Publications

Order by: publication date number of citations

• R-matrices and Miura operators in 5d Chern-Simons theory

  Nafiz Ishtiaque, Saebyeok Jeong, Yehao Zhou

  SciPost Phys. Core 8, 003 (2025) · published 13 January 2025 | Toggle abstract · pdf

  We derive Miura operators for $W$- and $Y$-algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative $\mathfrak{gl}(1)$ Chern-Simons theory. The expectation value, viewed as the transition amplitude for states in the defect theories forming representations of the affine Yangian of $\mathfrak{gl}(1)$, satisfies the Yang-Baxter equation and is thus interpreted as an R-matrix. To achieve this, we identify the representations associated with the line and surface defects by calculating the operator product expansions (OPEs) of local operators on the defects, as conditions that anomalous Feynman diagrams cancel each other. We then evaluate the expectation value of the defect intersection using Feynman diagrams. When the line and surface defects are specified, we demonstrate that the expectation value precisely matches the Miura operators and their products.

  2 citations

• Fermionic tensor network methods

  Quinten Mortier, Lukas Devos, Lander Burgelman, Bram Vanhecke, Nick Bultinck, Frank Verstraete, Jutho Haegeman, Laurens Vanderstraeten

  SciPost Phys. 18, 012 (2025) · published 10 January 2025 | Toggle abstract · pdf

  We show how fermionic statistics can be naturally incorporated in tensor networks on arbitrary graphs through the use of graded Hilbert spaces. This formalism allows the use of tensor network methods for fermionic lattice systems in a local way, avoiding the need of a Jordan-Wigner transformation or the explicit tracking of leg crossings by swap gates in 2D tensor networks. The graded Hilbert spaces can be readily integrated with other internal and lattice symmetries, and only require minor extensions to an existing tensor network software package. We review and benchmark the fermionic versions of common algorithms for matrix product states and projected entangled-pair states.

  8 citations

• Universal performance gap of neural quantum states applied to the Hofstadter-Bose-Hubbard model

  Eimantas Ledinauskas, Egidijus Anisimovas

  SciPost Phys. 18, 011 (2025) · published 10 January 2025 | Toggle abstract · pdf

  Neural Quantum States (NQS) have demonstrated significant potential in approximating ground states of many-body quantum systems, though their performance can be inconsistent across different models. This study investigates the performance of NQS in approximating the ground state of the Hofstadter-Bose-Hubbard (HBH) model, an interacting boson system on a two-dimensional square lattice with a perpendicular magnetic field. Our results indicate that increasing magnetic flux leads to a substantial increase in energy error, up to three orders of magnitude. Importantly, this decline in NQS performance is consistent across different optimization methods, neural network architectures, and physical model parameters, suggesting a significant challenge intrinsic to the model. Despite investigating potential causes such as wave function phase structure, quantum entanglement, fractional quantum Hall effect, and the variational loss landscape, the precise reasons for this degradation remain elusive. The HBH model thus proves to be an effective testing ground for exploring the capabilities and limitations of NQS. Our study highlights the need for advanced theoretical frameworks to better understand the expressive power of NQS which would allow a systematic development of methods that could potentially overcome these challenges.

• Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach

  Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov

  SciPost Phys. 18, 010 (2025) · published 10 January 2025 | Toggle abstract · pdf

  By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tails. This makes the standard Hubbard-Stratonovich transformation inapplicable to such problems. We used, instead, the functional Hubbard-Stratonovich transformation which allowed to solve the problem analytically for large sizes of matrices. We show that $\rho(E)$ depends crucially on the control parameter that drives the system through the transition between the ergodic and the fractal phases and it can be used as an order parameter.

  2 citations

• Codebase release 1.0 for QDarts

  Jan A. Krzywda, Weikun Liu, Evert van Nieuwenburg, Oswin Krause

  SciPost Phys. Codebases 43-r1.0 (2025) · published 9 January 2025 | Toggle abstract · src

  We present QDarts, an efficient simulator for realistic charge stability diagrams of quantum dot array (QDA) devices in equilibrium states. It allows for pinpointing the location of concrete charge states and their transitions in a high-dimensional voltage space (via arbitrary two-dimensional cuts through it), and includes effects of finite tunnel coupling, non-constant charging energy and a simulation of noisy sensor dots. These features enable close matching of various experimental results in the literature, and the package hence provides a flexible tool for testing QDA experiments, as well as opening the avenue for developing new methods of device tuning.

