arXiv subjects

Julian Siegl

Publications and source records attributed to Julian Siegl.

6 recordsLinked to original sources

arXiv2025

Consecutive-gap ratio distribution for crossover ensembles

The study of spectrum statistics, such as the consecutive-gap ratio distribution, has revealed many interesting properties of many-body complex systems. Here we propose a two-parameter surmise expression for such distribution to describe the crossover between the Gaussian orthogonal ensemble (GOE) and Poisson statistics. This crossover is observed in the isotropic Heisenberg spin-$1/2$ chain with disordered local field, exhibiting the Many-Body Localization (MBL) transition. Inspired by the analysis of stability in dynamical systems, this crossover is presented as a flow pattern in the parameter space, with the Poisson statistics being the fixed point of the system, which represents the MBL phase. We also analyze an isotropic Heisenberg spin-$1/2$ chain with disordered local exchange coupling and a zero magnetic field. In this case, the system never achieves the MBL phase because of the spin rotation symmetry. This case is more sensitive to finite-size effects than the previous one, and thus the flow pattern resembles a two-dimensional random walk close to its fixed point. We propose a system of linearized stochastic differential equations to estimate this fixed point. We study the continuous-state Markov process that governs the probability of finding the system close to this fixed point as the disorder strength increases. In addition, we discuss the conditions under which the stationary probability distribution is given by a bivariate normal distribution.

cond-mat.dis-nn↗

arXiv2025

A universal route to chiral Ising superconductivity in monolayer TaS$_2$ and NbSe$_2$

We investigate Ising superconductivity in two archetypal intrinsic superconductors, monolayer 1H-TaS$_2$ and 1H-NbSe$_2$, in a bottom-up approach. Using ab initio-based tight-binding parameterizations for the relevant low-energy d-bands, the screened interaction is evaluated microscopically, in a scheme including Bloch overlaps. In direct space, the screened potential displays for both systems long-range Friedel oscillations alternating in sign. Upon scaling, the oscillation pattern becomes universal, with the periodic features locked to the lattice. Solving the momentum-resolved gap equations, a chiral ground state with p-like symmetry is generically found. Due to the larger Ising spin-orbit coupling, the chiral gap is more anisotropic in TaS$_2$ than in NbSe$_2$. This is reflected in tunneling spectra displaying V-shaped features for the former, in quantitative agreement with low-temperature scanning tunneling experiments on TaS$_2$. At the same time, our results reconcile the apparent discordance with hard gap tunneling spectra reported for the sibling NbSe$_2$.

cond-mat.supr-con↗

arXiv2025

From Thermalization to Multifractality: Spin-Spin Correlation in Disordered $SU(2)$-Invariant 1D Heisenberg Spin Chains

We investigate spin correlations in one-dimensional $SU(2)$-invariant Heisenberg chains with exchange disorder for spin lengths $S=1/2$ and $S=1$. In the weak-disorder regime, the eigenmodes of the spin-spin correlation matrix are delocalized, consistent with ergodic behavior. Under strong disorder, the system enters a quasi-localized multifractal phase characterized by exponentially decaying, dimer-like spin correlations. Finite-size scaling of the inverse participation ratios of the correlation-matrix eigenmodes yields a correlation dimension, $D_2\approx 0.37-0.39$, confirming the stability of a multifractal regime that is distinct from both the ergodic limit ($D_2=1$) and the fully localized limit ($D_2=0$).

cond-mat.dis-nn↗

arXiv2025

Friedel oscillations and chiral superconductivity in monolayer NbSe$_2$

In 1965 Kohn and Luttinger proposed a genuine electronic mechanism for superconductivity. Despite the bare electrostatic interaction between two electrons being repulsive, in a metal electron-hole fluctuations can give rise to Friedel oscillations of the screened Coulomb potential. Cooper pairing among the electrons then emerges when taking advantage of the attractive regions. The nature of the leading pairing mechanism in some two-dimensional transition metal dichalcogenides is still debated. Focusing on NbSe$_2$, we show that superconductivity can be induced by the Coulomb interaction when accounting for screening effects on the trigonal lattice with multiple orbitals. Using ab initio-based tight-binding parametrizations for the relevant low-energy d-bands, we evaluate the screened interaction microscopically, in a scheme including Bloch overlaps. In the direct space, we find long-range Friedel oscillations alternating in sign, a key to the Kohn-Luttinger mechanism. The momentum-resolved gap equations predict two degenerate solutions at the critical temperature Tc, signaling the unconventional nature of the pairing. Their complex linear combination, i.e., a chiral gap with p-like symmetry, provides the ground state of the system. Our prediction of a fully gapped chiral phase well below Tc is in excellent agreement with the spectral function extracted from tunneling spectroscopy measurements of single-layer NbSe$_2$.

cond-mat.supr-con↗

arXiv2023

Imperfect Many-Body Localization in Exchange-Disordered Isotropic Spin Chains

We investigate many-body localization in isotropic Heisenberg spin chains with the local exchange parameters being subject to quenched disorder. Such systems incorporate a nonabelian symmetry in their Hamiltonian by an invariance under global SU(2)-rotations. Nonabelian symmetries are predicted to hinder the emergence of a many-body localized phase even in presence of strong disorder. We report on numerical studies using exact diagonalization for chains of common spin length 1/2 and 1. The averaged consecutive-gap ratios display a transition compatible with a crossover from an ergodic phase at small disorder strength to an incompletely localized phase at stronger disorder. The sample-to-sample variance of the averaged consecutive-gap ratio displays a maximum at the transition and distinguishes the incompletely localized phase from a fully many-body localized phase by its scaling behavior.

cond-mat.dis-nn↗

arXiv2023

A particle conserving approach to AC-DC driven interacting quantum dots with superconducting leads

The combined action of a DC bias and a microwave drive on the transport characteristic of a superconductor-quantum dot-superconductor junction is investigated. To cope with time dependent non-equilibrium effects and interactions in the quantum dot, we develop a general formalism for the dynamics of the density operator based on a particle conserving approach to superconductivity. Without invoking a broken U (1) symmetry, we identify a dynamical phase connected to the coherent transfer of Cooper pairs across the junction. In the weak coupling limit, we show that besides quasiparticle transport, proximity induced superconducting correlations manifest in anomalous pair tunneling involving the transfer of a Cooper pair. The resulting generalized master equation in presence of the microwave drive showcases the characteristic bichromatic response due to the combination of the AC Josephson effect and an AC voltage. Analytical expressions for all harmonics in the driving frequency of both the current and the reduced dot operator are given for arbitrary driving strength. For the net DC current the resulting photon assisted processes give rise to rich current-voltage characteristics. In addition to photon assisted subgap transport we find regions of total current inversion in the stability diagram. There, the junction acts as a pump with the net DC current flowing against the applied DC bias. The first harmonic of the current, being closely related to the nonlinear dynamic susceptibility of the junction, is discussed at finite applied DC bias.

cond-mat.mes-hall↗