arXiv subjects

Tobias Helbig

Publications and source records attributed to Tobias Helbig.

17 recordsLinked to original sources

arXiv2026

Dual Gauge Theory for Two Dimensional Superfluid Turbulence

We describe turbulent hydrodynamics of superfluids in two spatial dimensions via the dynamics of point-like vortices coupled to an emergent 2+1 dimensional $U(1)$ gauge field. The cascade of superfluid kinetic energy is equivalently described by a cascade of dual electric field energies. We study superfluid turbulence using the equations of motion of the dual gauge theory in the presence of a drive and dissipation. In the limit that the vortices are point-like, the dual equations of motion directly yield the hydrodynamical equations of the superfluid. We obtain a turbulent cascade consistent with Kolmogorov's scaling law for two dimensional fluid turbulence. We observe clustering of like-signed vortices and compute the kinetic energy flux to show that the turbulent regime exhibits an inverse energy cascade.

cond-mat.quant-gas↗

arXiv2026

Momentum-Space Entanglement Signatures and Spinon Breakdown in the $J_1$-$J_2$ Zig-Zag Heisenberg Chain

We investigate the resilience of spinon quasiparticles in the $J_1$-$J_2$ zig-zag spin chain ($J_2>0$) from the viewpoint of momentum-space entanglement. For small $J_2$, we show that deconfined spinons survive well past the liquid-dimer transition before eventually collapsing towards the Majumdar-Ghosh point. In the highly frustrated zig-zag regime ($J_2 \gg |J_1|$), we model the system as two coupled Heisenberg chains and by Fourier transforming each subchain individually, a framework we dub the double-spinon description. While continuum field theories predict that this decoupled phase is strictly unstable to any finite inter-chain coupling, our analysis reveals that the double-spinon description remains robust over an extensive parameter regime. Notably, we find a stark asymmetry in spinon stability reflecting the underlying renormalization group flow: ferromagnetic coupling ($J_{1} < 0$) is marginally irrelevant and sustains fractionalization deep into the spiral phase, whereas antiferromagnetic coupling ($J_{1} > 0$) is marginally relevant and drives confinement much earlier. The ultimate breakdown of this fractionalized description is driven by a continuum of inter-chain excitations which manifests itself as a sharp ground-state momentum shift distinct from macroscopic thermodynamic phase boundaries. Our results establish momentum cut entanglement analysis as a tool to trace the quasiparticle resilience of spinons, as we show that treating the zig-zag Heisenberg chain as two coupled SU(2)$_1$ Wess-Zumino-Witten models provides a theoretical framework for strongly frustrated quantum magnets applicable beyond the decoupled limit.

cond-mat.str-el↗

arXiv2026

Superconductivity and magnetism in bilayer nickelates: itinerant perspective

We study superconductivity and magnetism in bilayer nickelates from an itinerant perspective. Starting from a tight binding fit to recent ARPES measurements on compressively strained thin films, we incorporate the standard set of onsite repulsive interactions among partially filled $e_g$ orbitals: intra-orbital $U$, inter-orbital $U'$, Hund's coupling $J_H$ and a pair hopping $J_P$. We obtain the effective pairing interaction by dressing these bare interactions with particle-hole fluctuations via the RPA. In the strong Hund's coupling regime, we find that $s$-wave superconductivity and $(π/2, π/2)$ SDW order are the favored ground states. With weaker Hund's coupling, we find that $d$-wave pairing and $(π, π)$ SDW are the leading ground states. Our results are qualitatively consistent with earlier DMRG studies, and point to the key role played by Hund's coupling in determining the nature of superconductivity and magnetism in this system.

cond-mat.supr-con↗

arXiv2025

Origin of Spin Stripes in Bilayer Nickelate La$_3$Ni$_2$O$_7$

The bilayer nickelate La$_3$Ni$_2$O$_7$ has recently emerged as a high-temperature superconductor with unusual spin stripe order in its ambient pressure phase. We propose a microscopic Hamiltonian that faithfully reflects the crystalline symmetry of this system, with the primary aim of addressing its unconventional magnetism at ambient pressure. Using state-of-the-art density matrix renormalization group calculations, we show that $(\pi/2,\pi/2)$ spin stripe order arises in our model at sizable Hund's coupling $J_H$ from a hidden quasi-one-dimensionality and persists over a range of electron concentrations. In the more symmetric high-pressure regime, our model exhibits enhanced interlayer pairing tendencies when the interlayer antiferromagnetic coupling $J_{\bot}$ becomes sufficiently large. Our results provide a microscopic origin of the diagonal spin stripes and identify Hund's coupling $J_H$ and interlayer coupling $J_{\bot}$ as key ingredients governing magnetic order and pairing tendencies in La$_3$Ni$_2$O$_7$.

