arXiv subjects

A. Schellenberger

Publications and source records attributed to A. Schellenberger.

5 recordsLinked to original sources

arXiv2026

Quantitative approach for the Dicke-Ising chain with an effective self-consistent matter Hamiltonian

In the thermodynamic limit, the Dicke-Ising chain maps exactly onto an effective self-consistent matter Hamiltonian with the photon field acting solely as a self-consistent effective field. As a consequence, no quantum correlations between photons and spins are needed to understand the quantum phase diagram. This enables us to determine the quantum phase diagram in the thermodynamic limit using numerical linked-cluster expansions combined with density matrix renormalization group calculations (NLCE+DMRG) to solve the resulting self-consistent matter Hamiltonian. This includes magnetically ordered phases with significantly improved accuracy compared to previous estimates. For ferromagnetic Ising couplings, we refine the location of the multicritical point governing the change in the order of the superradiant phase transition, reaching a relative accuracy of $10^{-4}$. For antiferromagnetic Ising couplings, we confirm the existence of the narrow antiferromagnetic superradiant phase in the thermodynamic limit. The effective matter Hamiltonian framework identifies the antiferromagnetic superradiant phase as the many-body ground state of an antiferromagnetic transverse-field Ising model with longitudinal field. This phase emerges through continuous Dicke-type polariton condensation from the antiferromagnetic normal phase, followed by a first-order transition to the paramagnetic superradiant phase. Thus, NLCE+DMRG provides a precise determination of the Dicke-Ising phase diagram in one dimension by solving the self-consistent effective matter Hamiltonian.

quant-ph↗

arXiv2025

Absence of topological order in the $U(1)$ checkerboard toric code

We investigate the $U(1)$ checkerboard toric code which corresponds to the $U(1)$-symmetry enriched toric code with two distinct star sublattices. One can therefore tune from the limit of isolated stars to the uniform system. The uniform system has been conjectured to possess non-Abelian topological order based on quantum Monte Carlo simulations suggesting a non-trivial ground-state degeneracy depending on the compactification of the finite clusters. Here we show that these non-trivial properties can be naturally explained in the perturbative limit of isolated stars. Indeed, the compactification dependence of the ground-state degeneracy can be traced back to geometric constraints stemming from the plaquette operators. Further, the ground-state degeneracy is fully lifted in fourth-order degenerate perturbation theory giving rise to a non-topological phase with confined fracton excitations. These fractons are confined for small perturbations so that they cannot exist as single low-energy excitation in the thermodynamic limit but only as topologically trivially composite particles. However, the confinement scale is shown to be surprisingly large so that finite-size gaps are extremely small on finite clusters up to the uniform limit which is calculated explicitly by high-order series expansions. Our findings suggest that these gaps were not distinguished from finite-size effects by the recent quantum Monte Carlo simulation in the uniform limit. All our results therefore point towards the absence of topological order in the $U(1)$ checkerboard toric code along the whole parameter axis.

cond-mat.str-el↗

arXiv2023

Series expansions in closed and open quantum many-body systems with multiple quasiparticle types

The established approach of perturbative continuous unitary transformations (pCUTs) constructs effective quantum many-body Hamiltonians as perturbative series that conserve the number of one quasiparticle type. We extend the pCUT method to similarity transformations - dubbed $\mathrm{pcst}^{\texttt{++}}$ - allowing for multiple quasiparticle types with complex-valued energies. This enlarges the field of application to closed and open quantum many-body systems with unperturbed operators corresponding to arbitrary superimposed ladder spectra. To this end, a generalized counting operator is combined with the quasiparticle generator for open quantum systems recently introduced by Schmiedinghoff and Uhrig (arXiv:2203.15532). The $\mathrm{pcst}^{\texttt{++}}$ then yields model-independent block-diagonal effective Hamiltonians and Lindbladians allowing a linked-cluster expansion in the thermodynamic limit similar to the conventional pCUT method. We illustrate the application of the $\mathrm{pcst}^{\texttt{++}}$ method by discussing representative closed, open, and non-Hermitian quantum systems.

cond-mat.str-el↗

arXiv2022

Dynamic structure factor of the antiferromagnetic Kitaev model in large magnetic fields

We investigate the dynamic structure factor of the antiferromagnetic Kitaev honeycomb model in a magnetic field by applying perturbative continuous unitary transformations about the high-field limit. One- and two-quasiparticle properties of the dressed elementary spin-flip excitations of the high-field polarized phase are calculated which account for most of the spectral weight in the dynamic structure factor. We discuss the evolution of spectral features in these quasiparticle sectors in terms of one-quasiparticle dispersions, two-quasiparticle continua, the formation of antibound states, and quasiparticle decay. In particular, a comparably strong spectral feature above the upper edge of the upmost two-quasiparticle continuum represents three antibound states which form due to nearest-neighbor density-density interactions.

cond-mat.str-el↗

arXiv2020

Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field

The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field for the ferro- and antiferromagnetic case. While for the limiting case of the isotropic long-range XY model we can extract the elementary one quasi-particle dispersion analytically and calculate two quasi-particle excitation energies quantitatively in a numerical fashion, for the long-range Ising limit as well as in the intermediate regime we use perturbative continuous unitary transformations on white graphs in combination with classical Monte Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit. This enables us to determine the quantum-critical breakdown of the high-field polarized phase by analyzing the gap-closing including associated critical exponents and multiplicative logarithmic corrections. In addition, for the ferromagnetic isotropic XY model we determined the critical exponents $z$ and $ν$ analytically by a bosonic quantum-field theory.

cond-mat.str-el↗