Publications

Order by: publication date number of citations

• NISQ algorithm for the matrix elements of a generic observable

  Rebecca Erbanni, Kishor Bharti, Leong-Chuan Kwek, Dario Poletti

  SciPost Phys. 15, 180 (2023) · published 30 October 2023 | Toggle abstract · pdf

  The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian without explicitly preparing its eigenstates. By means of numerical simulations we show that this approach finds many of the matrix elements for the one and two qubits cases. Specifically, while in the first case, one can initialize the ansatz parameters over a broad interval, in the latter the optimization landscape can significantly slow down the speed of convergence and one should therefore be careful to restrict the initialization to a smaller range of parameters.

• Line operators in 4d Chern-Simons theory and Cherkis bows

  Nafiz Ishtiaque, Yehao Zhou

  SciPost Phys. 16, 052 (2024) · published 22 February 2024 | Toggle abstract · pdf

  We show that the phase spaces of a large family of line operators in 4d Chern-Simons theory with GL$_n$ gauge group are given by Cherkis bow varieties with $n$ crosses. These line operators are characterized by Hanany-Witten type brane constructions involving D3, D5, and NS5 branes in an $\Omega$-background. Linking numbers of the five-branes and mass parameters for the D3 brane theories determine the phase spaces and in special cases they correspond to vacuum moduli spaces of 3d $\mathcal{N}=4$ quiver theories. Examples include line operators that conjecturally create T, Q, and L-operators in integrable spin chains.

• Anisotropic Zeeman Splitting in YbNi4P2

  Sara Karbassi, Saman Ghannadzadeh, Kristin Kliemt, Manuel Brando, Cornelius Krellner, Sven Friedemann

  SciPost Phys. 5, 056 (2018) · published 30 November 2018 | Toggle abstract · pdf

  The electronic structure of heavy-fermion materials is highly renormalised at low temperatures with localised moments contributing to the electronic excitation spectrum via the Kondo effect. Thus, heavy-fermion materials are very susceptible to Lifshitz transitions due to the small effective Fermi energy arising on parts of the renormalised Fermi surface. Here, we study Lifshitz transitions that have been discovered in YbNi4P2 in high magnetic fields. We measure the angular dependence of the critical fields necessary to induce a number of Lifshitz transitions and find it to follow a simple Zeeman-shift model with anisotropic g-factor. This highlights the coherent nature of the heavy quasiparticles forming a renormalised Fermi surface. We extract information on the orientation of the Fermi surface parts giving rise to the Lifshitz transitions and we determine the anisotropy of the effective g-factor to be $\eta \approx 3.8$ in good agreement with the crystal field scheme of YbNi4P2.

• Massless Rarita-Schwinger equations: Half and three halves spin solution

  Mauricio Valenzuela, Jorge Zanelli

  SciPost Phys. 16, 065 (2024) · published 4 March 2024 | Toggle abstract · pdf

  Counting the degrees of freedom of the massless Rarita-Schwinger theory is revisited using Behrends-Fronsdal projectors. The identification of the gauge invariant part of the vector-spinor is thus straightforward, consisting of spins 1/2 and 3/2. The validity of this statement is supported by the explicit solution found in the standard gamma-traceless gauge. Since the obtained systems are deterministic -free of arbitrary functions of time- we argue that the often-invoked residual gauge symmetry lacks fundamental grounding and should not be used to enforce new external constraints. The result is verified by the total Hamiltonian dynamics. We conclude that eliminating the spin-1/2 mode via the extended Hamiltonian dynamics would be acceptable if the Dirac conjecture was assumed; however, this framework does not accurately describe the original Lagrangian system.

• Quantum oscillations in an impurity-band Anderson insulator

  Nigel R. Cooper, Jack Kelsall

  SciPost Phys. 15, 118 (2023) · published 27 September 2023 | Toggle abstract · pdf

  We show that for a system of localized electrons in an impurity band, which form an Anderson insulating state at zero temperature, there can appear quantum oscillations of the magnetization, i.e. the Anderson insulator can exhibit the de Haas-van Alphen effect. This is possible when the electronic band from which the localized states are formed has an extremum that traces out a nonzero area in reciprocal space. Our work extends existing theories for clean band insulators of this form to the situation where they host an impurity band. We show that the energies of these impurity levels oscillate with magnetic field, and compute the conditions under which these oscillations can dominate the de Haas-van Alphen effect. We discuss our results in connection with experimental measurements of quantum oscillations in Kondo insulators, and propose other experimental systems where the impurity band contribution can be dominant.