cond-mat.supr-con↗

arXiv2025

How pairing mechanism dictates topology in valley-polarized superconductors with Berry curvature

We investigate how the pairing mechanism influences topological superconductivity in valley-polarized systems with Berry curvature. We demonstrate that short-range attractive interactions, such as those mediated by phonons, favor superconducting states where the Bogoliubov-de Gennes (BdG) Chern number has the same sign as the Berry curvature. In contrast, overscreened repulsive interactions, as in the Kohn-Luttinger mechanism, favor superconducting states where the BdG Chern number has the opposite sign as the Berry curvature. We establish these trends in a fully controlled limit and apply them to a recently reported chiral superconductor in rhombohedral multilayer graphene. Our theory provides a concrete experimental criterion for distinguishing between different pairing mechanisms in valley-polarized topological superconductors.

cond-mat.supr-con↗

arXiv2024

Theory of Eigenstate Thermalisation

If we prepare an isolated, interacting quantum system in an eigenstate and perturb a local observable at an initial time, its expectation value will relax towards a thermal expectation value, even though the time evolution of the system is deterministic. The eigenstate thermalization hypothesis (ETH) of Deutsch and Srednicki suggests that this is possible because each eigenstate of the full quantum system acts as a thermal bath to its subsystems, such that the reduced density matrices of the subsystems resemble thermal density matrices. Here, we use the observation that the eigenvalue distribution of interacting quantum systems is a Gaussian under very general circumstances, and Dyson Brownian motion random matrix theory, to derive the ETH and thereby elevate it from hypothesis to theory. Our analysis provides a derivation of statistical mechanics which neither requires the concepts of ergodicity or typicality, nor that of entropy. Thermodynamic equilibrium follows solely from the applicability of quantum mechanics to large systems and the absence of integrability.

quant-ph↗

arXiv2023

Realizing efficient topological temporal pumping in electrical circuits

Quantized adiabatic transport can occur when a system is slowly modulated over time. In most realizations however, the efficiency of such transport is reduced by unwanted dissipation, back-scattering, and non-adiabatic effects. In this work, we realize a topological adiabatic pump in an electrical circuit network that supports remarkably stable and long-lasting pumping of a voltage signal. We further characterize the topology of our system by deducing the Chern number from the measured edge band structure. To achieve this, the experimental setup makes use of active circuit elements that act as time-variable voltage-controlled inductors.

cond-mat.other↗

arXiv2023

Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states.

cond-mat.mes-hall↗

arXiv2022

Simulating hyperbolic space on a circuit board

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a "hyperbolic drum", and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter.

cond-mat.other↗

arXiv2022

Observation of cnoidal wave localization in non-linear topolectric circuits

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of non-linearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a non-linear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the non-linear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the non-linear regime, where the cnoidal eccentricity decreases from edge to bulk.

cond-mat.mes-hall↗

arXiv2020

Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits

We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry $\mathcal{PT}$ and chiral symmetry anti-$\mathcal{PT}$ ($\mathcal{APT}$). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of $\mathcal{PT}$ symmetric gain and loss on localized edge and defect states in a non-Hermitian Su--Schrieffer--Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the $\mathcal{APT}$ symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel $\mathcal{PT}$ symmetric $\mathbb{Z}_2$ invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not $\mathcal{PT}$ symmetric, the topological defect state disappears and only reemerges when $\mathcal{APT}$ symmetry is reached, while the topological edge states always prevail and only experience a shift in eigenvalue. Our findings unveil a future route for topological defect engineering and tuning in non-Hermitian systems of arbitrary dimension.

