arXiv subjects

Elio J. König

Publications and source records attributed to Elio J. König.

At least 19 recordsLinked to original sources

arXiv2026

Parafermions in polarized $ν=2/3$ Fractional Quantum (Anomalous) Hall Heterostructures

Motivated by recent experimental signatures of fractional Chern insulators in 2D quantum materials, we investigate the realization of $\mathbb Z_3$ parafermion zero modes (PZMs) on edges of spin-polarized $ν=2/3$ fractional quantum Hall states which are proximitized by superconductors. Unlike the spin-unpolarized Halperin state, the polarized $ν=2/3$ edge contains counterpropagating electron and fractional quasihole modes, giving rise to a plethora of competing tunneling and pairing processes. We focus on the vicinity of the fixed point where these modes reorganize into decoupled charge and neutral sectors, with the neutral sector describing an emergent dipole degree of freedom. Using bosonization and renormalization group analysis, we lay out the parameter space in which the interedge dipole interactions gap the neutral sector to stabilize one dominant tunneling and one dominant pairing channel resulting in a double sine-Gordon model in the charge sector which supports $\mathbb{Z}_3$ PZMs at domain walls. We discuss both clean and disordered systems. In clean systems this mechanism requires a certain degree of control of the interaction strength and range. In contrast, disorder can provide a more generic route: While short-ranged, edge-uncorrelated disorder % on the two edges suppresses the simultaneous pinning required for stable parafermion modes, when the disorder on the two edges is sufficiently correlated, as expected for smooth disorder potentials, the parameter regime hosting PZMs increases.

cond-mat.mes-hall↗

arXiv2026

Tractable model for a fractionalized Fermi liquid (FL$^*$) on a square lattice

Motivated by the continued interest in Fermi-surface reconstruction without symmetry breaking, we present an analytically tractable microscopic model of a fractionalized Fermi liquid (FL$^*$) on a square lattice and discuss its potential relevance to the cuprates. As in ancilla-qubit constructions, the model is related to Kondo lattice systems, but in this case, the conduction electrons interact with a $\mathbb{Z}_2$ spin liquid of the Yao--Lee type, with a Majorana Fermi surface. The associated $\mathbb Z_2$ gauge theory is static so that the model can be analytically solved to leading-logarithic accuracy. There are two phases: one in which the fractionalized fermions of the spin liquid hybridize with conduction electrons to form a common Fermi surface violating the naive Luttinger count, and one in which they remain decoupled. We discuss the salient features of the small Fermi-surface phase, including analytically derived momentum dependent coherence factors responsible for the appearance of Fermi arcs à la Yang-Rice-Zhang. We further discuss the impact of quantum and thermal fluctuations, including a strong diamagnetic response and a logarithmically divergent Sommerfeld coefficient at the onset of the pseudogap.

cond-mat.str-el↗

arXiv2026

Flux-induced Aharonov-Bohm Oscillation in the Tunneling Spectroscopy of Kitaev Spin Liquids

Identifying emergent flux excitations and signatures of their mutual statistics with itinerant Majorana fermions remains a central challenge in Kitaev spin liquids. We show that an isolated $π$ flux imprints an intrinsic Aharonov-Bohm-like interference pattern on the charge-neutral Majorana continuum. Spatially resolved scanning tunneling microscopy with inelastic electron tunneling spectroscopy (STM-IETS) probes this oscillation in the local dynamical spin response as a function of both bias voltage and tip-flux separation, reflecting the $π$ phase acquired by Majorana trajectories encircling the flux. We show that large-scale exact diagonalization of the Kitaev honeycomb model and a complementary low-energy continuum theory yield consistent radial oscillations. These results provide a finite-energy, spatially resolved tunneling signature of a preexisting flux and a diagnostic of fermion-flux mutual statistics without requiring manipulation of individual anyons in the Kitaev spin liquid.

