Coordinates
Department of Physics and Materials Science
Université du Luxembourg
162a, avenue de la Faïencerie
L-1511 Luxembourg
Luxembourg

Office: BRB 1.07
Tel: +352 46 66 44 6692
Email: andreas.haller@uni.lu
Research interests
Collective effects and emergent phases from interacting particles are fascinating topics that form one of the pillars of condensed matter theory. I find it particularly intriguing to study phenomena which are associated with topological concepts, e.g. the characterization of phases beyond the Landau paradigm by non-local order parameters. Nontrivial topological matter typically hosts low-energy states which feature a high level of robustness against external perturbations, e.g. random disorder and temperature. In my research, I strive to get a better understanding of the semiclassical and quantum mechanical properties of nanoscale devices hosting (topological) quasiparticles, such as Skyrmions, and exotic fractional bound modes, e.g. Majorana fermions or - generalizations thereof - parafermions. In non-interacting systems, topological invariants of many insulators and superconductors are derived from geometric quantities of the underlying band structure. These geometric terms influence the dynamics of wave packets in the material and give rise to countless examples of 'anomalous' behavior, e.g. the Hall effect. In a collaboration between members from TMQS and the quantum design group at the university of Dresden, I study the behavior of semiclassical wave packets in Weyl semimetals subject to a spatial modulation of the linear dispersion and the relation to trajectories in curved space-time.
Publications
[8]
Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying Z2n symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.
[7]
Skyrmions are topological magnetic textures which can arise in non-centrosymmetric ferromagnetic materials. In most systems experimentally investigated to date, skyrmions emerge as classical objects. However, the discovery of skyrmions with nanometer length scales has sparked interest in their quantum properties. Quantum corrections to the classical magnetic textures have already been considered in the semiclassical regime. Here, we go beyond this limit by investigating quantum skyrmions in the deep quantum regime. We use density matrix renormalization group techniques to study two-dimensional spin-1/2 Heisenberg ferromagnets with Dzyaloshinskii-Moriya interactions and discover a broad region in the zero temperature phase diagram which hosts quantum skyrmion lattice ground states. We argue that this novel quantum skyrmion phase can be detected experimentally in the magnetization profile via local magnetic polarization measurements as well as in the spin structure factor measurable via neutron scattering experiments. Finally, we explore the resulting quantum skyrmion state, analyze its real space polarization profile and show that it is a non-classical state featuring entanglement between quasiparticle and environment mainly localized near the boundary spins of the skyrmion.
[6]
Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitations of the homogeneous superfluid with enhanced periodic modulations are phonons, find the central charge to be c=1, and show that the velocity of sound, extracted from the intrinsic level splitting for finite systems, matches with the propagation velocity of local excitations in dynamical simulations. This suggests that the low-energy spectrum of the phase under investigation is effectively captured by a spinless Luttinger liquid, for which we find consistent results between the Luttinger parameter obtained from the linear dependence of the structure factor and the algebraic decay of the one-body density matrix.
[5]
Ladder models of ultracold atoms offer a versatile platform for the experimental and theoretical study of different phenomena and phases of matter linked to the interplay between artificial gauge fields and interactions. Strongly correlated helical states are known to appear for specific ratios of the particle and magnetic flux densities, and they can often be interpreted as a one-dimensional limit of fractional quantum Hall states, thus being called pretopological. Their signatures, however, are typically hard to observe due to the small gaps characterizing these states. Here we investigate bosonic ladder models at filling factor ν=1. Based on bosonization, renormalization group, and matrix product state simulations we pinpoint two strongly correlated helical phases appearing at this resonance. We show that one of them can be accessed in systems with two-species hardcore bosons and on-site repulsions only, thus amenable for optical lattice experiments. Its signatures are sizable and stable over a broad range of parameters for realistic system sizes.
[4]
