arXiv subjects

Viktor Bekassy

Publications and source records attributed to Viktor Bekassy.

3 recordsLinked to original sources

arXiv2025

Probing Fractional Quantum Hall states in weakly interacting Fermi gases

Quantum gases are used to simulate the physics of the lowest Landau level (LLL) with neutral atoms, which in the simplest setup is achieved by rotating the gas at the confining harmonic trap frequency, a requirement that is difficult to achieve in practice. We point out that for weakly interacting Fermi gases, this rapid-rotation limit is not needed to access the LLL: As a direct consequence of first-order perturbation theory, many-body wave functions of states in the LLL remain unchanged at any rotation, and only their energies shift. This implies that even in the absence of rotations or for moderate rotations frequencies, LLL states are present as excited states at finite angular momentum. For fermions with contact interactions, these states are exact eigenstates of a paradigmatic model of Fractional Quantum Hall (FQH) states described by a single Haldane pseudopotential ($V_1$ for spin-polarized and $V_0$ for spinful systems), which realizes exact Laughlin and Haldane wave functions. We suggest that recently developed excitation and imaging techniques for rotating few-fermion systems allow for a detailed experimental investigation of FQH wave functions and to study the crossover to large particle number. We illustrate this for $N = 6$ spin-balanced fermions

cond-mat.quant-gas↗

arXiv2024

Scale and conformal invariance in rotating interacting few-fermion systems

We show that rotating two-dimensional Fermi gases possess a nonrelativistic scale and conformal invariance at weak but nonzero interactions, where the scale invariance of universal short-range interactions is not yet broken by quantum effects. We demonstrate the symmetry in the excitation spectrum of few-fermion ensembles in a harmonic trap obtained by exact diagonalization. The excitation spectrum is shown to split in a set of primary states and derived excited states that consist of breathing modes as well as two different center-of-mass excitations, which describe cyclotron and guiding-center excitations of the total particle cloud. Furthermore, the conformal symmetry is manifest in the many-body wave function, where it dictates the form of the hyperradial component, which we demonstrate using Monte Carlo sampling of few-body wave functions.

cond-mat.quant-gas↗

arXiv2022

Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases

Two-dimensional Fermi gases with universal short-range interactions are known to exhibit a quantum anomaly, where a classical scale and conformal invariance is broken by quantum effects at strong coupling. We argue that in a quasi two-dimensional geometry, a conformal window remains at weak interactions. Using degenerate perturbation theory, we verify the conformal symmetry by computing the energy spectrum of mesoscopic particle ensembles in a harmonic trap, which separates into conformal towers formed by so-called primary states and their center-of-mass and breathing-mode excitations, the latter having excitation energies at precisely twice the harmonic oscillator energy. In addition, using Metropolis importance sampling, we compute the hyperradial distribution function of the many-body wave functions, which are predicted by the conformal symmetry in closed analytical form. The weakly interacting Fermi gas constitutes a system where the nonrelativistic conformal symmetry can be revealed using elementary methods, and our results are testable in current experiments on mesoscopic Fermi gases.

cond-mat.quant-gas↗