arXiv subjects

Titus Neupert

Publications and source records attributed to Titus Neupert.

At least 109 records · Page 6Linked to original sources

arXiv2021

Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4\times 4^3$ and $4 \times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin-liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

cond-mat.str-el↗

arXiv2021

Topological Materials Discovery from Crystal Symmetry

Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline insulators (TCIs), and 3D topological semimetals (TSMs). Most recently, through complete analyses of symmetry-allowed band structures - including the theory of Topological Quantum Chemistry (TQC) - researchers have determined crystal-symmetry-enhanced Wilson-loop and complete symmetry-based indicators for nonmagnetic topological phases, leading to the discovery of higher-order TCIs and TSMs. The recent application of TQC and related methods to high-throughput materials discovery has revealed that over half of all of the known stoichiometric, solid-state, nonmagnetic materials are topological at the Fermi level, over 85% of the known stoichiometric materials host energetically isolated topological bands, and that just under $2/3$ of the energetically isolated bands in known materials carry the stable topology of a TI or TCI. In this Review, we survey topological electronic materials discovery in nonmagnetic crystalline solids from the prediction of the first 2D and 3D TIs to the recently introduced methods that have facilitated large-scale searches for topological materials. We also discuss future venues for the identification and manipulation of solid-state topological phases, including charge-density-wave compounds, magnetic materials, and 2D few-layer devices.

cond-mat.mtrl-sci↗

arXiv2021

Neural Network Evolution Strategy for Solving Quantum Sign Structures

Feed-forward neural networks are a novel class of variational wave functions for correlated many-body quantum systems. Here, we propose a specific neural network ansatz suitable for systems with real-valued wave functions. Its characteristic is to encode the all-important rugged sign structure of a quantum wave function in a convolutional neural network with discrete output. Its training is achieved through an evolutionary algorithm. We test our variational ansatz and training strategy on two spin-1/2 Heisenberg models, one on the two-dimensional square lattice and one on the three-dimensional pyrochlore lattice. In the former, our ansatz converges with high accuracy to the analytically known sign structures of ordered phases. In the latter, where such sign structures are a priory unknown, we obtain better variational energies than with other neural network states. Our results demonstrate the utility of discrete neural networks to solve quantum many-body problems.

cond-mat.str-el↗

arXiv2021

Exceptional Topological Insulators

We introduce the exceptional topological insulator (ETI), a non-Hermitian topological state of matter that features exotic non-Hermitian surface states which can only exist within the three-dimensional topological bulk embedding. We show how this phase can evolve from a Weyl semimetal or Hermitian three-dimensional topological insulator close to criticality when quasiparticles acquire a finite lifetime. The ETI does not require any symmetry to be stabilized. It is characterized by a bulk energy point gap, and exhibits robust surface states that cover the bulk gap as a single sheet of complex eigenvalues or with a single exceptional point. The ETI can be induced universally in gapless solid-state systems, thereby setting a paradigm for non-Hermitian topological matter.

cond-mat.mes-hall↗

arXiv2021

Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model

The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In particular, fractional Chern insulators in bands with Chern number $|C|>1$ can demonstrate richer physical properties than continuum Landau level states and have recently been detected in experiments. Motivated by this, we examine the stability of fractional Chern insulators with higher Chern number in the Hofstadter model, using large-scale infinite density matrix renormalization group simulations on a thin cylinder. We confirm the existence of fractional states in bands with Chern numbers $C=1,2,3,4,5$ at the filling fractions predicted by the generalized Jain series [Phys. Rev. Lett. 115, 126401 (2015)]. Moreover, we discuss their metal-to-insulator phase transitions, as well as the subtleties in distinguishing between physical and numerical stability. Finally, we comment on the relative suitability of fractional Chern insulators in higher Chern number bands for proposed modern applications.

