arXiv subjects

Andreas Haller

Publications and source records attributed to Andreas Haller.

18 recordsLinked to original sources

arXiv2025

Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures

Motivated by recent observations of fractional Chern insulators (FCIs) in the vicinity of superconducting (SC) phases, we study fractional quantum (anomalous) Hall-superconductor heterostructures in the presence of $U(1)$ order-parameter fluctuations and particularly focus on the case of $\nu = 2/3$ quantum Hall states leading to $\mathbb Z_3$ parafermions. We first employ a phenomenological field theory to qualitatively determine the phase diagram. Furthermore, we generalize a previously established alternating pattern of superconductor and tunneling regions, coupled to fractional quantum Hall edge states, to map the problem onto a topological Josephson junction chain involving lattice parafermions. Using density matrix renormalization group simulations, we establish a phase diagram composed of Mott insulating phases and two different Luttinger liquids whose fundamental excitations carry charges 2e and $2e/3$, respectively. In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii-Kosterlitz-Thouless (BKT) type as well as a continuous $\mathbb Z_3 \times U(1)$ second-order phase transition characterized by central charge c = 9/5. We finally extract information about a possible ground state degeneracy and comment on the stability of parafermionic edge states in the presence of fluctuations. These theoretical foundations can be expected to be of practical importance for gate-defined FCI-SC heterostructures in moir\'e materials, in which broad superconducting transitions indicative of strong order parameter fluctuations were observed.

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arXiv2025

Regularized Micromagnetic Theory for Bloch Points

Magnetic singularities known as Bloch points (BPs) present a fundamental challenge for micromagnetic theory, which is based on the assumption of a fixed magnetization vector length. Due to the divergence of the effective field at a BP, classical micromagnetics fails to adequately describe BP dynamics. To address this issue, we propose a regularized micromagnetic model in which the magnetization vector can vary in length but not exceed a threshold value. More specifically, the magnetization is treated as an order parameter constrained to a S3-sphere. This constraint respects fundamental properties of local spin expectation values in quantum systems. We derive the corresponding regularized Landau-Lifshitz-Gilbert equation and the analogue of the Thiele equation describing the steady motion of spin textures under various external stimuli. We demonstrate the applicability of our theory by modeling the dynamics of several magnetic textures containing BPs, including domain walls in nanowires, chiral bobbers, and magnetic dipolar strings. The presented results extend micromagnetic theory by incorporating a regularized description of BP dynamics.

cond-mat.mes-hall↗

arXiv2025

Skyrmionic Schr\"odinger cat states in monoaxial chiral magnets

We study the low-energy excitation spectra of a spin-1/2 quantum Heisenberg model with a monoaxial Dzyaloshinskii-Moriya interaction. Using the density matrix renormalization group method, our analysis reveals a degeneracy between skyrmion and antiskyrmion states, enabling the formation of a mesoscopic Schr\"odinger cat state - a quantum superposition of these topologically distinct textures. To characterize this nontrivial state, we compute two-point spin correlation functions, highlighting signatures accessible via neutron scattering experiments. Furthermore, we demonstrate that applying a magnetic field gradient induces a coherent time evolution of the cat state, offering a controllable mechanism for its manipulation. These findings provide a framework for the detection of skyrmionic Schr\"odinger cat states in quantum magnets.

cond-mat.mes-hall↗

arXiv2025

Quantum geometry in the dynamics of band-projected operators

We study the dynamics of electrons in crystalline solids in the presence of inhomogeneous external electric and magnetic fields. We present a manifestly gauge-invariant operator-based approach without relying on a semiclassical wavepacket construction, and derive the field-induced corrections to the equations of motion at the operator level. This includes the Berry curvature induced anomalous velocity and contributions arising from the quantum geometry of the Bloch bands. We show explicitly how these multi-band effects are manifested in an effective single band approximation. We present a formalism that allows for a systematic expansion to an arbitrary order in the inhomogeneity of the applied fields, as well as a way to compute the matrix elements in Bloch basis.

