition

  Yi-Neng Zhou

  SciPost Phys. Core 6, 023 (2023) · published 30 March 2023 | Toggle abstract · pdf

  The measurement-induced phase transition (MIPT) occurs when the system is evolving under unitary evolution together with local measurements followed by post-selection. We propose a generalized version of the Lindblad master equation as a continuous equation, to describe the dynamics of the second Rényi entropy in the MIPT. This generalized Lindblad equation explicitly takes into account the post-selection in the MIPT, which is realized as the Einstein-Podolsky-Rosen (EPR) state projection in the equation. Also, this generalized Lindblad equation preserves the Hermitian, unit trace, and positive definiteness of the density matrix. We further use the hard-core Bose-Hubbard model as a concrete example to numerically confirm that our generalized Lindblad equation is applicable to describing the MIPT.

  3 citations