cond-mat.str-el↗

arXiv2026

Anomalous Hall effect in rhombohedral graphene

Motivated by recent experiments on rhombohedral stacked multilayer graphene and the observation of the anomalous Hall effect in a spontaneous spin-valley polarized quarter metal state, we calculate the anomalous Hall conductivity for this system in the presence of two types of impurities: weak and dense as well as sparse and strong. Our calculation of $σ_{xy}$ is based on the Kubo-Streda diagrammatic approach. In a model with Gaussian disorder applicable to weak dense impurities, this involves all non-crossing diagrams (intrinsic, side-jump and Gaussian skew-scattering contributions) and additionally diagrams with two intersecting impurities, X and $Ψ$, representing diffractive skew-scattering processes. A "Mercedes star" diagram (non-Gaussian skew scattering) is furthermore included to treat in the case of strong, sparse impurities. We supplement our asymptotically exact analytical solutions for an isotropic model without warping effects by semi-numerical calculations accounting perturbatively for warping, which plays a crucial role in the low-energy band structure.

cond-mat.mes-hall↗

arXiv2026

Many-Body Entanglement Properties of Finite Interacting Fermionic Hamiltonians

We analyze many-body entanglement in interacting fermionic systems by using the $M$-body reduced density matrix. We demonstrate that if a particle number conserving fermionic Hamiltonian contains only up to $M$-body interaction terms, then its $N$-particle ground state cannot be maximally $M$-body entangled. As a key step in the proof, we show that the energy expectation value of a maximally $M$-body mixed state is equal to the spectral mean of the Hamiltonian on the corresponding $N$-particle subspace. We further demonstrate that the many-body entanglement structure of a ground state can place quantitative constraint on the interaction strength of its parent Hamiltonian. We illustrate the theorem and its implications in Hubbard and extended SYK models. Going beyond ground states, we analyze entanglement generation under unitary dynamics from Slater-determinant initial states in these models. We determine early-time growth and estimate entanglement saturation times. Finally, we derive explicit symmetry-refined saturation upper bounds for $M$-body entanglement in the presence of an Abelian symmetry.

quant-ph↗

arXiv2026

Topological Floquet Green's function zeros

Motivated by recent advances in digital quantum emulation using noisy intermediate-scale quantum (NISQ) devices and an increased interest in topological Green's function zeros in condensed matter systems, we here study Green's function zeros in topological Floquet systems. We concentrate on interacting Kitaev-like Floquet chains (or equivalently transverse field Ising circuits) and introduce Floquet Green's-function-based topological invariants for the corresponding symmetry class BDI. In the vicinity of special points in the free fermion phase diagram and using tailor-made interactions which lead to the Floquet version of symmetric mass generation, we analytically calculate both edge and bulk Green's functions. Just as in the case of continuum time evolution, topological bands of Green's function zeros may also contribute to the topological invariant. However, contrary to the case of continuum time evolution, Floquet Green's functions can have zeros even in the absence of interactions. Finally, we also discuss an implementation of this Floquet system in a digital quantum emulator: We present a circuit which encodes the interaction under consideration and pinpoint the observables carrying information about the topological Green's function boundary zeros.

cond-mat.mes-hall↗

arXiv2025

Phases of Quasi-One-Dimensional Fractional Quantum (Anomalous) Hall - Superconductor Heterostructures

Motivated by recent observations of fractional Chern insulators (FCIs) in the vicinity of superconducting (SC) phases, we study fractional quantum (anomalous) Hall-superconductor heterostructures in the presence of $U(1)$ order-parameter fluctuations and particularly focus on the case of $ν= 2/3$ quantum Hall states leading to $\mathbb Z_3$ parafermions. We first employ a phenomenological field theory to qualitatively determine the phase diagram. Furthermore, we generalize a previously established alternating pattern of superconductor and tunneling regions, coupled to fractional quantum Hall edge states, to map the problem onto a topological Josephson junction chain involving lattice parafermions. Using density matrix renormalization group simulations, we establish a phase diagram composed of Mott insulating phases and two different Luttinger liquids whose fundamental excitations carry charges 2e and $2e/3$, respectively. In agreement with analytical considerations using conformal field theory, we numerically find transitions of Berezinskii-Kosterlitz-Thouless (BKT) type as well as a continuous $\mathbb Z_3 \times U(1)$ second-order phase transition characterized by central charge c = 9/5. We finally extract information about a possible ground state degeneracy and comment on the stability of parafermionic edge states in the presence of fluctuations. These theoretical foundations can be expected to be of practical importance for gate-defined FCI-SC heterostructures in moiré materials, in which broad superconducting transitions indicative of strong order parameter fluctuations were observed.