cond-mat.str-el↗

arXiv2021

$N$-band Hopf insulator

We study the generalization of the three-dimensional two-band Hopf insulator to the case of many bands, where all the bands are separated from each other by band gaps. The obtained $\mathbb{Z}$ classification of such a $N$-band Hopf insulator is related to the quantized isotropic magnetoelectric coefficient of its bulk. The boundary of a $N$-band Hopf insulator can be fully gapped, and we find that there is no unique way of dividing a finite system into bulk and boundary. Despite this non-uniqueness, we find that the magnetoelectric coefficient of the bulk and the anomalous Hall conductivity of the boundary are quantized to the same integer value. We propose an experiment where the quantized boundary effect can be measured in a non-equilibrium state.

cond-mat.mes-hall↗

arXiv2021

Multicellularity of delicate topological insulators

Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the method of symmetry-based indicators. Despite having a symmetric, exponentially-localized Wannier representation, each Wannier function cannot be completely localized to a single primitive unit cell in the bulk. Such multicellular topology is shown to be neither stable, nor fragile, but delicate, i.e., the topology can be nullified by adding trivial bands to either valence or conduction band.

cond-mat.mes-hall↗

arXiv2021

Discovery of unconventional chiral charge order in kagome superconductor KV3Sb5

Intertwining quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional charge order in a kagome material KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2x2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2x2 charge modulation exhibits an intensity reversal in real-space, signaling charge ordering. At impurity-pinning free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral CDW in the frustrated kagome lattice, which can not only lead to large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.

cond-mat.supr-con↗

arXiv2021

Lecture Notes on Topological Crystalline Insulators

We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like mirror or rotational symmetries. To deduce the topological properties, we use non-Abelian Wilson loops. We also discuss in detail higher-order topological insulators with hinge and corner states, and in particular present interacting bosonic models for the latter class of systems.

cond-mat.mes-hall↗

arXiv2021

Simulating a ring-like Hubbard system with a quantum computer

We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed. We locate this transition and solve for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer. Our results are enabled by a variational ansatz that takes full advantage of the maximal set of commuting $\mathbb{Z}_2$ symmetries of the problem and a Lanczos-inspired error mitigation algorithm. They are a benchmark on the way to exploiting near term quantum simulators for quantum many-body problems.

quant-ph↗

arXiv2021

Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures

We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological invariants. In particular, we express the three-dimensional winding number of point-gapped non-Hermitian systems, which is defined as an integral over the whole Brillouin zone, in terms of symmetry eigenvalues at high-symmetry momenta. Furthermore, for time-reversal symmetric non-Hermitian topological insulators, we find that symmetry indicators characterize the associated Chern-Simons form, whose evaluation usually requires a computationally expensive choice of smooth gauge. In each case, we discuss the non-Hermitian surface states associated with nontrivial symmetry indicators.

cond-mat.mes-hall↗

arXiv2021

Abelian topological order of $ν=2/5$ and $3/7$ fractional quantum Hall states in lattice models

Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the topological entanglement entropy as an indicator of Abelian statistics to investigate the single-component $ν=2/5$ and $3/7$ states for the Hofstadter model in the band mixing regime. We perform many-body simulations using the infinite cylinder density matrix renormalization group and present an efficient algorithm to construct the area law of entanglement, which accounts for both numerical and statistical errors. Using this algorithm, we show that the $ν=2/5$ and $3/7$ states exhibit Abelian topological order in the case of two-body nearest-neighbor interactions. Moreover, we discuss the sensitivity of the proposed method and fractional quantum Hall states with respect to interaction range and strength.

cond-mat.str-el↗

arXiv2021

Hamiltonian reconstruction as metric for variational studies

Variational approaches are among the most powerful modern techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in variational quantum eigensolvers. However, self-consistent evaluation of the quality of variational wavefunctions is a notoriously hard task. Using a recently developed Hamiltonian reconstruction method, we propose a multi-faceted approach to evaluating the quality of neural-network based wavefunctions. Specifically, we consider convolutional neural network (CNN) and restricted Boltzmann machine (RBM) states trained on a square lattice spin-1/2 $J_1$-$J_2$ Heisenberg model. We find that the reconstructed Hamiltonians are typically less frustrated, and have easy-axis anisotropy near the high frustration point. Furthermore, the reconstructed Hamiltonians suppress quantum fluctuations in the large $J_2$ limit. Our results highlight the critical importance of the wavefunction's symmetry. Moreover, the multi-faceted insight from the Hamiltonian reconstruction reveals that a variational wave function can fail to capture the true ground state through suppression of quantum fluctuations.

