arXiv subjects

Gergely Barcza

Publications and source records attributed to Gergely Barcza.

At least 19 recordsLinked to original sources

arXiv2026

Shuttling of $\mathbb{Z}_4$ parafermions in an electronic ladder model

Parafermions with non-Abelian statistics have been proposed as a promising platform for quantum computation, potentially enabling a broader set of topologically protected gates than Majorana fermions. The experimental and theoretical exploration of these exotic quasiparticles remains challenging, as their stability is linked to strong electron-electron interactions. A key step toward practical applications is the controlled shuttling of parafermionic modes, which is required for implementing geometric braiding operations. In the present work, we investigate the real-time dynamics of the elementary shuttling process by applying a combination of the density matrix renormalization group and the time-dependent variational principle approaches. We analyze the transport of $\mathbb{Z}_4$ parafermion edge states and assess the corresponding adiabatic speed limit under experimentally relevant conditions.

cond-mat.str-el↗

arXiv2026

An extended ab initio theory of the V$_{\text{B}}^-$ center in hBN: excited states, Jahn-Teller distortion, and pressure dependence

Ensembles of negatively charged boron vacancy (V$_{\text{B}}^-$) centers in hexagonal boron nitride (hBN) have emerged as a two-dimensional spin qubit system interfaced with optics to advance nanoscale quantum sensing. However, a comprehensive description of its optically detected magnetic resonance (ODMR) signal remains challenging due to the strongly correlated nature of the excited electronic states involved in its optical cycle. In this work, we model the energetics, structural relaxation, and transition rates of the V$_{\text{B}}^-$ center using a high-level wave-function-based electron correlation method (CASSCF-NEVPT2). We provide a thorough analysis of the excited state fine structure and pseudo Jahn-Teller effects, singlet-triplet quasi-degeneracies, photoluminescence parameters, intersystem crossing pathways, and stress-dependence of the fine structure and decay parameters. Our findings not only clarify the fundamental behavior of the V$_{\text{B}}^-$ center in hBN but also establish the theoretical foundation for advancing the V$_{\text{B}}^-$ center's readout for integrated 2D quantum sensors.

cond-mat.mtrl-sci↗

arXiv2025

Assessing the Reliability of Truncated Coupled Cluster Wavefunction: Estimating the Distance from the Exact Solution

A new approach is proposed to assess the reliability of the truncated wavefunction methods by estimating the deviation from the full configuration interaction (FCI) wavefunction. While typical multireference diagnostics compare some derived property of the solution with the ideal picture of a single determinant, we try to answer a more practical question, how far is the solution from the exact one. Using the density matrix renormalization group (DMRG) method to provide an approximate FCI solution for the self-consistently determined relevant active space, we compare the low-level CI expansions and one-body reduced density matrixes to determine the distance of the two solutions ($\tilde{d}_\Phi$, $\tilde{d}_\gamma$). We demonstrate the applicability of the approach for the CCSD method by benchmarking on the W4-17 dataset, as well as on transition metal-containing species. We also show that the presented moderate-cost, purely wavefunction-based metric is truly unique in the sense that it does not correlate with any popular multireference measures. We also explored the usage of CCSD natural orbitals ($\tilde{d}_{\gamma,\mathrm{NO}}$) and its effect on the active space size and the metric. The proposed diagnostic can also be applied to other wavefunction approximations, and it has the potential to provide a quality measure for post-Hartree-Fock procedures in general.

physics.chem-ph↗

arXiv2025

Identifying high-energy electronic states of NV$^-$ centers in diamond

The negatively charged nitrogen-vacancy center in diamond is a prototype photoluminescent point defect spin qubit with promising quantum technology applications, enabled by its efficient optical spin polarization and readout. Its low-lying electronic states and optical spin polarization cycle have been well characterized over decades, establishing it as a benchmark system for state-of-the-art computational methods in point defect research. While the optical cycle is well understood, a comprehensive energetic analysis of higher-lying states has received less attention until recently. In this joint experimental theoretical study, we identify and characterize five high-energy states beyond those involved in the optical cycle. Using transient absorption spectroscopy, we determine their transition energies and relative oscillator strengths. Additionally, we perform two independent numerical studies employing two state-of-the-art post-DFT methods to support the experimental findings and assign energy levels. These results enhance our understanding of the NV center's energy spectrum and providing a broader reference for benchmarking high-level first-principles methods.

