[8] 
Teixeira, Raphael L. R. C. and Haller, Andreas and Singh, Roshni and Mathew, Amal and Idrisov, Edvin G. and da Silva, Luis G. G. V. Dias and Schmidt, Thomas L., Overlap of parafermionic zero modes at a finite distance, (2022)
Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zeroenergy 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 oneinstanton gas approximation and show how finitesize effects can give rise to higherorder parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finitesize corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems.

[7] 
Haller, Andreas and Groenendijk, Solofo and Habibi, Alireza and Michels, Andreas and Schmidt, Thomas L., Quantum Skyrmion Lattices in Heisenberg Ferromagnets, (2021)
Skyrmions are topological magnetic textures which can arise in noncentrosymmetric 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 twodimensional spin1/2 Heisenberg ferromagnets with DzyaloshinskiiMoriya 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 nonclassical state featuring entanglement between quasiparticle and environment mainly localized near the boundary spins of the skyrmion.

[6] 
Kottmann, Korbinian and Haller, Andreas and Acín, Antonio and Astrakharchik, Grigory E. and Lewenstein, Maciej, Supersolidsuperfluid phase separation in the extended BoseHubbard model, Phys. Rev. B 104, 174514 (2021)
Recent studies have suggested a new phase in the extended BoseHubbard model in one dimension at integer filling. In this work, we show that this new phase is phaseseparated 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 phaseseparated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and stringorder 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 lowenergy 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 onebody density matrix.

[5] 
Haller, Andreas and MatsoukasRoubeas, Apollonas S. and Pan, Yueting and Rizzi, Matteo and Burrello, Michele, Exploring helical phases of matter in bosonic ladders, Phys. Rev. Research 2, 043433 (2020)
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 onedimensional 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 twospecies hardcore bosons and onsite 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] 
Haller, Andreas and Massignan, Pietro and Rizzi, Matteo, Detecting topology through dynamics in interacting fermionic wires, Phys. Rev. Research 2, 033200 (2020)
We describe a protocol to read out the topological invariant of interacting 1D chiral models, based on measuring the mean chiral displacement of timeevolving bulk excitations. We present analytical calculations and numerical Matrix Product State simulations of interacting SuSchriefferHeeger (SSH) chains, demonstrating how the mean chiral displacement allows to distinguish between topological insulator, trivial insulator and symmetrybroken phases. Finally, we provide an experimental blueprint for realizing a model displaying these three phases and describe how to detect those.

[3] 
Haller, Andreas and Rizzi, Matteo and Filippone, Michele, Drude weight increase by orbital and repulsive interactions in fermionic ladders, Phys. Rev. Research 2, 023058 (2020)
In strictly onedimensional systems, repulsive interactions tend to reduce particle mobility on a lattice. Therefore, the Drude weight, controlling the divergence at zerofrequency of optical conductivities in perfect conductors, is lower than in noninteracting cases. We show that this is not the case when extending to quasionedimensional ladder systems. Relying on bosonization, perturbative and matrix product states (MPS) calculations, we show that nearestneighbor interactions and magnetic fluxes provide a bias between back and forwardscattering 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] 
Schmoll, Philipp and Haller, Andreas and Rizzi, Matteo and Orús, Román, Quantum criticality on a chiral ladder: An SU(2) infinite density matrix renormalization group study, Phys. Rev. B 99, 205121 (2019)
In this paper we study the groundstate properties of a ladder Hamiltonian with chiral SU(2)invariant spin interactions, a possible first step toward the construction of truly twodimensional nontrivial systems with chiral properties starting from quasionedimensional 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 smallsize 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 finiteentanglement scaling data show that the groundstate 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 spinspin and dimerdimer correlation functions, as well as the algebraic convergence of the groundstate 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 spin1/2 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 WessZuminoWitten theory. Moreover, we explain in detail how to construct matrix product operators for SU(2)invariant threespin interactions, something that had not been addressed with sufficient depth in the literature.

[1] 
Andreas Haller and Matteo Rizzi and Michele Burrello, The resonant state at filling factor ν = 1/2 in chiral fermionic ladders, New Journal of Physics 20, 053007 (2018)
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 onedimensional (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 quasi1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlinlike states.
