arXiv subjects

Titus Neupert

Publications and source records attributed to Titus Neupert.

At least 145 records · Page 8Linked to original sources

arXiv2019

Topolectrical circuit realization of topological corner modes

Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk spectral gap, reflection symmetries and a spectral symmetry. Here we introduce a topolectrical circuit design for realizing such corner modes experimentally and report measurements in which the modes appear as topological boundary resonances in the corner impedance profile of the circuit. Whereas the quantized bulk quadrupole moment of an electronic crystal does not have a direct analogue in the classical topolectrical-circuit framework, the corner modes inherit the identical form from the quantum case. Due to the flexibility and tunability of electrical circuits, they are an ideal platform for studying the reflection symmetry-protected character of corner modes in detail. Our work therefore establishes an instance where topolectrical circuitry is employed to bridge the gap between quantum theoretical modelling and the experimental realization of topological band structures.

cond-mat.mes-hall↗

arXiv2019

Atomic limit and inversion-symmetry indicators for topological superconductors

Symmetry indicators have proven to be extremely helpful in identifying topologically non-trivial crystalline insulators using symmetry-group representations of their Bloch states. An extension of this approach to superconducting systems requires defining an appropriate atomic limit for Bogoliubov-de-Gennes Hamiltonians. Here, we introduce such a notion of atomic limit and derive a $\mathbb{Z}_{2^d}$-valued symmetry indicator for inversion-symmetric superconductors of $d$ dimensions. This indicator allows for a refined topological classification including higher-order phases for systems in the superconducting symmetry classes D and DIII. We further elucidate the bulk-boundary correspondence of these phases using Dirac surface theories. Requiring only the normal-state band structure and the superconducting order-parameter symmetry as an input, this indicator is well suited for a search of topological superconductors using first-principles calculations.

cond-mat.supr-con↗

arXiv2019

Ground state degeneracy of non-Abelian topological phases from coupled wires

We construct a family of two-dimensional non-Abelian topological phases from coupled wires using a non-Abelian bosonization approach. We then demonstrate how to determine the nature of the non-Abelian topological order (in particular, the anyonic excitations and the topological degeneracy on the torus) realized in the resulting gapped phases of matter. This paper focuses on the detailed case study of a coupled-wire realization of the bosonic $su(2)^{\,}_{2}$ Moore-Read state, but the approach we outline here can be extended to general bosonic $su(2)^{\,}_{k}$ topological phases described by non-Abelian Chern-Simons theories. We also discuss possible generalizations of this approach to the construction of three-dimensional non-Abelian topological phases.

cond-mat.str-el↗

arXiv2019

Topological photocurrent responses from chiral surface Fermi arcs

The nonlinear optical responses from topological semimetals are crucial in both understanding the fundamental properties of quantum materials and designing next-generation light-sensors or solar-cells. However, previous work was focusing on the optical effects from bulk states only, disregarding topological surface responses. Here we propose a new (hitherto unknown) surface-only topological photocurrent response from chiral Fermi arcs. Using the ideal topological chiral semimetal RhSi as a representative, we quantitatively compute the topologically robust photocurrents from Fermi arcs on different surfaces. By rigorous crystal symmetry analysis, we demonstrate that Fermi arc photocurrents can be perpendicular to the bulk injection currents regardless of the choice of materials' surface. We then generalize this finding to all cubic chiral space groups and predict material candidates. Our theory reveals a powerful notion where common crystalline-symmetry can be used to induce universal topological responses as well as making it possible to completely disentangle bulk and surface topological responses in many conducting material families.

cond-mat.mes-hall↗

arXiv2019

Orbitally selective breakdown of Fermi liquid quasiparticles in Ca$_{1.8}$Sr$_{0.2}$RuO$_4$