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arXiv2025

Stability and Nucleation of Dipole Strings in Uniaxial Chiral Magnets

We report on the stability of the magnetic dipole string (DS), a three-dimensional magnetic texture formed by two coupled Bloch points with opposite topological charges, separated by an equilibrium distance. Previous studies demonstrated the stability of such configurations through geometric confinement or coupling with local perturbations in the magnetization field, such as skyrmion strings or dislocations in helical modulations. Here, we show that, in uniaxial chiral magnets, an isolated DS remains stable in an unperturbed vacuum, thus representing a true three-dimensional soliton. The phase diagram illustrates the stability of the DS embedded in the conical or helical phases across a broad range of material parameters and external magnetic fields. Using the geodesic nudged elastic band method applied to a regularized micromagnetic model, we demonstrate that isolated DSs are protected from collapse by an energy barrier. Stochastic spin-lattice simulations demonstrate that DSs can spontaneously nucleate during in-field annealing. This work aims to stimulate the experimental observation of DSs and further exploration of uniaxial chiral magnets.

cond-mat.mes-hall↗

arXiv2024

Quantum Skyrmion Liquid

Skyrmions are topological magnetic textures, mostly treated classically, studied extensively due to their potential spintronics applications due to their topological stability. However, it remains unclear what physical phenomena differentiate a classical from a quantum skyrmion. We present numerical evidence for the existence of a quantum skyrmion liquid (SkL) phase in quasi-one-dimensional lattices which has no classical counterpart. The transition from a conventional quantum skyrmion crystal (SkX) to a field-polarized phase (FP) is found to be of second order while the analogous classical transition near zero temperature is first-order due to a missing SkL phase. As an indicator of the quantum mechanical origin of the SkL phase, we find concentrated entanglement (indicated by the concurrence) around the skyrmion center, which we attribute to the uncertainty in the skyrmion position resulting from the non-commutativity of the skyrmion coordinate operators. The latter also gives rise to a nontrivial kinetic energy in the presence of an atomic lattice. The SkL phase emerges when the kinetic energy dominates over the skyrmion-skyrmion interaction energy. It is tied to the breaking of discrete translational invariance of the skyrmion crystal and occurs when the skyrmion radius is comparable with the size of the magnetic unit cell. In contrast to the long-range order present in the SkX phase, spin-spin correlations in the SkL phase exponentially decay with distance, indicating the fluid-like behavior of uncorrelated skyrmions. The emergence of kinetic energy-induced quantum SkL phase serves as a strong indication of the possible Bose-Einstein condensation of skyrmions in higher-dimensional systems. Our findings are effectively explained by microscopic theories like collective coordinate formalism and trial wave functions, effectively enhancing our understanding of the numerical findings.

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arXiv2024

Quantum and classical magnetic Bloch points

A Bloch point represents a three-dimensional hedgehog singularity of a magnetic vector field in which the magnetization vanishes. However, standard micromagnetic theory, developed for magnetic moments of fixed lengths, lacks full applicability in studying such singularities. To address this gap, we study a Bloch point in a quantum Heisenberg model for the case of spin-1/2 particles. Performing an exact diagonalization of the Hamiltonian as well as using density matrix renormalization group techniques, we obtain the ground state, which can be used to recover the corresponding magnetization profile. Our findings demonstrate a variation of the spin length in the quantum model, leading smoothly to zero magnetization at the Bloch point. Our results indicate the necessity of generalizing the classical micromagnetic model by adding the third degree of freedom of the spins: the ability to change its length. To this end, we introduce the micromagnetic $\mathbb{S}_{3}$-model, which enables the description of magnets with and without Bloch point singularities.

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arXiv2024

Quantum Magnetic Skyrmion Operator

We propose a variational wave function to represent quantum skyrmions as bosonic operators. The operator faithfully reproduces two fundamental features of quantum skyrmions: their classical magnetic order and a "quantum cloud" of local spin-flip excitations. Using exact numerical simulations of the ground states of a 2D chiral magnetic model, we find two regions in the single-skyrmion state diagram distinguished by their leading quantum corrections. We use matrix product state simulations of the adiabatic braiding of two skyrmions to verify that the operator representation of skyrmions is valid at large inter-skyrmion distances. Our work demonstrates that skyrmions can be approximately coarse-grained and represented by bosonic quasiparticles, which paves the way toward a field theory of many-skyrmion quantum phases and, unlike other approaches, incorporates the microscopic quantum fluctuations of individual skyrmions.