• Four-quark scatterings in QCD I

  Wei-jie Fu, Chuang Huang, Jan M. Pawlowski, Yang-yang Tan

  SciPost Phys. 14, 069 (2023) · published 13 April 2023 | Toggle abstract · pdf

  We investigate dynamical chiral symmetry breaking and the emergence of mesonic bound states from the infrared dynamics of four-quark scatterings. Both phenomena originate from the resonant scalar-pseudoscalar channel of the four-quark scatterings, and we compute the functional renormalisation group (fRG) flows of the Fierz-complete four-quark interaction of up and down quarks with its $t$ channel momentum dependence. This is done in the isospin symmetric case, also including the flow of the quark two-point function. This system can be understood as the fRG analogues of the complete Bethe-Salpeter equations and quark gap equation. The pole mass of the pion is determined from both direct calculations of the four-quark flows in the Minkowski regime of momenta and the analytic continuation based on results in the Euclidean regime, which are consistent with each other.

• Beyond Fermi's golden rule with the statistical Jacobi approximation

  David M. Long, Dominik Hahn, Marin Bukov, Anushya Chandran

  SciPost Phys. 15, 251 (2023) · published 22 December 2023 | Toggle abstract · pdf

  Many problems in quantum dynamics can be cast as the decay of a single quantum state into a continuum. The time-dependent overlap with the initial state, called the fidelity, characterizes this decay. We derive an analytic expression for the fidelity after a quench to an ergodic Hamiltonian. The expression is valid for both weak and strong quenches, and timescales before finiteness of the Hilbert space limits the fidelity. It reproduces initial quadratic decay and asymptotic exponential decay with a rate which, for strong quenches, differs from Fermi's golden rule. The analysis relies on the statistical Jacobi approximation (SJA), which was originally applied in nearly localized systems, and which we here adapt to well-thermalizing systems. Our results demonstrate that the SJA is predictive in disparate regimes of quantum dynamics.

• Manifold curvature and Ehrenfest forces with a moving basis

  Jessica F. K. Halliday, Emilio Artacho

  SciPost Phys. 12, 020 (2022) · published 13 January 2022 | Toggle abstract · pdf

  Known force terms arising in the Ehrenfest dynamics of quantum electrons and classical nuclei, due to a moving basis set for the former, can be understood in terms of the curvature of the manifold hosting the quantum states of the electronic subsystem. Namely, the velocity-dependent terms appearing in the Ehrenfest forces on the nuclei acquire a geometrical meaning in terms of the intrinsic curvature of the manifold, while Pulay terms relate to its extrinsic curvature.

• Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry

  Nikolai A. Stepanov, Mikhail A. Skvortsov

  SciPost Phys. 13, 021 (2022) · published 16 August 2022 | Toggle abstract · pdf

  We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney's problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half plane. We formulate the problem of statistical description of this never-falling trajectory and solve it by a field-theoretical technique assuming a white-noise driving. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistic properties of the never-falling trajectory are expressed in terms of the zero mode of the corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, which however is written for the "square root" of the probability distribution function. Our results for the statistics of the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of strong driving (no gravitation), we obtain an exact analytical solution for the instantaneous joint probability distribution function of the pendulum's angle and its velocity.

• The origin of the period-$2T/7$ quasi-breathing in disk-shaped Gross-Pitaevskii breathers

  Jordi Torrents, Vanja Dunjko, Marina Gonchenko, Gregory E. Astrakharchik, Maxim Olshanii

  SciPost Phys. 12, 092 (2022) · published 14 March 2022 | Toggle abstract · pdf

  We address the origins of the quasi-periodic breathing observed in [Phys. Rev.\ X vol. 9, 021035 (2019)] in disk-shaped harmonically trapped two-dimensional Bose condensates, where the quasi-period $T_{\text{quasi-breathing}}\sim$~$2T/7$ and $T$ is the period of the harmonic trap. We show that, due to an unexplained coincidence, the first instance of the collapse of the hydrodynamic description, at $t^{*} = \arctan(\sqrt{2})/(2\pi) T \approx T/7$, emerges as a `skillful impostor' of the quasi-breathing half-period $T_{\text{quasi-breathing}}/2$. At the time $t^{*}$, the velocity field almost vanishes, supporting the requisite time-reversal invariance. We find that this phenomenon persists for scale-invariant gases in all spatial dimensions, being exact in one dimension and, likely, approximate in all others. In $\bm{d}$ dimensions, the quasi-breathing half-period assumes the form $T_{\text{quasi-breathing}}/2 \equiv t^{*} = \arctan(\sqrt{d})/(2\pi) T$. Remaining unresolved is the origin of the period-$2T$ breathing, reported in the same experiment.