We present a comprehensive angle-resolved photoemission spectroscopy study of Ca$_{1.8}$Sr$_{0.2}$RuO$_4$. Four distinct bands are revealed and along the Ru-O bond direction their orbital characters are identified through a light polarization analysis and comparison to dynamical mean-field theory calculations. Bands assigned to $d_{xz}, d_{yz}$ orbitals display Fermi liquid behavior with fourfold quasiparticle mass renormalization. Extremely heavy fermions - associated with a predominantly $d_{xy}$ band character - are shown to display non-Fermi-liquid behavior. We thus demonstrate that Ca$_{1.8}$Sr$_{0.2}$RuO$_4$ is a hybrid metal with an orbitally selective Fermi liquid quasiparticle breakdown.

cond-mat.str-el↗

arXiv2019

Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States

The use of artificial neural networks to represent quantum wave-functions has recently attracted interest as a way to solve complex many-body problems. The potential of these variational parameterizations has been supported by analytical and numerical evidence in controlled benchmarks. While approaching the end of the early research phase in this field, it becomes increasingly important to show how neural-network states perform for models and physical problems that constitute a clear open challenge for other many-body computational methods. In this paper we start addressing this aspect, concentrating on a presently unsolved model describing two-dimensional frustrated magnets. Using a fully convolutional neural network model as a variational ansatz, we study the frustrated spin-1/2 J1-J2 Heisenberg model on the square lattice. We demonstrate that the resulting predictions for both ground-state energies and properties are competitive with, and often improve upon, existing state-of-the-art methods. In a relatively small region in the parameter space, corresponding to the maximally frustrated regime, our ansatz exhibits comparatively good but not best performance. The gap between the complexity of the models adopted here and those routinely adopted in deep learning applications is, however, still substantial, such that further improvements in future generations of neural-network quantum states are likely to be expected.

cond-mat.str-el↗

arXiv2019

Negative flat band magnetism in a spin-orbit coupled correlated kagome magnet

It has long been speculated that electronic flat band systems can be a fertile ground for hosting novel emergent phenomena including unconventional magnetism and superconductivity. Although flat bands are known to exist in a few systems such as heavy fermion materials and twisted bilayer graphene, their microscopic roles and underlying mechanisms in generating emergent behavior remain elusive. Here we use scanning tunneling microscopy to elucidate the atomically resolved electronic states and their magnetic response in the kagome magnet Co3Sn2S2. We observe a pronounced peak at the Fermi level, which is identified to arise from the kinetically frustrated kagome flat band. Increasing magnetic field up to +-8T, this state exhibits an anomalous magnetization-polarized Zeeman shift, dominated by an orbital moment in opposite to the field direction. Such negative magnetism can be understood as spin-orbit coupling induced quantum phase effects tied to non-trivial flat band systems. We image the flat band peak, resolve the associated negative magnetism, and provide its connection to the Berry curvature field, showing that Co3Sn2S2 is a rare example of kagome magnet where the low energy physics can be dominated by the spin-orbit coupled flat band. Our methodology of probing band-resolved ordering phenomena such as spin-orbit magnetism can also be applied in future experiments to elucidate other exotic phenomena including flat band superconductivity and anomalous quantum transport.

cond-mat.mes-hall↗

arXiv2019

Topological many-body scar states in dimensions 1, 2, and 3

We propose an exact construction for atypical excited states of a class of non-integrable quantum many-body Hamiltonians in one dimension (1D), two dimensions (2D), and three dimensins (3D) that display area law entanglement entropy. These examples of many-body `scar' states have, by design, other properties, such as topological degeneracies, usually associated with the gapped ground states of symmetry protected topological phases or topologically ordered phases of matter.

cond-mat.other↗

arXiv2018

Neural Network-based Classification of Crystal Symmetries from X-Ray Diffraction Patterns

Machine learning algorithms based on artificial neural networks have proven very useful for a variety of classification problems. Here we apply them to a well-known problem in crystallography, namely the classification of X-ray diffraction patterns (XRD) of inorganic powder specimens by the respective crystal system and space group. Over 100 000 theoretically computed powder XRD patterns were obtained from inorganic crystal structure databases and used to train a deep dense neural network. For space group classification, we obtain an accuracy of around 54% on experimental data. Finally, we introduce a scheme where the network has the option to refuse the classification of XRD patterns that would be classified with a large uncertainty. This enhances the accuracy on experimental data to 82% at the expense of having half of the experimental data unclassified. With further improvements of neural network architecture and experimental data availability, machine learning constitutes a promising complement to classical structure determination methodology.