cond-mat.str-el↗

arXiv2025

Multichannel topological Kondo models and their low-temperature conductances

In the multichannel Kondo effect, overscreening of a magnetic impurity by conduction electrons leads to a frustrated exotic ground state. It has been proposed that multichannel topological Kondo (MCTK) model involving topological Cooper pair boxes with $M$ Majorana modes [SO($M$) "spin"] and $N$ spinless electron channels exhibits an exotic intermediate coupling fixed point. This intermediate fixed point has been analyzed through large-$N$ perturbative calculations, which gives a zero-temperature conductance decaying as $1/N^2$ in the large-$N$ limit. However, the conductance at this intermediate fixed point has not been calculated for generic $N$. Using representation theory, we verify the existence of this intermediate-coupling fixed point and find the strong-coupling effective Hamiltonian for the case $M=4$. Using conformal field theory techniques for SO($M$), we generalize the notion of overscreening and conclude that the MCTK model is an overscreened Kondo model. We find the fixed-point finite-size energy spectrum and the leading irrelevant operator (LIO). We express the fixed-point conductance in terms of the modular S-matrix of SO($M$) for general $N$, confirming the previous large-$N$ result. We describe the finite-temperature corrections to the conductance by the LIO and find that they are qualitatively different for the cases $N=1$ and $N\geq2$ due to the different fusion outcomes with the current operator. We also compare the multichannel topological Kondo model to the topological symplectic Kondo model.

cond-mat.str-el↗

arXiv2025

Design and benchmarks for emulating Kondo dynamics on a quantum chip

Motivated by recent advances in digital quantum simulation and the overall prospective of solving correlated many-electron problems using quantum algorithms, we design a gate-based quantum circuit that emulates the dynamics of the Kondo impurity model. We numerically determine the impurity magnetization, entanglement between impurity and fermionic sites and energy as a function of time (i.e.~circuit depth) for various initial states and find universal long-time dynamics. We complement the numerical simulations for moderate system size with an asymptotically exact analytical solution that is effective in the limit of large system sizes and for starting states corresponding to a filled Fermi sea. This work opens up the perspective of studying the dynamics of electronic quantum many-body states on quantum chips of the NISQ era.

cond-mat.str-el↗

arXiv2025

Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix

Fermionic Hamiltonians play a critical role in quantum chemistry, one of the most promising use cases for near-term quantum computers. However, since encoding nonlocal fermionic statistics using conventional qubits results in significant computational overhead, fermionic quantum hardware, such as fermion atom arrays, were proposed as a more efficient platform. In this context, we here study the many-body entanglement structure of fermionic $N$-particle states by concentrating on $M$-body reduced density matrices (DMs) across various bipartitions in Fock space. The von Neumann entropy of the reduced DM is a basis independent entanglement measure which generalizes the traditional quantum chemistry concept of the one-particle DM entanglement, which characterizes how a single fermion is entangled with the rest. We carefully examine upper bounds on the $M$-body entanglement, which are analogous to the volume law of conventional entanglement measures. To this end we establish a connection between $M$-body reduced DM and the mathematical structure of hypergraphs. Specifically, we show that a special class of hypergraphs, known as $t$-designs, corresponds to maximally entangled fermionic states. Finally, we explore fermionic many-body entanglement in random states. We semianalytically demonstrate that the distribution of reduced DMs associated with random fermionic states corresponds to the trace-fixed Wishart-Laguerre random matrix ensemble. In the limit of large single-particle dimension $D$ and a non-zero filling fraction, random states asymptotically become absolutely maximally entangled.