cond-mat.str-el↗

arXiv2023

Counting interacting electrons in one dimension

The calculation of the full counting statistics of the charge within a finite interval of an interacting one-dimensional system of electrons is a fundamental, yet as of now unresolved problem. Even in the non-interacting case, charge counting turns out to be more difficult than anticipated because it necessitates the calculation of a nontrivial determinant and requires regularization. Moreover, interactions in a one-dimensional system are best described using bosonization. However, this technique rests on a long-wavelength approximation and is a priori inapplicable for charge counting due to the sharp boundaries of the counting interval. To mitigate these problems, we investigate the counting statistics using several complementary approaches. To treat interactions, we develop a diagrammatic approach in the fermionic basis, which makes it possible to obtain the cumulant generating function up to arbitrary order in the interaction strength. Importantly, our formalism preserves charge quantization in every perturbative order. We derive an exact expression for the noise and analyze its interaction-dependent logarithmic cutoff. We compare our fermionic formalism with the results obtained by other methods, such as the Wigner crystal approach and numerical calculations using the density-matrix renormalization group. Surprisingly, we show good qualitative agreement with the Wigner crystal for weak interactions, where the latter is in principle not expected to apply.

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arXiv2023

Perfectly localized Majorana corner modes in fermionic lattices

Focusing on examples of Majorana zero modes on the corners of a two-dimensional lattice, we introduce a method to find parameter regions where the Majorana modes are perfectly localized on a single site. Such a limit allows us to study the dimerization structure of the sparse bulk Hamiltonian that results in the higher-order topology of the system. Furthermore, such limits typically provide an analytical understanding of the system energy scales. Based on the dimerization structure we extract from the two-dimensional model, we identify a more general stacking procedure to construct Majorana zero modes in arbitrary corners of a $d$-dimensional hypercube, which we demonstrate explicitly in $d\leq3$.

cond-mat.mes-hall↗

arXiv2022

Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals

We study electronic transport in Weyl semimetals with spatially varying nodal tilt profiles. We find that the flow of electrons can be guided precisely by judiciously chosen tilt profiles. In a broad regime of parameters, we show that electron flow is described well by semiclassical equations of motion similar to the ones governing gravitational attraction. This analogy provides a physically transparent tool for designing tiltronic devices like electronic lenses. The analogy to gravity circumvents the notoriously difficult full-fledged description of inhomogeneous solids. A comparison to microscopic lattice simulations shows that it is only valid for trajectories sufficiently far from analogue black holes. We finally comment on the Berry curvature-driven transverse motion and relate the latter to spin precession physics.

cond-mat.mes-hall↗

arXiv2022

Overlap of parafermionic zero modes at a finite distance

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 $\mathbb{Z}_{2n}$ 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.

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arXiv2021

Quantum Skyrmion Lattices in Heisenberg Ferromagnets

Skyrmions are topological magnetic textures that 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. Here, we simulate the ground states of two-dimensional spin-$1/2$ Heisenberg lattices with Dzyaloshinskii-Moriya interactions and discover a broad region in the zero-temperature phase diagram which hosts quantum skyrmion lattices. We argue that the quantum skyrmion lattice 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.

cond-mat.str-el↗

arXiv2021

Supersolid-Superfluid phase separation in the extended Bose-Hubbard model

Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling [1,2]. 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.

cond-mat.quant-gas↗

arXiv2021

Exploring helical phases of matter in bosonic ladders

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 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.

cond-mat.quant-gas↗

arXiv2020

Detecting topology through dynamics in interacting fermionic wires

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.

cond-mat.quant-gas↗

arXiv2019

Drude weight increase by orbital and repulsive interactions in fermionic ladders

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 non-interacting 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 counter-intuitively 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.

cond-mat.quant-gas↗

arXiv2019

Quantum criticality on a chiral ladder: an $SU(2)$ iDMRG study

In this paper we study the ground state properties of a ladder Hamiltonian with chiral $SU(2)$-invariant spin interactions, a possible first step towards the construction of truly two dimensional non-trivial 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 (iDMRG). 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.

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