arXiv subjects

Tilen Cadez

Publications and source records attributed to Tilen Cadez.

14 recordsLinked to original sources

arXiv2026

Marked vertex search on disordered graphs with Rosenzweig-Porter phases

Quantum marked vertex search algorithms are known to outperform their classical counterparts, yet their behavior in the presence of disorder remains largely unexplored. Here, we address this gap by studying marked vertex search on disordered random graphs. To introduce disorder, we implement the Rosenzweig-Porter (RP) model, a random matrix ensemble with tunable ergodic, non-ergodic extended, and localized phases, on Erd\H{o}s-R\'enyi (ER) graphs. This produces a doubly random system where ER graph connectivity randomizes which interactions exist, while RP disorder controls their strength and `on-site' potentials, providing a two-parameter framework to study quantum dynamics on disordered networks. First, we show that the characteristic Wigner-Dyson-to-Poisson spectral crossover of the RP ensemble survives under graph constraints across the sparse-to-dense range, and we derive an analytical estimate for the finite-size localization boundary that shifts systematically with the graph edge probability $p$, consistent with a resonant-hybridization argument. Thereafter, using this disordered graph ensemble, we study the marked vertex search problem and find that search performance tracks the underlying quantum phase directly. Counterintuitively, the ergodic phase, despite supporting fast transport, yields lower success probability than the localized phase, which achieves high success probability at the cost of significantly longer search times. These results establish a direct and quantitative link between random matrix disorder on graphs and the performance of continuous-time quantum walk search, and suggest that disorder, rather than being merely an obstacle, can be exploited as a tunable parameter in quantum search protocols.

quant-ph↗

arXiv2026

Emergence of chiral $p$-wave and $d$-wave states in $g$-wave altermagnets

Altermagnets emerge as a novel platform for realizing unconventional superconductivity through their exotic momentum-dependent spin-splitting of electronic band structures. Recent experiments have uncovered a novel form of altermagnetism with distinctive $g$-wave symmetry in CrSb. However, the potential for unconventional superconductivity arising from $g$-wave altermagnetism in such systems remains largely unexplored. In this study, we discover the emergence of chiral superconducting states in three-dimensional $g$-wave altermagnetic metals. Through systematic self-consistent mean-field analysis on the extended attractive Hubbard model combined with $g$-wave altermagnetic exchange fields in a three-dimensional hexagonal lattice, as observed in CrSb, we find that the altermagnetic spin splitting of Fermi surfaces favors chiral $p$-wave states as the dominant pairing channel under strong altermagnetic fields and high electron densities, while chiral $d$-wave states become predominant under weak altermagnetic fields and intermediate electron densities. Conversely, at weak altermagnetic fields and typical electron densities, non-chiral $s$-, extended $s$-, or $f$-wave states become stabilized. We also showcase the possible experimental detection using the quasiparticle energy dispersions and the density of states to distinguish different pairing symmetries. These findings underscore the potential of $g$-wave altermagnets to host sought-after chiral and gapless superconductivity.

cond-mat.supr-con↗

arXiv2026

Structural constraints on mobility edges in one-dimensional quasiperiodic systems

Mobility edges commonly arise in one-dimensional quasiperiodic systems once exact self-duality is broken, yet their origin is typically understood only at the level of individual Hamiltonians. Here we show that mobility edge positions are not independent spectral features of individual Hamiltonians, but are structurally constrained across quasiperiodic Hamiltonians related by an isospectral duality. Using a bichromatic Aubry--Andr\'e model as a minimal setting, we demonstrate that this constraint is encoded in an exact identity for Lyapunov exponents derived from the Thouless formula. As a consequence, the mobility edge positions are restricted to a reduced set of energies. In the self-dual limit, these mobility edge positions coincide at a single localization--delocalization transition. This structural constraint enforces a linear critical scaling of the physical Lyapunov spectrum near the self-dual point. Numerical results confirm a critical exponent consistent with the standard Aubry--Andr\'e value of $\nu = 1$, while simultaneously revealing a novel, non-universal energy-dependent prefactor.

cond-mat.dis-nn↗

arXiv2025

Neural Scaling Laws for Deep Regression

Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language models highlights the importance of these laws, their application to deep regression models remains largely unexplored. Here, we empirically investigate neural scaling laws in deep regression using a parameter estimation model for twisted van der Waals magnets. We observe power-law relationships between the loss and both training dataset size and model capacity across a wide range of values, employing various architectures--including fully connected networks, residual networks, and vision transformers. Furthermore, the scaling exponents governing these relationships range from 1 to 2, with specific values depending on the regressed parameters and model details. The consistent scaling behaviors and their large scaling exponents suggest that the performance of deep regression models can improve substantially with increasing data size.

