Publications

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Gate-defined Kondo lattices with valley-helical quantum dot arrays

Antonio L. R. Manesco

SciPost Phys. 19, 024 (2025) · published 18 July 2025 | · pdf

Kondo physics and heavy-fermion behavior has been predicted and observed in moiré materials. The electric tunability of moiré materials allows an in-situ study of Kondo lattices' phase diagrams, which is not possible with their intermetallic counterparts. However, moiré platforms rely on twisting, which introduces twisting angle disorder and undesired buckling. Here we propose device layouts for one- and two-dimensional gate-defined superlattices in Bernal bilayer graphene where localized states couple to dispersive valley-helical modes. We show that, under electronic interactions, these superlattices are described by an electrically-tunable Kondo-Heisenberg model.

1 citation
Anderson impurities in edge states with nonlinear and dissipative perturbations

Vinayak M. Kulkarni, N. S. Vidhyadhiraja

SciPost Phys. 19, 036 (2025) · published 13 August 2025 | · pdf

We show that exceptional points (EPs) and non-Hermitian behavior can emerge dynamically in impurity models with Hermitian microscopic origins. Using perturbative renormalization group (RG) analysis, Fock-space diagonalization, and spin-spin relaxation time calculations, we demonstrate that nonlinear (NL) dispersion and anisotropic pseudochiral ($\mathcal{PC}$) interactions generate complex fixed points and spectral defectiveness. The effective Kondo model features a square-root RG invariant linking planar and longitudinal Dzyaloshinskii-Moriya (DM) couplings, driving the onset of EPs. Our analysis reveals dissipative fixed points stabilized by an emergent Lie algebra structure and a scaling collapse in relaxation dynamics. Across both single- and two-impurity extensions, we identify a universal "sign-reversion" (SR) regime near critical NL coupling, where anisotropy preserves $\mathcal{PC}$ symmetry and SR serves as a signature of non-Hermitian flow. These results establish a new class of non-Hermitian criticality generated through RG evolution in otherwise Hermitian systems.

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Properties of fermionic systems with the path-integral ground state method

Sebastian Ujevic, Vinicius Zampronio, Bruno R. de Abreu, Silvio A. Vitiello

SciPost Phys. Core 6, 031 (2023) · published 20 April 2023 | · pdf

We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure $^4$He systems demonstrate most of the features of the method. Complementarily, for pure $^3$He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate $^3$He-$^4$He mixtures, demonstrating the method's robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature $T = 0$ without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the $^3$He kinetic energy in the mixture.

1 citation
Scattering theory of higher order topological phases

R. Johanna Zijderveld, Isidora Araya Day, Anton R. Akhmerov

SciPost Phys. 19, 058 (2025) · published 27 August 2025 | · pdf

The surface states of intrinsic higher order topological phases are protected by the spatial symmetries of a finite sample. This property makes the existing scattering theory of topological invariants inapplicable: the scattering geometry is either incompatible with the symmetry or does not probe the bulk topology. We resolve this obstacle by using a symmetric scattering geometry that probes transport from the inside to the outside of the sample. We demonstrate that the intrinsic higher order topology is captured by the flux dependence of the reflection matrix. Our finding follows from identifying the spectral flow of a flux line as a signature of higher order topology. We show how this scattering approach applies to several examples of higher order topological insulators and superconductors. Our theory provides an alternative approach for proving bulk-edge correspondence in intrinsic higher order topological phases, especially in the presence of disorder.

1 citation
Downfolding the Su-Schrieffer-Heeger model

Arne Schobert, Jan Berges, Tim Wehling, Erik van Loon

SciPost Phys. 11, 079 (2021) · published 20 October 2021 | · pdf

Charge-density waves are responsible for symmetry-breaking displacements of atoms and concomitant changes in the electronic structure. Linear response theories, in particular density-functional perturbation theory, provide a way to study the effect of displacements on both the total energy and the electronic structure based on a single ab initio calculation. In downfolding approaches, the electronic system is reduced to a smaller number of bands, allowing for the incorporation of additional correlation and environmental effects on these bands. However, the physical contents of this downfolded model and its potential limitations are not always obvious. Here, we study the potential-energy landscape and electronic structure of the Su-Schrieffer-Heeger (SSH) model, where all relevant quantities can be evaluated analytically. We compare the exact results at arbitrary displacement with diagrammatic perturbation theory both in the full model and in a downfolded effective single-band model, which gives an instructive insight into the properties of downfolding. An exact reconstruction of the potential-energy landscape is possible in a downfolded model, which requires a dynamical electron-biphonon interaction. The dispersion of the bands upon atomic displacement is also found correctly, where the downfolded model by construction only captures spectral weight in the target space. In the SSH model, the electron-phonon coupling mechanism involves exclusively hybridization between the low- and high-energy bands and this limits the computational efficiency gain of downfolded models.