cond-mat.mtrl-sci↗

arXiv2024

A simple electronic ladder model harboring $\mathbb{Z}_4$ parafermions

Parafermions are anyons with the potential for realizing non-local qubits that are resilient to local perturbations. Compared to Majorana zero modes, braiding of parafermions implements an extended set of topologically protected quantum gates. This, however, comes at the price that parafermionic zero modes can not be realized in the absence of strong interactions whose theoretical description is challenging. In the present work, we construct a simple lattice model for interacting spinful electrons with parafermionic zero energy modes. The explicit microscopic nature of the considered model highlights new realization avenues for these exotic excitations in recently fabricated quantum dot arrays. By density matrix renormalization group calculations, we identify a broad range of parameters, with well-localized zero modes, whose parafermionic nature is substantiated by their unique $8π$ periodic Josephson spectrum.

cond-mat.str-el↗

arXiv2024

A charge transfer mechanism for optically addressable solid-state spin pairs

Optically detected magnetic resonance (ODMR) with no resolvable zero-field splitting has been observed from emitters in hexagonal boron nitride across a broad range of wavelengths, but so far an understanding of their microscopic structure and the physical origin of ODMR has been lacking. Here we perform comprehensive measurements and modelling of the spin-resolved photodynamics of ensembles and single emitters, and uncover a universal model that accounts, and provides an intuitive physical explanation, for all key experimental features. The model, inspired by the radical-pair mechanism from spin chemistry, assumes a pair of nearby point defects -- a primary optically active defect and a secondary defect. Charge transfer between the two defects creates a metastable weakly coupled spin pair with ODMR naturally arising from selection rules. Using first-principle calculations, we show that simple defect pairs made of common carbon defects provide a plausible microscopic explanation. Our optical-spin defect pair (OSDP) model resolves several previously open questions including the asymmetric envelope of the Rabi oscillations, the large variability in ODMR contrast amplitude and sign, and the wide spread in emission wavelength. It may also explain similar phenomena observed in other wide bandgap semiconductors such as GaN. The presented framework will be instrumental in guiding future theoretical and experimental efforts to study and engineer solid-state spin pairs.

cond-mat.mes-hall↗

arXiv2024

Accurate and convergent energetics of color centers by wavefunction theory

Ab initio description of point defects in semiconductors, characterized by in-gap states of significant multideterminant character, presents a longstanding theoretical challenge for density functional theory (DFT) methods. In this study, we devise a wavefunction theory (WFT) based ab initio methodology as a competing alternative approach. Specifically, we apply perturbation theory (NEVPT2 level) on top of a defect-localized many-body wavefunction (CASSCF level), which provides a balanced description of dynamic and static correlation effects, respectively. This quantum chemical methodology, exemplified for the NV$^-$ center in diamond in this study, is not only used for the calculation of energies and properties, but also for geometry optimization, performed for each electronic state individually. By relaxing cluster models of increasing size and investigating convergence behavior, we quantitatively reproduce (i) the full energy spectrum of NV$^-$ including the recently characterized high-energy states, (ii) the effect of Jahn-Teller distortion on measurable properties, (iii) the fine structure of ground and excited states, (iv) the pressure dependence of zero-phonon lines. Our findings showcase that applying conventional wave-function-based quantum chemistry on carefully crafted clusters can be a robust routine tool for discussing defect-state energetics.

cond-mat.mtrl-sci↗

arXiv2024

Carbon-contaminated topological defects in hexagonal boron nitride for quantum photonics

Topological defects, such as Stone-Wales defects and grain boundaries, are common in 2D materials. In this study, we investigate the intricate interplay of topological defects and carbon contamination in hexagonal boron nitride revealing an intriguing class of color centers. We demonstrate that both carbon contamination and strain can stabilize Stone-Wales configurations and give rise to emitters with desirable optical properties in the visible spectral range. Inspired by these results, we further demonstrate that carbon atoms at grain boundaries can resolve energetic B-B and N-N bonds leading to highly favorable atomic structures that may facilitate the accumulation of carbon contamination at the boundaries. Similarly to contaminated Stone-Wales defects, carbon-doped grain boundaries can also give rise to color centers emitting in the visible spectral range with short radiative lifetime and high Debye-Waller factors. Our discoveries shed light on an exciting class of defects and pave the way toward the identification of color centers and single photon emitters in hBN.

cond-mat.mtrl-sci↗

arXiv2023

First principles theory of the nitrogen interstitial in hBN: a plausible model for the blue emitter