cond-mat.str-el↗

arXiv2021

Flat bands with fragile topology through superlattice engineering on single-layer graphene

'Magic'-angle twisted bilayer graphene has received a lot of interest due to its flat bands with potentially non-trivial topology that lead to intricate correlated phases. A spectrum with flat bands, however, does not require a twist between multiple sheets of van der Waals materials, but rather can be realized with the application of an appropriate periodic potential. Here, we propose the imposition of a tailored periodic potential onto a single graphene layer through local perturbations that could be created via lithography or adatom manipulation, which also results in an energy spectrum featuring flat bands. Our first-principle calculations for an appropriate decoration of graphene with adatoms indeed show the presence of flat bands in the spectrum. Furthermore, we reveal the topological nature of the flat bands through a symmetry-indicator analysis. This non-trivial topology manifests itself in corner-localized states with a filling anomaly as we show using a tight-binding model. Our proposal of a single decorated graphene sheet provides a new versatile route to study correlated phases in topologically non-trivial, flat band structures.

cond-mat.mes-hall↗

arXiv2021

Towards a Topological Quantum Chemistry description of correlated systems: the case of the Hubbard diamond chain

The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal topological properties of all possible band insulators in all space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between the mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems-which can be described within band theory. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topological phases which are not adiabatically connected to any band insulator. In this work we address the many facettes of this question by considering the specific example of a Hubbard diamond chain. This model features a Mott insulator, a trivial insulating phase and an obstructed atomic limit phase. Here we discuss the nature of the Mott insulator and determine the phase diagram and topology of the interacting model with infinite density matrix renormalization group calculations, variational Monte Carlo simulations and with many-body topological invariants. We then proceed by considering a generalization of the TQC formalism to Green's functions combined with the concept of topological Hamiltonian to identify the topological nature of the phases, using cluster perturbation theory to calculate the Green's functions. The results are benchmarked with the above determined phase diagram and we discuss the applicability and limitations of the approach and its possible extensions.

cond-mat.str-el↗

arXiv2020

Efficient Learning of a One-dimensional Density Functional Theory

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result---energy and charge density distribution of the ground state---is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.

cond-mat.dis-nn↗

arXiv2020

IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures

We present IrRep - a Python code that calculates the symmetry eigenvalues of electronic Bloch states in crystalline solids and the irreducible representations under which they transform. As input it receives bandstructures computed with state-of-the-art Density Functional Theory codes such as VASP, Quantum Espresso, or Abinit, as well as any other code that has an interface to Wannier90. Our code is applicable to materials in any of the 230 space groups and double groups preserving time-reversal symmetry with or without spin-orbit coupling included, for primitive or conventional unit cells. This makes IrRep a powerful tool to systematically analyze the connectivity and topological classification of bands, as well as to detect insulators with non-trivial topology, following the Topological Quantum Chemistry formalism: IrRep can generate the input files needed to calculate the (physical) elementary band representations and the symmetry-based indicators using the CheckTopologicalMat routine of the Bilbao Crystallographic Server. It is also particularly suitable for interfaces with other plane-waves based codes, due to its flexible structure.

cond-mat.mtrl-sci↗

arXiv2020

Non-Abelian chiral spin liquid on a simple non-Archimedean lattice

We extend the scope of Kitaev spin liquids to non-Archimedean lattices. For the pentaheptite lattice, which results from the proliferation of Stone-Wales defects on the honeycomb lattice, we find an exactly solvable non-Abelian chiral spin liquid with spontaneous time reversal symmetry breaking due to lattice loops of odd length. Our findings call for potential extensions of exact results for Kitaev models which are based on reflection positivity, which is not fulfilled by the pentaheptite lattice. We further elaborate on potential realizations of our chiral spin liquid proposal in strained $α$-RuCl$_3$.

cond-mat.str-el↗