quant-ph↗

arXiv2025

Topologically enabled superconductivity: possible implications for rhombohedral graphene

We present a topological mechanism for superconductivity emerging from Chern-2 insulators. While, naively, time-reversal symmetry breaking is expected to prevent superconductivity, it turns out that the opposite is the case: An explicit model calculation for a generalized attractive-U Haldane-Hubbard model demonstrates that superconductivity is only stabilized near the quantum anomalous Hall state, but not near a trivial, time-reversal symmetric band insulator. As standard Bardeen-Cooper-Schrieffer-like mean-field theory fails to capture any superconducting state, we explain this using an effective fractionalized field theory involving fermionic chargeons, bosonic colorons and an emergent U(1) gauge field. When the chargeons form a gapped topological band structure, the proliferation of single monopoles of this gauge field is forbidden. However, long-ranged monopole-antimonopole correlations emerge, and we argue that those correspond to superconducting order. Using random phase approximation on top of extensive slave-rotor mean-field calculations we characterize coherence length and stiffness of the superconductor. Thereby, we deduce the phase diagram in parameter space and furthermore discuss the effect of doping, temperature and an external magnetic field. We complement the fractionalized theory with calculations using an effective spin model and Gutzwiller projected wavefunctions. While mostly based on a simple toy model, we argue that our findings contribute to a better understanding of superconductivity emerging out of spin- and valley polarized rhombohedral graphene multilayers in a parameter regime with nearby quantum anomalous Hall insulators.

cond-mat.str-el↗

arXiv2024

Quantum Restored Symmetry Protected Topological Phases

Symmetry protected topological (SPT) phases are fundamental quantum many-body states of matter beyond Landau's paradigm. Here, we introduce the concept of quantum restored SPTs (QRSPTs), where the protecting symmetry is spontaneously broken at each instance in time, but restored after time average over quantum fluctuations, so that topological features re-emerge. To illustrate the concept, we study a one-dimensional fermionic Su-Schrieffer-Heeger model with fluctuating superconducting order. We solve this problem in several limiting cases using a variety of analytical methods and compare them to numerical (density matrix renormalization group) simulations which are valid throughout the parameter regime. We thereby map out the phase diagram and identify a QRSPT phase with topological features which are reminiscent from (but not identical to) the topology of the underlying free fermion system. The QRSPT paradigm thereby stimulates a new perspective for the constructive design of novel topological quantum many-body phases.

cond-mat.str-el↗

arXiv2024

Emulating moiré materials with quasiperiodic circuit quantum electrodynamics

Topological bandstructures interfering with moiré superstructures give rise to a plethora of emergent phenomena, which are pivotal for correlated insulating and superconducting states of twisttronics materials. While quasiperiodicity was up to now a notion mostly reserved for solid-state materials and cold atoms, we here demonstrate the capacity of conventional superconducting circuits to emulate moiré physics in charge space. With two examples, we show that Hofstadter's butterfly and the magic-angle effect, are directly visible in spectroscopic transport measurements. Importantly, these features survive in the presence of harmonic trapping potentials due to parasitic linear capacitances. Our proposed platform benefits from unprecedented tuning capabilities, and opens the door to probe incommensurate physics in virtually any spatial dimension.

cond-mat.mes-hall↗

arXiv2024

Topological Quantum Computation on a Chiral Kondo Chain

We describe the chiral Kondo chain model based on the symplectic Kondo effect and demonstrate that it has a quantum critical ground state populated by non-Abelian anyons. We show that the fusion channel of two arbitrary anyons can be detected by locally coupling the two anyons to an extra single channel of chiral current and measuring the corresponding conductance at finite frequency. Based on such measurements, we propose that the chiral Kondo chain model with symplectic symmetry can be used for implementation of measurement-only topological quantum computations, and it possesses a number of distinct features favorable for such applications. The sources and effects of errors in the proposed system are analyzed, and possible material realizations are discussed.