cs.LG↗

arXiv2024

The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes

We present numerical results for the Rosenzweig Porter model for all symmetry classes of the Dyson threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the spectral properties as measures to explore the transition from Poisson to Wigner Dyson WD statistics. Furthermore, we performed thorough studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback Leibler KL divergences and the fidelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a finite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

cond-mat.stat-mech↗

arXiv2023

Machine learning wave functions to identify fractal phases

We demonstrate that an image recognition algorithm based on a convolutional neural network provides a powerful procedure to differentiate between ergodic, non-ergodic extended (fractal) and localized phases in various systems: single-particle models, including random-matrix and random-graph models, and many-body quantum systems. The network can be successfully trained on a small data set of only 500 wave functions (images) per class for a single model. The trained network can then be used to classify phases in the other models and is thus very efficient. We discuss the strengths and limitations of the approach.

cond-mat.dis-nn↗

arXiv2022

Delayed Thermalization in Mass-Deformed SYK

We study the thermalizing properties of the mass-deformed SYK model, in a regime of parameters where the eigenstates are ergodically extended over just portions of the full Fock space, as an all-to-all toy model of many-body localization. Our numerical results strongly support the hypothesis that, although considerably delayed, thermalization is still present in this regime. Our results add to recent studies indicating that many-body localization should be interpreted as a strict Fock-space localization.

cond-mat.str-el↗

arXiv2021

Metal-insulator transition in infinitesimally weakly disordered flatbands

We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence of (d + 1) local unitary transformations parametrized by angles $θ_i$. Without loss of generality, we consider the case of two flat bands separated by a finite gap $Δ$. The perturbed states originating from the flat bands are described by an effective tight binding network with finite on- and off-diagonal disorder strength which depends on the manifold angles $θ_i$. The original infinitesimal onsite disorder strength W is only affecting the overall scale of the effective Hamiltonian. Upon variation of the manifold angles for d = 1 and d = 2 we find that localization persists for any choice of local unitaries, and the localization length can be maximized for specific values of $θ_i$. Instead, in d = 3 we identify a non-perturbative metal-insulator transition upon varying the all bands flat manifold angles.

cond-mat.dis-nn↗

arXiv2021

Bethe strings in the spin dynamical structure factor of the Mott-Hubbard phase in one-dimensional fermionic Hubbard model

The spectra and role in the spin dynamical properties of bound states of elementary magnetic excitations named Bethe strings that occur in some integrable spin and electronic one-dimensional models have recently been identified and realized in several materials by experiments. Corresponding theoretical studies have usually relied on the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field. At the isotropic point, it describes the large onsite repulsion U limit of the spin degrees of freedom of the one-dimensional fermionic Hubbard model with one electron per site in a magnetic field h. In this paper we consider the thermodynamic limit and study the effects of lowering the latter quantum problem ratio u=U/4t, where t is the first-neighbor transfer integral, on the line-shape singularities in regions at and just above the lower thresholds of the transverse and longitudinal spin dynamical structure factors. The most significant spectral weight contribution from Bethe strings leads to a gapped continuum in the spectrum of the spin dynamical structure factor +-. Our study focuses on the line shape singularities at and just above the gapped lower threshold of that continuum, which have been identified in experiments. Our results are consistent with the contribution of Bethe strings to the spin dynamical structure factor zz being small at low spin densities and becoming negligible upon increasing that density. Our results provide physically important information about how electron itinerancy affects the spin dynamics.

cond-mat.str-el↗

arXiv2020

Spin-dependent two-photon Bragg scattering in the Kapitza-Dirac effect

We present the possibility of spin-dependent Kapitza-Dirac scattering based on a two-photon interaction only. The interaction scheme is inspired from a Compton scattering process, for which we explicitly show the mathematical correspondence to the spin-dynamics of an electron diffraction process in a standing light wave. The spin effect has the advantage that it already appears in a Bragg scattering setup with arbitrary low field amplitudes, for which we have estimated the diffraction count rate in a realistic experimental setup at available X-ray free-electron laser facilities.

quant-ph↗

arXiv2019

Effects of finite-range interactions on the one-electron spectral properties of TTF-TCNQ