1 citation
Codebase release 5.3 for EDIpack

Lorenzo Crippa, Igor Krivenko, Samuele Giuli, Gabriele Bellomia, Alexander Kowalski, Francesco Petocchi, Alberto Scazzola, Markus Wallerberger, Giacomo Mazza, Luca de Medici, Giorgio Sangiovanni, Massimo Capone, Adriano Amaricci

SciPost Phys. Codebases 58-r5.3 (2025) · published 24 September 2025 | · src

We present a next-generation version of EDIpack, a flexible, high-performance numerical library using Lanczos-based exact diagonalization to solve generic quantum impurity problems, such as those introduced in Dynamical Mean-Field Theory to describe extended strongly correlated materials. This new release efficiently solves impurity problems allowing for different broken-symmetry solutions, including superconductivity, featuring local spin-orbit coupling and/or electron-phonon coupling. It provides quick access to dynamical correlation functions on the entire complex frequency plane at zero and low-temperatures. The modular architecture of the software not only provides Fortran APIs but also includes bindings to C/C++, interfaces with Python and Julia or with TRIQS and w2dynamics research platforms, thus ensuring unprecedented level of inter-operability. The outlook includes further extensions to study quantum materials and cold atoms quantum simulators, as well as quantum information applications.

1 citation
Exact diagonalization, matrix product states and conformal perturbation theory study of a 3D Ising fuzzy sphere model

Andreas M. Läuchli, Loïc Herviou, Patrick H. Wilhelm, Slava Rychkov

SciPost Phys. 19, 076 (2025) · published 26 September 2025 | · pdf

Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to infinite-volume CFT data is facilitated by choosing the sphere $S^{d-1}$ as the spatial manifold. Recently, the fuzzy sphere regulator [Zhu et al, Phys. Rev. X 13, 021009 (2023)] has enabled such studies with exact rotational invariance, yielding impressive agreement with known 3D Ising CFT predictions, as well as new results. However, systematic improvements and a deeper understanding of finite-size corrections remain essential. In this work, we revisit the fuzzy sphere regulator, focusing on the original Ising model, with two main goals. First, we assess the robustness of this approach using Conformal Perturbation Theory (CPT), to which we provide a detailed guidebook. We demonstrate how CPT provides a unified framework for determining the critical point, the speed of light, and residual deviations from CFT predictions. Applying this framework, we study finite-size corrections and clarify the role of tuning the model in minimizing these effects. Second, we develop a novel method for extracting Operator Product Expansion (OPE) coefficients from fuzzy sphere data. This method leverages the sensitivity of energy levels to detuning from criticality, providing new insights into level mixing and avoided crossings in finite systems. Our work also includes validation of CPT in a 1+1D Ising model away from the integrable limit.

1 citation
A real-time approach to frequency-mixing spectroscopies: Application to sum and difference frequency generation in two-dimensional crystals

Mike N. Pionteck, Myrta Grüning, Simone Sanna, Claudio Attaccalite

SciPost Phys. 19, 129 (2025) · published 18 November 2025 | · pdf

We propose a computational framework to extract nonlinear response functions from real-time simulations in the presence of more than one external field. We apply this approach to the calculation of sum frequency generation (SFG) and difference frequency generation (DFG). SFG and DFG are second-order nonlinear processes where two lasers with frequencies $\omega_1$ and $\omega_2$ combine to produce a response at frequency $\omega = \omega_1 ± \omega_2$. Compared with other nonlinear responses such as second-harmonic generation, SFG and DFG allow for tunability over a larger range. Moreover, the optical response can be enhanced by selecting the two laser frequencies in order to match specific electron-hole transitions. To assess the approach, we calculate the SFG and DFG of two-dimensional crystals, h-BN and MoS$_2$ monolayers, from real-time solution of an effective Schrödinger equation. Within the effective Schrödinger equation, one can select from various levels of theory for the effective one-particle Hamiltonian to account for local-field effects and electron-hole interactions. We compare results obtained within the independent particle picture and including many-body effects. Such comparison allows us to identify and characterize excitonic features in the obtained spectra. Additionally, we demonstrate that our approach can also extract higher-order response functions, such as field-induced second-harmonic generation. We provide an example using the h-BN bilayer.

1 citation
LiHoF4 as a spin-half non-standard quantum Ising system

Tomer Dollberg, Moshe Schechter

SciPost Phys. 17, 028 (2024) · published 31 July 2024 | · pdf

LiHoF$_{4}$ is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of LiHoF$_{4}$ using the quantum Ising model has shown discrepancies in its phase diagram, particularly in the regime dominated by thermal fluctuations. In this study, we investigate the role of off-diagonal dipolar terms in LiHoF$_{4}$, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of LiHoF$_{4}$, including the off-diagonal dipolar terms perturbatively, both in the absence and presence of a transverse field. Our results encompass the full \boldmath{$B_{x}-T$} phase diagram, confirming the significance of the off-diagonal dipolar terms in reducing the zero-field critical temperature and determining the critical temperature's dependence on the transverse field. We also highlight the sensitivity of this mechanism to the crystal structure by comparing our calculations with the Fe$_{8}$ system.

1 citation
Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

Alexander Nikolaenko, Ya-Hui Zhang

SciPost Phys. 17, 034 (2024) · published 5 August 2024 | · pdf

Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling $J_K$ at fixed doping x. At large positive $J_K$, we confirm the expected conventional Luttinger liquid phase with $2k_F=\frac{1+x}{2}$ (in units of $2\pi$), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the $J_K ≤ 0$ side, our simulation finds the existence of a fractional Luttinger liquid (LL$\star$) phase with $2k_F=\frac{x}{2}$, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL$\star$) phase in higher dimensions. The LL$\star$ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive $J_K$. Then we mainly focus on the "critical regime" between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of $J_K$, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around $0.035 J$) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent $z=+$. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

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