Color centers in hexagonal boron nitride (hBN) have attracted considerable attention due to their remarkable optical properties enabling robust room temperature photonics and quantum optics applications in the visible spectral range. On the other hand, identification of the microscopic origin of color centers in hBN has turned out to be a great challenge that hinders in-depth theoretical characterization, on-demand fabrication, and development of integrated photonic devices. This is also true for the blue emitter, which is an irradiation damage in hBN emitting at 436 nm wavelengths with desirable properties. Here, we propose the negatively charged nitrogen split interstitial defect in hBN as a plausible microscopic model for the blue emitter. To this end, we carry out a comprehensive first principles theoretical study of the nitrogen interstitial. We carefully analyze the accuracy of first principles methods and show that the commonly used HSE hybrid exchange-correlation functional fails to describe the electronic structure of this defect. Using the generalized Koopman's theorem, we fine tune the functional and obtain a zero-phonon photoluminescence (ZPL) energy in the blue spectral range. We show that the defect exhibits high emission rate in the ZPL line and features a characteristic phonon side band that resembles the blue emitter's spectrum. Furthermore, we study the electric field dependence of the ZPL and numerically show that the defect exhibits a quadratic Stark shift for perpendicular to plane electric fields, making the emitter insensitive to electric field fluctuations in first order. Our work emphasize the need for assessing the accuracy of common first principles methods in hBN and exemplifies a workaround methodology. Furthermore, our work is a step towards understanding the structure of the blue emitter and utilizing it in photonics applications.

cond-mat.mtrl-sci↗

arXiv2023

Predicting the FCI energy of large systems to chemical accuracy from restricted active space density matrix renormalization group calculations

We theoretically derive and validate with large scale simulations a remarkably accurate power law scaling of errors for the restricted active space density matrix renormalization group (DMRG-RAS) method [arXiv:2111.06665] in electronic structure calculations. This yields a new extrapolation method, DMRG-RAS-X, which reaches chemical accuracy for strongly correlated systems such as the Chromium dimer, dicarbon up to a large cc-pVQZ basis, and even a large chemical complex like the FeMoco with significantly lower computational demands than previous methods. The method is free of empirical parameters, performed robustly and reliably in all examples we tested, and has the potential to become a vital alternative method for electronic structure calculations in quantum chemistry, and more generally for the computation of strong correlations in nuclear and condensed matter physics.

physics.chem-ph↗

arXiv2023

Symmetric carbon tetramers forming chemically stable spin qubits in hBN

Point defect quantum bits in semiconductors have the potential to revolutionize sensing at atomic scales. Currently, vacancy related defects, such as the NV center in diamond and the VB$^-$ in hexagonal boron nitride (hBN), are at the forefront of high spatial resolution and low dimensional sensing. On the other hand, vacancies' reactive nature and instability at the surface limit further developments. Here, we study the symmetric carbon tetramers in hBN and propose them as a chemically stable spin qubit for sensing in low dimensions. We utilize periodic-DFT and quantum chemistry approaches to reliably and accurately predict the electronic, optical, and spin properties of the studied defect. We show that the nitrogen centered symmetric carbon tetramer gives rise to spin state dependent optical signals with strain sensitive intersystem crossing rates. Furthermore, the weak hyperfine coupling of the defect to their spin environments results in a reduced electron spin resonance linewidth that may enhance sensitivity.

cond-mat.mtrl-sci↗

arXiv2022

Towards large-scale restricted active space calculations inspired by the Schmidt decomposition

We present an alternative, memory-efficient, Schmidt decomposition-based description of the inherently bipartite restricted active space (RAS) scheme, which can be implemented effortlessly within the density matrix renormalization group (DMRG) method via the dynamically extended active space procedure. Benchmark calculations are compared against state-of-the-art results of C$_2$ and Cr$_2$, which are notorious for their multi-reference character. Our results for ground and excited states together with spectroscopic constants demonstrate that the proposed novel approach, dubbed as DMRG-RAS, which is variational and free of uncontrolled method errors, has the potential to outperfom conventional methods for strongly correlated molecules.

physics.chem-ph↗

arXiv2021

Fermionic systems for quantum information people

The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan--Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems.

quant-ph↗

arXiv2021

Quantum sensor in a single layer van der Waals material

Point defect qubits in semiconductors have demonstrated their outstanding high spatial resolution sensing capabilities of broad multidisciplinary interest. Two-dimensional (2D) semiconductors hosting such sensors have recently opened up new horizons for sensing in the subnanometer scales in 2D heterostructures. However, controlled creation of quantum sensor in a single layer 2D materials with high sensitivity has been elusive so far. Here, we report on a novel 2D quantum sensor, the VB2 centre in hexagonal boron nitride (hBN), with superior sensing capabilities. The centre's inherently low symmetry configuration gives rise to unique electronic and spin properties that implement a qubit in a 2D material with unprecedented sensitivity. The qubit is decoupled from its dense spin environment at low magnetic fields that gives rise to the reduction of the spin resonance linewidth and elongation of the coherence time. The VB2 centre is also equipped with a classical memory that can be utilized in storing population information. Using scanning transmission electron microscopy imaging, we confirm the presence of the point defect structure in free standing monolayer hBN created by electron beam irradiation. Our results provide a new material solution towards atomic-scale sensing in low dimensions.

cond-mat.mes-hall↗

arXiv2021

Sensitivity of Coupled Cluster Electronic Properties on the Reference Determinant: Can Kohn-Sham Orbitals Be More Beneficial than Hartree-Fock Orbitals?

