arXiv subjects

Martin Greiter

Publications and source records attributed to Martin Greiter.

At least 19 recordsLinked to original sources

arXiv2026

A Pfaffian quantum Hall state of ultracold bosons

Fractional quantum Hall states are a cornerstone of topological physics, hosting fractionally charged quasiparticles with exotic statistics that promise to enable topologically protected quantum information processing. Among these, the Pfaffian state introduced by Moore and Read implements a p-wave pairing structure that supports excitations with non-Abelian exchange statistics. Despite extensive study in electronic systems, direct access to its pairing structure has remained limited. Here we realize a three-particle bosonic Pfaffian state of ultracold $^{87}\mathrm{Rb}$ atoms in an optical lattice subject to a Floquet-engineered synthetic magnetic field. Using a Bayesian-optimized adiabatic protocol, we prepare a state exhibiting Pfaffian pairing correlations. Site-resolved measurements of multi-point density correlations reveal a pronounced suppression of short-range three-body coincidences, reflecting the underlying pairing structure. We further probe the state's transport response through Hall drift measurements. Our results establish a bottom-up approach to engineering non-Abelian topological order and lay the groundwork for future explorations of anyonic braiding in synthetic matter.

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↗

arXiv2024

Chiral Gapless Spin Liquid in Hyperbolic Space

We analyze the Kitaev model on the $\{9,3\}$ hyperbolic lattice. The $\{9,3\}$ is formed by a regular tricoordinated tiling of nonagons, where the 3-color coding of bonds according to the inequivalent Kitaev Ising spin couplings yields the natural generalization of the original Kitaev model for Euclidean regular honeycomb tiling. Upon investigation of the bulk spectrum for large finite size droplets, we identify a gapless chiral $\mathbb{Z}_2$ spin liquid state featuring spontaneous time reversal symmetry breaking. Due to its non-commutative translation group structure, such type of hyperbolic spin liquid is conjectured to feature chiral quasiparticles with a potentially non-Abelian Bloch profile.

cond-mat.str-el↗

arXiv2024

Topological Edge State Nucleation in Frequency Space and its Realization with Floquet Electrical Circuits

We build Floquet-driven capactive circuit networks to realize topological states of matter in the frequency domain. We find the Floquet circuit network equations of motion to reveal a potential barrier which effectively acts as a boundary in frequency space. By implementing a Su-Shrieffer-Heeger Floquet lattice model and measuring the associated circuit Laplacian and characteristic resonances, we demonstrate how topological edge modes can nucleate at such a frequency boundary.

cond-mat.mes-hall↗

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↗

arXiv2024

Simulating Holographic Conformal Field Theories on Hyperbolic Lattices

We demonstrate how table-top settings combining hyperbolic lattices with nonlinear dynamics universally encode aspects of the bulk-boundary-correspondence between gravity in anti-de-Sitter (AdS) space and conformal field theory (CFT). Our concrete and broadly applicable holographic toy model simulates gravitational self-interactions in the bulk and features an emergent CFT with nontrivial correlations on the boundary. We measure the CFT data contained in the two- and three-point functions and clarify how a thermal CFT is simulated through an effective black hole geometry. As a concrete example, we propose and simulate an experimentally feasible protocol to measure the holographic CFT using electrical circuits.

cond-mat.mes-hall↗

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↗

arXiv2022

Fractional Statistics

The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter $\theta$. $\theta = 0, \pi$ correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, $\theta$ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern--Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase $\theta$ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the $\nu = 1/3$ fractional quantum Hall state has been observed both in scattering and in interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.

cond-mat.str-el↗

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↗

arXiv2022

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↗

arXiv2021

Anyons in One Dimension

I give a non-technical account of fractional statistics in one dimension. In systems with periodic boundary conditions, the crossing of anyons is always uni-directional, and the fractional phase $\theta$ acquired by the anyons gives rise to fractional shifts in the spacings of the relative momenta, ${\Delta p =2\pi\hbar/L\, (|\theta|/\pi+n)}$. The fractional shift $\theta/\pi$ is a good quantum number of interacting anyons, even though the single particle momenta, and hence the non-negative integers $n$, are generally not.

quant-ph↗

arXiv2021

Interlinking and the Emergence of Classical Physics in Quantum Theory

The main argument by proponents of Many-World interpretations of quantum mechanics is that as more and more previously disentangled degrees of freedom become entangled with the microscopic degree we measure, there is no way of telling when the measurement (in the sense of a collapse of the wave function) should occur. Here, we introduce the concept of quantum interlinking, and argue that all macroscopic objects in the universe are connected through links of mutual entanglement while the objects themselves are (for the most part) not entangled. The measurement occurs when the degree we measure becomes entangled with any macroscopic object, and hence interlinked with all of them. This picture resolves long standing paradoxes such as Schr\"odinger's cat and EPR.

quant-ph↗

arXiv2021

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↗

arXiv2021

Adiabatic Construction of Hierarchical Quantum Hall States

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions $\nu=p/(p(m-1)+1)$ with $m$ odd, from integer Hall states at $\nu=p$ through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.

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

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

Turbulent hydrodynamics in strongly correlated Kagome metals

A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids are not amenable to the perturbative methods of Fermi liquid theory, but can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene, which possesses Dirac dispersions at low energies as well as significant Coulomb interactions between the electrons. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes of their band structure provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in stoichiometric Scandium (Sc) Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction and hence reflects the strength of the correlations, is enhanced by a factor of about 3.2 as compared to graphene, due to orbital hybridization. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put, for the first time, the turbulent flow regime described by holography within the reach of experiments.

cond-mat.str-el↗

arXiv2019

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 $\alpha$-RuCl$_3$.

cond-mat.str-el↗