cond-mat.str-el↗

arXiv2024

Topological Kondo effect with spinful Majorana fermions

Motivated by the importance of studying topological superconductors beyond the mean-field approximation, we here investigate mesoscopic islands of time reversal invariant topological superconductors (TRITOPS). We characterize the spectrum in the presence of strong order parameter fluctuations in the presence of an arbitrary number of Kramers pairs of Majorana edge states and study the effect of coupling the Coulomb blockaded island to external leads. In the case of an odd fermionic parity on the island, we derive an unconventional Kondo Hamiltonian in which metallic leads couple to both topological Majorana degrees of freedom (which keep track of the parity in different leads) and the overall spin-1/2 in the island. For the simplest case of a single wire (two pairs of Majorana edge states), we demonstrate that anisotropies are irrelevant in the weak coupling renormalization group flow. This permits us to solve the Kondo problem in the vicinity of a Toulouse-like point using Abelian Bosonization. We demonstrate a residual ground state entropy of $\ln(2)$, which is protected by spin-rotation symmetry, but reduced to $\ln(\sqrt{2})$ (as in the spinless topological Kondo effect) by symmetry breaking perturbations. In the symmetric case, we further demonstrate the simultaneous presence of both Fermi liquid and non-Fermi liquid like thermodynamics (depending on the observable) and derive charge and spin transport signatures of the Coulomb blockaded island.

cond-mat.str-el↗

arXiv2023

Quasiperiodic circuit quantum electrodynamics

Superconducting circuits are an extremely versatile platform to realize quantum information hardware and to emulate topological materials. We here show how a simple arrangement of capacitors and conventional superconductor-insulator-superconductor junctions can realize an even broader class of systems, in the form of a nonlinear capacitive element which is quasiperiodic with respect to the quantized Cooper-pair charge. Our setup allows to create protected Dirac points defined in the transport degrees of freedom, whose presence leads to a suppression of the classical finite-frequency current noise. Furthermore, the quasiperiodicity can emulate Anderson localization in charge space, measurable via vanishing charge quantum fluctuations. The realization by means of the macroscopic transport degrees of freedom allows for a straightforward generalization to arbitrary dimensions and implements truly non-interacting versions of the considered models. As an outlook, we discuss potential ideas to simulate a transport version of the magic-angle effect known from twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2023

Topological Green's function zeros in an exactly solved model and beyond

The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we here study an exactly integrable, local model for a fractionalized topological insulator. Using a controlled perturbation theory about this limit, we demonstrate the existence of topological bands of zeros in the exact fermionic Green's function and show that {in this model} they do affect the topological invariant of the system, but not the quantized transport response. Close to (but prior to) the Higgs transition signaling the breakdown of fractionalization, the topological bands of zeros acquire a finite ``lifetime''. We also discuss the appearance of edge states and edge zeros at real space domain walls separating different phases of the system. This model provides a fertile ground for controlled studies of the phenomenology of Green's function zeros and the underlying exactly solvable lattice gauge theory illustrates the synergetic cross-pollination between solid-state theory, high-energy physics and quantum information science.

cond-mat.str-el↗

arXiv2023

Topological quantum criticality from multiplicative topological phases

Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to understanding of topological condensed matter physics, and the extension to gapless SPTs provides essential understanding of their consequences. In this work, we identify a fundamental connection between gapless SPTs and recently-introduced multiplicative topological phases, demonstrating that multiplicative topological phases are an intuitive and general approach to realizing concrete models for gapless SPTs. In particular, they are naturally well-suited to realizing higher-dimensional, stable, and intrinsic gapless SPTs through combination of canonical topological insulator and semimetal models with critical gapless models in symmetry-protected tensor product constructions, opening avenues to far broader and deeper investigation of topology via short-range entanglement.

cond-mat.str-el↗