cond-mat.dis-nn↗

arXiv2018

Many-body localization and delocalization in large quantum chains

We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to $L=100$ spins, i.e., much larger than $L \simeq 20$ that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent $β$ which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent $β_Λ$ which characterizes the decay of a Schmidt gap in the entanglement spectrum, (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder $W_c$ that separates the ergodic and many-body localized regimes, compared to the values of $W_c$ in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents $β$ and $β_Λ$ increase, with increasing $L$, for relatively small $L$ but saturate for $L \simeq 50$, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the "learning by confusion" machine learning approach that can determine $W_c$.

cond-mat.dis-nn↗

arXiv2018

Custodial glide symmetry of quantum spin Hall edge modes in WTe$_2$ monolayer

A monolayer of WTe$_2$ has been shown to display quantum spin Hall (QSH) edge modes persisting up to 100~K in transport experiments. Based on density-functional theory calculations and symmetry-based model building including the role of correlations and substrate support, we develop an effective electronic model for WTe$_2$ which fundamentally differs from other prototypical QSH settings: we find that the extraordinary robustness of quantum spin Hall edge modes in WTe$_2$ roots in a glide symmetry due to which the topological gap opens away from high-symmetry points in momentum space. While the indirect bulk gap is much smaller, the glide symmetry implies a large direct gap of up to 1~eV in the Brillouin zone region of the dispersing edge modes, and hence enables sharply boundary-localized QSH edge states depending on the specific boundary orientation.

cond-mat.mes-hall↗

arXiv2018

Topological quantum properties of chiral crystals

Chiral crystals are materials whose lattice structure has a well-defined handedness due to the lack of inversion, mirror, or other roto-inversion symmetries. These crystals represent a broad, important class of quantum materials; their structural chirality has been found to allow for a wide range of phenomena in condensed matter physics, including skyrmions in chiral magnets, unconventional pairing in chiral superconductors, nonlocal transport and unique magnetoelectric effects in chiral metals, as well as enantioselective photoresponse. Nevertheless, while these phenomena have been intensely investigated, the topological electronic properties of chiral crystals have still remained largely uncharacterized. While recent theoretical advances have shown that the presence of crystalline symmetries can protect novel band crossings in 2D and 3D systems, we present a new class of Weyl fermions enforced by the absence of particular crystal symmetries. These "Kramers-Weyl" fermions are a universal topological electronic property of all nonmagnetic chiral crystals with spin-orbit coupling (SOC); they are guaranteed by lattice translation, structural chirality, and time-reversal symmetry, and unlike conventional Weyl fermions, appear at time-reversal-invariant momenta (TRIMs). We cement this finding by identifying representative chiral materials in the majority of the 65 chiral space groups in which Kramers-Weyl fermions are relevant to low-energy physics. By combining our analysis with the results of previous works, we determine that all point-like nodal degeneracies in nonmagnetic chiral crystals with relevant SOC carry nontrivial Chern numbers. We further show that, beyond the previous phenomena allowed by structural chirality, Kramers-Weyl fermions enable unusual phenomena, such as a novel electron spin texture, chiral bulk Fermi surfaces over large energy windows.

cond-mat.mes-hall↗

arXiv2018

Higher order symmetry-protected topological states for interacting bosons and fermions

Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges. Here, we explore symmetry protected topological phases in strongly interacting many-body systems with this generalized bulk-boundary correspondence. We introduce several exactly solvable bosonic lattice models as candidates for interacting higher order symmetry protected topological (HOSPT) phases protected by spatial symmetries, and develop a topological field theory that captures the non-trivial nature of the gapless corner and hinge modes. We show how, for rotational symmetry, this field theory leads to a natural relationship between HOSPT phases and conventional SPT phases with an enlarged internal symmetry group. We also explore the connection between bosonic and fermionic HOSPT phases in the presence of strong interactions, and comment on the implications of this connection for the classification of interacting fermionic HOSPT phases. Finally, we explore how gauging internal symmetries of these phases leads to topological orders characterized by nontrivial braiding statistics between topological vortex excitations and geometrical defects related to the spatial symmetry.

