arXiv subjects

Dániel Varjas

Publications and source records attributed to Dániel Varjas.

14 recordsLinked to original sources

arXiv2026

The geometry of the Hermitian matrix space and the Schrieffer--Wolff transformation

In quantum mechanics, the Schrieffer--Wolff (SW) transformation (also called quasi-degenerate perturbation theory) is known as an approximative method to reduce the dimension of the Hamiltonian. We present a geometric interpretation of the SW transformation: We prove that it induces a local coordinate chart in the space of Hermitian matrices near a $k$-fold degeneracy submanifold. Inspired by this result, we establish a `distance theorem': we show that the standard deviation of $k$ neighboring eigenvalues of a Hamiltonian equals the distance of this Hamiltonian from the corresponding $k$-fold degeneracy submanifold, divided by $\sqrt{k}$. Furthermore, we investigate one-parameter perturbations of a degenerate Hamiltonian, and prove that the standard deviation and the pairwise differences of the eigenvalues lead to the same order of splitting of the energy eigenvalues, which in turn is the same as the order of distancing from the degeneracy submanifold. As applications, we prove the `protection' of Weyl points using the transversality theorem, and infer geometrical properties of certain degeneracy submanifolds based on results from quantum error correction and topological order.

quant-ph↗

arXiv2026

AKLT Hamiltonian from Hubbard tripods

We investigate how the spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) Hamiltonian can emerge from a microscopic fermionic model based on half-filled Hubbard tripods. We first show that a single tripod hosts a robust threefold-degenerate low-energy manifold corresponding to an effective $S = 1$ degree of freedom. This manifold prevails over a broad range of interactions and remains stable against moderate disorder. We then combine exact diagonalization with fourth-order quasi-degenerate perturbation theory to derive an effective bilinear-biquadratic spin model for a pair of coupled tripods and identify coupling regimes where the target ratio is approached. In particular, tuning leg-center hopping together with two symmetry-inequivalent leg-leg hoppings yields the characteristic singlet-triplet degeneracy associated with a biquadratic-to-bilinear ratio close to 1/3. Extending the analysis to three tripods, we compare nonequivalent coupling geometries and find a strategy that suppresses unwanted longer-range and multispin terms while preserving the target nearest-neighbor couplings in the weak-coupling regime. These results establish a concrete bottom-up route from Hubbard clusters to valence-bond-solid spin physics in tunable quantum-dot arrays.

cond-mat.str-el↗

arXiv2026

Fermi surface and topology of multiband superconductor BeAu

The chiral material BeAu was recently identified as a multiband type-I superconductor with a critical temperature of 3.2 K. As a member of the B20 crystal family (space group $P2_13$), its band structure hosts multifold fermions at high-symmetry points, unpaired Weyl points and even nodal surfaces. This renders BeAu an appealing system to investigate the interplay between superconductivity and topology. Here we present a comprehensive first-principles analysis of BeAu's electronic structure focusing on its Fermi surface's topology and the implications for superconductivity. Together with the presence of four- and six-fold fermions at high-symmetry points, we identify several additional isolated Weyl points near the Fermi level. We also determine the associated topological edge states -- the surface Fermi arcs. Computing the Chern number associated to different Fermi surface sheets, we show that BeAu harbors a $ν= 4$ topological superconducting phase in the presence of $s$-wave pairing of alternating sign ($s_\pm$ pairing). Notably, we also identify a Fermi surface with a Chern number of +6; the highest value reported to date. Finally, our analysis reveals strong inhomogeneity in the orbital character of electronic states at the Fermi level, suggesting a link to the observed multigap superconductivity.

cond-mat.supr-con↗

arXiv2025

Effective Hamiltonians for Ge/Si core/shell nanowires from higher order perturbation theory

We theoretically explore the electronic structure of holes in cylindrical Germanium/Silicon core/shell nanowires using a perturbation theory approach. The approach yields a set of interpretable and transferable effective low-energy models for the lowest few sub-bands up to fifth order for experimentally relevant growth directions. In particular, we are able to resolve higher order cross terms e.g., the dependency of the effective mass on the magnetic field. Our study reveals orbital inversions of the lowest sub-bands for low-symmetry growth directions, leading to significant changes of the lower order effective coefficients. We demonstrate a reduction of the direct Rashba spin-orbit interaction due to competing symmetry effects for low-symmetry growth directions. Finally, we find that the effective mass of the confined holes can diverge yielding quasi flat bands interesting for correlated states. We show how one can tune the effective mass of a single spin band allowing one to tune the effective mass selectively to its divergent points.