  1 citation

• QDarts: A quantum dot array transition simulator for finding charge transitions in the presence of finite tunnel couplings, non-constant charging energies and sensor dots

  Jan A. Krzywda, Weikun Liu, Evert van Nieuwenburg, Oswin Krause

  SciPost Phys. Codebases 43 (2025) · published 9 January 2025 | Toggle abstract · pdf

  We present QDarts, an efficient simulator for realistic charge stability diagrams of quantum dot array (QDA) devices in equilibrium states. It allows for pinpointing the location of concrete charge states and their transitions in a high-dimensional voltage space (via arbitrary two-dimensional cuts through it), and includes effects of finite tunnel coupling, non-constant charging energy and a simulation of noisy sensor dots. These features enable close matching of various experimental results in the literature, and the package hence provides a flexible tool for testing QDA experiments, as well as opening the avenue for developing new methods of device tuning.

  1 citation

• Excitonic Bloch equations from first principles

  Gianluca Stefanucci, Enrico Perfetto

  SciPost Phys. 18, 009 (2025) · published 9 January 2025 | Toggle abstract · pdf

  The ultrafast conversion of coherent excitons into incoherent excitons, as well as the subsequent exciton diffusion and thermalization, are central topics in current scientific research due to their relevance in optoelectronics, photovoltaics and photocatalysis. Current approaches to the exciton dynamics rely on model Hamiltonians that depend on already screened electron-electron and electron-phonon couplings. In this work, we subject the state-of-the-art methods to scrutiny using the ab initio Hamiltonian for electrons and phonons. We offer a rigorous and intuitive proof demonstrating that the exciton dynamics governed by model Hamiltonians is affected by an overscreening of the electron-phonon interaction. The introduction of an auxiliary exciton species, termed the irreducible exciton, enables us to formulate a theory free from overscreening and derive the excitonic Bloch equations. These equations describe the time-evolution of coherent, irreducible, and incoherent excitons during and after the optical excitation. They are applicable beyond the linear regime, and predict that the total number of excitons is preserved when the external fields are switched off.

  5 citations

• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories

  Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng

  SciPost Phys. 18, 008 (2025) · published 9 January 2025 | Toggle abstract · pdf

  We explore exact generalized symmetries in the standard 2+1d lattice $\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. The non-invertible algebra involves a lattice condensation operator, which creates a toric code ground state from a product state. Another model has a mixed anomaly between a 1-form symmetry and an ordinary symmetry. This anomaly enforces a nontrivial transition in the phase diagram, consistent with the "Higgs=SPT" proposal. Finally, we discuss how the symmetries and anomalies in these two models are related by gauging, which is a 2+1d version of the Kennedy-Tasaki transformation.

  23 citations

• Compactness of quantics tensor train representations of local imaginary-time propagators

  Haruto Takahashi, Rihito Sakurai, Hiroshi Shinaoka

  SciPost Phys. 18, 007 (2025) · published 8 January 2025 | Toggle abstract · pdf

  Space-time dependence of imaginary-time propagators, vital for ab initio and many-body calculations based on quantum field theories, has been revealed to be compressible using Quantum Tensor Trains (QTTs) [Phys. Rev. X 13, 021015 (2023)]. However, the impact of system parameters, like temperature, on data size remains underexplored. This paper provides a comprehensive numerical analysis of the compactness of local imaginary-time propagators in QTT for one-time/-frequency objects and two-time/-frequency objects, considering truncation in terms of the Frobenius and maximum norms. To study worst-case scenarios, we employ random pole models, where the number of poles grows logarithmically with the inverse temperature and coefficients are random. The Green's functions generated by these models are expected to be more difficult to compress than those from physical systems. The numerical analysis reveals that these propagators are highly compressible in QTT, outperforming the state-of-the-art approaches such as intermediate representation and discrete Lehmann reprensentation. For one-time/-frequency objects and two-time/-frequency objects, the bond dimensions saturate at low temperatures, especially for truncation in terms of the Frobenius norm. We provide counting-number arguments for the saturation of bond dimensions for the one-time/-frequency objects, while the origin of this saturation for two-time/-frequency objects remains to be clarified. This paper's findings highlight the critical need for further research on the selection of truncation methods, tolerance levels, and the choice between imaginary-time and imaginary-frequency representations in practical applications.

  9 citations

• Enhancement of stability of metastable states in the presence of Lévy noise

  Alexander A. Dubkov, Claudio Guarcello, Bernardo Spagnolo

  SciPost Phys. 18, 006 (2025) · published 8 January 2025 | Toggle abstract · pdf

  The barrier-crossing event for superdiffusion characterized by symmetric Lévy flights is analyzed. Starting from the fractional Fokker-Planck equation, we derive an integro-differential equation along with the necessary conditions to calculate the mean residence time of a particle within a fixed interval. We consider an arbitrary smooth potential profile, particularly metastable, with a sink and Lévy noise characterized by both an arbitrary index $\alpha$ and arbitrary noise intensity parameter. For the specific case of Lévy flights with an index $\alpha = 1$ and a cubic metastable potential, a closed expression for the mean residence time is obtained in quadratures. The analytical results reveal an enhancement of the mean residence time in the metastable state due to the influence of Lévy noise.

  10 citations