The electronic dispersions of the quasi-one-dimensional organic conductor TTF-TCNQ are studied by angle-resolved photoelectron spectroscopy (ARPES) with higher angular resolution and accordingly smaller step width than in previous studies. Our experimental results suggest that a refinement of the single-band 1D Hubbard model that includes finite-range interactions is needed to explain these photoemission data. To account for the effects of these finite-range interactions we employ a mobile quantum impurity scheme that describes the scattering of fractionalized particles at energies above the standard Tomonaga-Luttinger liquid limit. Our theoretical predictions agree quantitatively with the location in the $(k,ω)$ plane of the experimentally observed ARPES structures at these higher energies. The nonperturbative microscopic mechanisms that control the spectral properties are found to simplify in terms of the exotic scattering of the charge fractionalized particles. We find that the scattering occurs in the unitary limit of (minus) infinite scattering length, which limit occurs within neutron-neutron interactions in shells of neutron stars and in the scattering of ultracold atoms but not in perturbative electronic condensed-matter systems. Our results provide important physical information on the exotic processes involved in the finite-range electron interactions that control the high-energy spectral properties of TTF-TCNQ. Our results also apply to a wider class of 1D and quasi-1D materials and systems that are of theoretical and potential technological interest.

cond-mat.str-el↗

arXiv2019

Robust one-dimensionality at twin-grain-boundaries in MoSe$_{2}$

We show that 1D electron states confined at twin-grain-boundaries in MoSe$_{2}$ can be modeled by a three-orbital tight binding model including a minimum set of phenomenological hopping terms. The confined states are robust to the details of the defect hopping model, which agrees with their experimental ubiquity. Despite a valley Chern number which is finite and opposite on both sides of the defect, there is no topological protection of the confined states. This turns out to be an essential feature to have only one confined electronic band, in agreement with experiments, instead of two, as the bulk-edge correspondence would imply. Modeling the confined state as a 1D interacting electronic system allows us to unveil a mobile quantum impurity type behavior at energy scales beyond the Tomonaga-Luttinger liquid with an interaction range which extends up to the lattice spacing, in excellent agreement with ARPES measurements.

cond-mat.mes-hall↗

arXiv2019

Edge and bulk localization of Floquet topological superconductors

We study the bulk and edge properties of a driven Kitaev chain, where the driving is performed as instantaneous quenches of the on-site energies. We identify three periodic driving regimes: low period, which is equivalent to a static model, with renormalized parameters obtained from the Baker-Campbell-Hausdorff (BCH) expansion; intermediate period, where the first order BCH expansion breaks down; and high period when the quasienergy gap at $ω/2$ closes. We investigate the dynamical localization properties for the case of quasiperiodic potential driving as a function of its amplitude and the pairing strength, obtaining regimes with extended, critical and localized bulk states, if the driving is performed at high frequencies. In these, we characterize wave-packet propagation, obtaining ballistic, subdiffusive and absence of spreading, respectively. In the intermediate period regime, we find an additional region in the phase diagram with a mobility edge between critical and localized states. Further, we investigate the stability of these phases under time-aperiodicity on the drivings, observing that the system eventually thermalizes: It results in featureless random states which can be described by the symmetry of the Hamiltonian. In a system with open edges, we find that both Majorana and fermionic localized edge modes can be engineered with a spatially quasiperiodic potential. Besides, we demonstrate the possibility of creating multiple Majorana $0$ and $π$ modes in a driven setting, even if the underlying static Hamiltonian is in its trivial phase. Lastly, we study the robustness of the Majorana modes against the aperiodicity in the driving period, showing that the ones created via quasiperiodic potential are more robust to the decoherence. Moreover, we find an example where Majorana mode is robust, provided that it is chosen from a special point in the topological region.

cond-mat.supr-con↗

arXiv2017

Angle resolved photoemission spectroscopy reveals spin charge separation in metallic MoSe2 grain boundary

Material line defects are one-dimensional structures but the search and proof of electron behaviour consistent with the reduced dimension of such defects has been so far unsuccessful. Here we show using angle resolved photoemission spectroscopy that twin-grain boundaries in the layered semiconductor MoSe2 exhibit parabolic metallic bands. The one-dimensional nature is evident from a charge density wave transition, whose periodicity is given by kF/π, consistent with scanning tunneling microscopy and angle resolved photoemission measurements. Most importantly, we provide evidence for spin- and charge-separation, the hallmark of one-dimensional quantum liquids. Our studies show that the spectral line splits into distinctive spinon and holon excitations whose dispersions exactly follow the energy-momentum dependence calculated by a Hubbard model with suitable finite-range interactions. Our results also imply that quantum wires and junctions can be isolated in line defects of other transition metal dichalcogenides, which may enable quantum transport measurements and devices.

cond-mat.str-el↗