cond-mat.mes-hall↗

arXiv2025

Non-unitary Time Evolution via the Chebyshev Expansion Method

The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion method extends well beyond this constraint: It remains valid across the entire complex plane and is thus suitable for arbitrary non-Hermitian matrices. We identify that numerical rounding errors are the primary source of errors encountered when applying the method outside the conventional spectral bounds, and they are not caused by fundamental limitations. By carefully selecting the spectral radius and the time step, we show how these errors can be effectively suppressed, enabling accurate time evolution calculations in non-Hermitian systems. We derive an analytic upper bound for the rounding error, which serves as a practical guideline for selecting time steps in numerical simulations. As an application, we illustrate the performance of the method by computing the time evolution of wave packets in the Hatano-Nelson model.

cond-mat.mes-hall↗

arXiv2025

Birth Quota of Non-Generic Degeneracy Points

Weyl points are generic and stable features in the energy spectrum of Hamiltonians that depend on a three-dimensional parameter space. Non-generic isolated two-fold degeneracy points, such as multi-Weyl points, split into Weyl points upon a generic perturbation that removes the fine-tuning or protecting symmetry. The number of the resulting Weyl points is at least $|Q|$, where $Q$ is the topological charge associated to the non-generic degeneracy point. Here, we show that such a non-generic degeneracy point also has a birth quota, i.e., a maximum number of Weyl points that can be born from it upon any perturbation. The birth quota is a local multiplicity associated to the non-generic degeneracy point, an invariant of map germs known from singularity theory. This holds not only for the case of a three-dimensional parameter space with a Hermitian Hamiltonian, but also for the case of a two-dimensional parameter space with a chiral-symmetric Hamiltonian. We illustrate the power of this result for band structures of two- and three-dimensional crystals. Our work establishes a strong and powerful connection between singularity theory and topological band structures, and more broadly, parameter-dependent quantum systems.

cond-mat.mes-hall↗

arXiv2025

Multifold degeneracy points of quantum systems and singularities of matrix varieties

Parameter-dependent quantum systems often exhibit energy degeneracy points, whose comprehensive description naturally lead to the application of methods from singularity theory. A prime example is an electronic band structure where two energy levels coincide in a point of momentum space. It may happen, and this case is the focus of our work, that three or more levels coincide at a parameter point, called multifold degeneracy. Upon a generic perturbation, such a multifold degeneracy point is dissolved into a set of Weyl points, that is, generic two-fold degeneracy points. In this work, we provide an upper bound to the number of Weyl points born from the multifold degeneracy point. To compute this upper bound, we describe the geometric degeneracy variety in the space of complex matrices. We compute its multiplicity at certain singular points corresponding to a multifold degeneracy, and the multiplicity of holomorphic map germs with respect to this variety. Our work covers physics and mathematics aspects in detail, and attempts to bridge the two disciplines and communities. For self-containedness, we survey examples of multi-fold degeneracies in quantum systems and condensed-matter physics, as well as the established tools of local algebraic geometry that we use to identify the upper bound.

math-ph↗

arXiv2024

Stability of Weyl node merging processes under symmetry constraints

Changes in the number of Weyl nodes in Weyl semimetals occur through merging processes, usually involving a pair of oppositely charged nodes. More complicated processes involving multiple Weyl nodes are also possible, but they typically require fine tuning and are thus less stable. In this work, we study how symmetries affect the allowed merging processes and their stability, focusing on the combination of a two-fold rotation and time-reversal ($C_2\mathcal{T}$) symmetry. We find that, counter-intuitively, processes involving a merging of three nodes are more generic than processes involving only two nodes. Our work suggests that multi-Weyl-merging may be observed in a large variety of quantum materials, and we discuss SrSi$_2$ and bilayer graphene as potential candidates

cond-mat.mes-hall↗

arXiv2023

Robust quantisation of circular photogalvanic effect in multiplicative topological semimetals