Coupled cluster calculations are traditionally performed over Hartree-Fock reference orbitals (HF-CC methodology). However, it has been repeatedly argued in the literature that the use of a Kohn-Sham reference (KS-CC methodology) might result in improved performance relative to HF-CC at the same computational cost. In the present theoretical study, we re-examine the relation of HF-CC and KS-CC methods by comparing the results of widely applied truncated CC calculations (CCSD, CCSD(T), CCSDT) to the limit of full configuration interaction (FCI), which in contrast to wave-function diagnostics with vague physical meaning or experimental data with considerable uncertainty serves as an undebatable reference point of accuracy. We find that apart from incidental exceptions, the Kohn-Sham referenced CC methods show systematic deterioration compared to HF-CC, that is, the KS-CC molecular properties (electronic energy and density) are always farther from the FCI limit than those obtained from HF-CC at the same coupled cluster level. Furthermore, the introduction of common approximations (frozen core, density fitting) to the CC calculation results in significantly higher errors in the case of KS reference. We conclude that the use of KS reference orbitals is not expected to increase the reliability of low-level CC energetics. Nevertheless, molecular errors from the components of the studied chemical reaction might fortunately cancel out resulting in illusory improvement compared to HF-CC. It is also notable that the choice of reference orbitals has negligible influence on the results at sufficiently high CC levels which can be estimated by test calculations or by the magnitude of double amplitudes. Therefore, the application of KS-CC is not unreasonable as it might bypass the difficulties of HF convergence.

physics.chem-ph↗

arXiv2020

DMRG on top of plane-wave Kohn-Sham orbitals: case study of defected boron nitride

In this paper, we analyze the numerical aspects of the inherently multi-reference density matrix renormalization group (DMRG) calculations on top of the periodic Kohn-Sham density functional theory (DFT) using the complete active space (CAS) approach. Following the technical outline related to the computation of the Hamiltonian matrix elements and to the construction of the active space, we illustrate the potential of the framework by studying the vertical many-body energy spectrum of hexagonal boron nitride (hBN) nano-flakes embedding a single boron vacancy point defect with prominent multi-reference character. We investigate the consistency of the DMRG energy spectrum from the perspective of sample size, basis size, and active space selection protocol. Results obtained from standard quantum chemical atom-centered basis calculations and plane-wave based counterparts show excellent agreement. Furthermore, we also discuss the spectrum of the periodic sheet which is in good agreement with extrapolated data of finite clusters. These results pave the way toward applying DMRG method in extended correlated solid state systems, such as point qubit in wide band gap semiconductors.

cond-mat.str-el↗

arXiv2019

Symmetric single-impurity Kondo model on a tight-binding chain: a comparison of analytical and numerical ground-state approaches

We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurity-induced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model on a tight-binding chain with bandwidth $W=2{\cal D}$ and coupling strength $J_{\rm K}$. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact data obtained from the Density-Matrix Renormalization Group (DMRG) and from the Numerical Renormalization Group (NRG) methods. The Gutzwiller variational approach becomes exact in the strong-coupling limit and reproduces the ground-state properties from DMRG and NRG for large couplings. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally/locally to the impurity spin. The Yosida wave function provides qualitatively correct results in the weak-coupling limit. In DMRG, chains with about $10^3$ sites are large enough to describe the susceptibilities down to $J_{\rm K}/{\cal D}\approx 0.5$. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states $ρ_0(ε)$. To compare with results from Bethe Ansatz, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach $χ_0(J_{\rm K}\ll {\cal D})/(gμ_{\rm B})^2\approx \exp[1/(ρ_0(0)J_{\rm K})]/(2C{\cal D}\sqrt{πe ρ_0(0)J_{\rm K}})$, where $\ln(C)$ is the regularized first inverse moment of the density of states. Using NRG, we determine the universal sub-leading corrections up to second order in $ρ_0(0)J_{\rm K}$.

cond-mat.str-el↗

arXiv2019

Ab initio theory of negatively charged boron vacancy qubit in hBN

Highly correlated orbitals coupled with phonons in two-dimension are identified for paramagnetic and optically active boron vacancy in hexagonal boron nitride by first principles methods which are responsible for recently observed optically detected magnetic resonance signal. We report ab initio analysis of the correlated electronic structure of this center by density matrix renormalization group and Kohn-Sham density functional theory methods. By establishing the nature of the bright and dark states as well as the position of the energy levels, we provide a complete description of the magneto-optical properties and corresponding radiative and non-radiative routes which are responsible for the optical spin polarization and spin dependent luminescence of the defect. Our findings pave the way toward advancing the identification and characterization of room temperature quantum bits in two-dimensional solids.

cond-mat.mes-hall↗