We describe a protocol to read out the topological invariant of interacting 1D chiral models, based on measuring the mean chiral displacement of time-evolving bulk excitations. We present analytical calculations and numerical Matrix Product State simulations of interacting Su-Schrieffer-Heeger (SSH) chains, demonstrating how the mean chiral displacement allows to distinguish between topological insulator, trivial insulator and symmetry-broken phases. Finally, we provide an experimental blueprint for realizing a model displaying these three phases and describe how to detect those.
[3]
In strictly one-dimensional systems, repulsive interactions tend to reduce particle mobility on a lattice. Therefore, the Drude weight, controlling the divergence at zero-frequency of optical conductivities in perfect conductors, is lower than in noninteracting cases. We show that this is not the case when extending to quasi-one-dimensional ladder systems. Relying on bosonization, perturbative and matrix product states (MPS) calculations, we show that nearest-neighbor interactions and magnetic fluxes provide a bias between back- and forward-scattering processes, leading to linear corrections to the Drude weight in the interaction strength. As a consequence, Drude weights counterintuitively increase (decrease) with repulsive (attractive) interactions. Our findings are relevant for the efficient tuning of Drude weights in the framework of ultracold atoms trapped in optical lattices and equally affect topological edge states in condensed matter systems.
[2]
In this paper we study the ground-state properties of a ladder Hamiltonian with chiral SU(2)-invariant spin interactions, a possible first step toward the construction of truly two-dimensional nontrivial systems with chiral properties starting from quasi-one-dimensional ones. Our analysis uses a recent implementation by us of SU(2) symmetry in tensor network algorithms, specifically for infinite density matrix renormalization group. After a preliminary analysis with Kadanoff coarse graining and exact diagonalization for a small-size system, we discuss its bosonization and recap the continuum limit of the model to show that it corresponds to a conformal field theory, in agreement with our numerical findings. In particular, the scaling of the entanglement entropy as well as finite-entanglement scaling data show that the ground-state properties match those of the universality class of a c=1 conformal field theory (CFT) in (1+1) dimensions. We also study the algebraic decay of spin-spin and dimer-dimer correlation functions, as well as the algebraic convergence of the ground-state energy with the bond dimension, and the entanglement spectrum of half an infinite chain. Our results for the entanglement spectrum are remarkably similar to those of the spin-1/2 Heisenberg chain, which we take as a strong indication that both systems are described by the same CFT at low energies, i.e., an SU(2)_1 Wess-Zumino-Witten theory. Moreover, we explain in detail how to construct matrix product operators for SU(2)-invariant three-spin interactions, something that had not been addressed with sufficient depth in the literature.
[1]
Helical liquids have been experimentally realized in both nanowires and ultracold atomic chains as the result of strong spin–orbit interactions. In both cases the inner degrees of freedom can be considered as an additional space dimension, providing an interpretation of these systems as chiral synthetic ladders, with artificial magnetic fluxes determined by the spin–orbit terms. In this work, we characterize the helical state which appears at filling ν = 1/2: this state is generated by a gap arising in the spin sector of the corresponding Luttinger liquid and it can be interpreted as the one-dimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We study its main features, focusing on entanglement properties and correlation functions. The techniques developed here provide a key example for the study of similar quasi-1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlin-like states.
Scientific CV
After I finished my school education (German Abitur, 2011), I obtained my B.Sc. (2014), M.Sc. (2016), and PhD (2021) in theoretical physics at the Johannes Gutenberg University (Mainz, Germany) under supervision of Prof. Matteo Rizzi, Prof. Román Orús, Prof. Michele Burrello and Prof. Peter van Dongen. I investigated the effect of local interactions on static and dynamic properties in various 1D ladder systems.

My PhD position was funded by a scholarship of the Graduate School of Excellence Materials Science, and I later joined the interdisciplinary Max Planck Graduate Center (MPGC). Furthermore, I was awarded a travel grant of the COST AtomQT initiative (CA16221). After my PhD, graded summa cum laude, I joined the group of Prof. Thomas L. Schmidt at the University of Luxembourg.

You can click on the following URLs to download my B.Sc. and M.Sc. thesis. My PhD thesis contains copyright-restricted material, so I cannot share it openly here, but I am happy to send you a digital version upon request.