Nonlinear response signatures are increasingly recognized as useful probes of condensed matter systems, in particular for characterisation of topologically non-trivial states. The circular photogalvanic effect (CPGE) is particularly useful in study of topological semimetals, as the CPGE tensor quantises for well-isolated topological degeneracies in strictly linearly-dispersing band structures. Here, we study multiplicative Weyl semimetal band-structures, and find that the multiplicative structure robustly protects the quantization of the CPGE even in the case of non-linear dispersion. Computing phase diagrams as a function of Weyl node tilting, we find a variety of quantised values for the CPGE tensor, revealing that the CPGE is also a useful tool in detecting and characterising parent topology of multiplicative topological states.

cond-mat.mes-hall↗

arXiv2023

Structural spillage: an efficient method to identify non-crystalline topological materials

While topological materials are not restricted to crystals, there is no efficient method to diagnose topology in non-crystalline solids such as amorphous materials. Here we introduce the structural spillage, a new indicator that predicts the unknown topological phase of a non-crystalline solid, which is compatible with first-principles calculations. We illustrate its potential with tight-binding and first-principles calculations of amorphous bismuth, predicting a bilayer to be a new topologically nontrivial material. Our work opens up the efficient prediction of non-crystalline solids via first-principles and high-throughput searches.

cond-mat.mes-hall↗

arXiv2022

Weyl-point teleportation

In this work, we describe the phenomenon of Weyl-point teleportation. Weyl points usually move continuously in the configuration parameter space of a quantum system when the control parameters are varied continuously. However, there are special transition points in the control space where the continuous motion of the Weyl points is disrupted. In such transition points, an extended nodal structure (nodal line or nodal surface) emerges, serving as a wormhole for the Weyl points, allowing their teleportation in the configuration space. A characteristic side effect of the teleportation is that the motional susceptibility of the Weyl point diverges in the vicinity of the transition point, and this divergence is characterized by a universal scaling law. We exemplify these effects via a two-spin model and a Weyl Josephson circuit model. We expect that these effects generalize to many other settings including electronic band structures of topological semimetals.

cond-mat.mes-hall↗

arXiv2022

Obstructed insulators and flat bands in topological phase-change materials

Phase-change materials are ubiquitous in technology because of their ability to transition between amorphous and crystalline phases fast and reversibly, upon shining light or passing a current. Here we argue that to fully understand their electronic properties it is necessary to define a novel electronic phase: the amorphous obstructed insulator. It differs from an obstructed insulator crystal in that it presents localized edge or surface states irrespective of the sample termination. Consequently, we show that obstructed amorphous insulators in three-dimensions host a surface two-dimensional flat band, detectable using ARPES. Our work establishes basic models for materials where topological and obstructed properties can be switched on and off externally, including two-dimensional surface flatbands.

cond-mat.mes-hall↗

arXiv2020

Topological charge distributions of an interacting two-spin system

Quantum systems are often described by parameter-dependent Hamiltonians. Points in parameter space where two levels are degenerate can carry a topological charge. Here we theoretically study an interacting two-spin system where the degeneracy points form a nodal loop or a nodal surface in the magnetic parameter space, similarly to such structures discovered in the band structure of topological semimetals. We determine the topological charge distribution along these degeneracy geometries. We show that these non-point-like degeneracy patterns can be obtained not only by fine-tuning, but they can be stabilized by spatial symmetries. Since simple spin systems such as the one studied here are ubiquitous in condensed-matter setups, we expect that our findings, and the physical consequences of these nontrivial degeneracy geometries, are testable in experiments with quantum dots, molecular magnets, and adatoms on metallic surfaces.

cond-mat.mes-hall↗

arXiv2017

Orbital contributions to the electron g-factor in semiconductor nanowires

Recent experiments on Majorana fermions in semiconductor nanowires [Albrecht et al., Nat. 531, 206 (2016)] revealed a surprisingly large electronic Landé g-factor, several times larger than the bulk value - contrary to the expectation that confinement reduces the g-factor. Here we assess the role of orbital contributions to the electron g-factor in nanowires and quantum dots. We show that an LS coupling in higher subbands leads to an enhancement of the g-factor of an order of magnitude or more for small effective mass semiconductors. We validate our theoretical finding with simulations of InAs and InSb, showing that the effect persists even if cylindrical symmetry is broken. A huge anisotropy of the enhanced g-factors under magnetic field rotation allows for a straightforward experimental test of this theory.

cond-mat.mes-hall↗