physics.app-ph↗

arXiv2020

Imaging nodal knots in momentum space through topolectrical circuits

Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if constructed, probing their intricate linkages and topological "drumhead" surface states will be challenging due to the high precision needed. In this work, we overcome these practical and technical challenges with RLC circuits, transcending existing theoretical constructions which necessarily break reciprocity, by pairing nodal knots with their mirror image partners in a fully reciprocal setting. Our nodal knot circuits can be characterized with impedance measurements that resolve their drumhead states and image their 3D nodal structure. Doing so allows for reconstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomial. We illustrate our approach with large-scale simulations of various nodal knots and an experiment that maps out the topological drumhead region of a Hopf-link.

cond-mat.mes-hall↗

arXiv2020

Reciprocal skin effect and its realization in a topolectrical circuit

A system is non-Hermitian when it exchanges energy with its environment and non-reciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and non-reciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but reciprocal systems in two or more dimensions: Eigenmodes with opposite longitudinal momentum exhibit opposite transverse anomalous localization. We experimentally demonstrate the reciprocal skin effect in a passive RLC circuit, suggesting convenient alternative implementations in optical, acoustic, mechanical, and related platforms. Skin mode localization brings forth potential applications in directional and polarization detectors for electromagnetic waves.

cond-mat.mes-hall↗

arXiv2020

Efficient Light Funneling based on the non-Hermitian Skin Effect

In the last two decades, the ubiquitous effect of dissipation has proven to entail astonishing non-Hermitian features, rather than just being an inescapable nuisance. As an alternative route to non-Hermiticity, we tailor the anisotropy of a lattice, which constitutes an, up to now, barely exploited degree of freedom. In this case, the appearance of an interface dramatically alters the entire eigenmode spectrum, leading to the exponential localization of all modes at the interface, which goes beyond the expectations for Hermitian systems. This effect is dubbed "non-Hermitian skin effect". We experimentally demonstrate it by studying the propagation of light in a large scale photonic mesh lattice. For arbitrary excitations, we find that light is always transported to the interface, realizing a highly efficient funnel for light.

physics.optics↗

arXiv2019

Observation of bulk boundary correspondence breakdown in topolectrical circuits

The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of features like gain and loss, or periodic driving, qualitatively amends these laws. A contemporary frontier of meta-material research is the challenge open systems pose to the established characterization of topological matter. There, one of the most relied upon principles is the bulk-boundary correspondence (BBC), which intimately relates the properties of the surface states to the topological classification of the bulk. The presence of gain and loss, in combination with the violation of reciprocity, has recently been predicted to affect this principle dramatically. Here, we report the experimental observation of BBC violation in a non-reciprocal topolectric circuit. The circuit admittance spectrum exhibits an unprecedented sensitivity to the presence of a boundary, displaying an extensive admittance mode localization despite a translationally invariant bulk. Intriguingly, we measure a non-local voltage response due to broken BBC. Depending on the AC current feed frequency, the voltage signal accumulates at the left or right boundary, and increases as a function of nodal distance to the current feed.

cond-mat.mes-hall↗

arXiv2018

Chiral voltage propagation in a self-calibrated topolectrical Chern circuit

We propose an electric circuit array with topologically protected uni-directional voltage modes at its boundary. Instead of external bias fields or floquet engineering, we employ negative impedance converters with current inversion (INICs) to accomplish a non-reciprocal, time-reversal symmetry broken electronic network we call topolectrical Chern circuit (TCC). The TCC features an admittance bulk gap fully tunable via the resistors used in the INICs, along with a chiral voltage boundary mode reminiscent of the Berry flux monopole present in the admittance band structure. The active circuit elements in the TCC can be calibrated to compensate for dissipative loss.

cond-mat.mes-hall↗

arXiv2018

Band structure engineering and reconstruction in electric circuit networks

We develop an approach to design, engineer, and measure band structures in a synthetic crystal composed of electric circuit elements. Starting from the nodal analysis of a circuit lattice in terms of currents and voltages, our Laplacian formalism for synthetic matter allows us to investigate arbitrary tight-binding models in terms of wave number resolved Laplacian eigenmodes, yielding an admittance band structure of the circuit. For illustration, we model and measure a honeycomb circuit featuring a Dirac cone admittance bulk dispersion as well as flat band admittance edge modes at its bearded and zigzag terminations. We further employ our circuit band analysis to measure a topological phase transition in the topolectrical Su-Schrieffer-Heeger circuit.

cond-mat.mes-hall↗