cond-mat.str-el↗

arXiv2018

Symmetries and many-body excited states with neural-network quantum states

Artificial neural networks have been recently introduced as a general ansatz to compactly represent many- body wave functions. In conjunction with Variational Monte Carlo, this ansatz has been applied to find Hamil- tonian ground states and their energies. Here we provide extensions of this method to study properties of ex- cited states, a central task in several many-body quantum calculations. First, we give a prescription that allows to target eigenstates of a (nonlocal) symmetry of the Hamiltonian. Second, we give an algorithm that allows to compute low-lying excited states without symmetries. We demonstrate our approach with both Restricted Boltzmann machines states and feedforward neural networks as variational wave-functions. Results are shown for the one-dimensional spin-1/2 Heisenberg model, and for the one-dimensional Bose-Hubbard model. When comparing to available exact results, we obtain good agreement for a large range of excited-states energies. Interestingly, we also find that deep networks typically outperform shallow architectures for high-energy states.

cond-mat.str-el↗

arXiv2018

Topology in the Sierpiński-Hofstadter problem

Using the Sierpiński carpet and gasket, we investigate whether fractal lattices embedded in two-dimensional space can support topological phases when subjected to a homogeneous external magnetic field. To this end, we study the localization property of eigenstates, the Chern number, and the evolution of energy level statistics when disorder is introduced. Combining these theoretical tools, we identify regions in the phase diagram of both the carpet and the gasket, for which the systems exhibit properties normally associated to gapless topological phases with a mobility edge.

cond-mat.mes-hall↗

arXiv2018

Higher-Order Topological Insulators

Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. Their topological character is protected by spatio-temporal symmetries, of which we present two cases: (1) Chiral higher-order topological insulators protected by the combination of time-reversal and a four-fold rotation symmetry. Their hinge states are chiral modes and the bulk topology is $\mathbb{Z}_2$-classified. (2) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs and the bulk topology is $\mathbb{Z}$-classified. We provide the topological invariants for both cases. Furthermore we show that SnTe as well as surface-modified Bi$_2$TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.

cond-mat.mes-hall↗

arXiv2018

Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter

We study the entanglement entropy of gapped phases of matter in three spatial dimensions. We focus in particular on size-independent contributions to the entropy across entanglement surfaces of arbitrary topologies. We show that for low energy fixed-point theories, the constant part of the entanglement entropy across any surface can be reduced to a linear combination of the entropies across a sphere and a torus. We first derive our results using strong sub-additivity inequalities along with assumptions about the entanglement entropy of fixed-point models, and identify the topological contribution by considering the renormalization group flow; in this way we give an explicit definition of topological entanglement entropy $S_{\mathrm{topo}}$ in (3+1)D, which sharpens previous results. We illustrate our results using several concrete examples and independent calculations, and show adding "twist" terms to the Lagrangian can change $S_{\mathrm{topo}}$ in (3+1)D. For the generalized Walker-Wang models, we find that the ground state degeneracy on a 3-torus is given by $\exp(-3S_{\mathrm{topo}}[T^2])$ in terms of the topological entanglement entropy across a 2-torus. We conjecture that a similar relationship holds for Abelian theories in $(d+1)$ dimensional spacetime, with the ground state degeneracy on the $d$-torus given by $\exp(-dS_{\mathrm{topo}}[T^{d-1}])$.

cond-mat.str-el↗

arXiv2018

Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer

Entanglement properties are routinely used to characterize phases of quantum matter in theoretical computations. For example the spectrum of the reduced density matrix, or so-called "entanglement spectrum", has become a widely used diagnostic for universal topological properties of quantum phases. However, while being convenient to calculate theoretically, it is notoriously hard to measure in experiments. Here we use the IBM quantum computer to make the first ever measurement of the entanglement spectrum of a symmetry-protected topological state. We are able to distinguish its entanglement spectrum from those we measure for trivial and long-range ordered states.

cond-mat.mes-hall↗