Publications

Order by: publication date number of citations

• Greedy optimization of the geometry of Majorana Josephson junctions

  André Melo, Tanko Tanev, Anton R. Akhmerov

  SciPost Phys. 14, 047 (2023) · published 23 March 2023 | Toggle abstract · pdf

  Josephson junctions in a two-dimensional electron gas with spin-orbit coupling are a promising candidate to realize topological superconductivity. While it is known that the geometry of the junction strongly influences the size of the topological gap, the question of how to construct optimal geometries remains unexplored. We introduce a greedy numerical algorithm to optimize the shape of Majorana junctions. The core of the algorithm relies on perturbation theory and is embarrassingly parallel, which allows it to explore the design space efficiently. By introducing stochastic variations in the junction Hamiltonian, we avoid overfitting geometries to specific system parameters. Furthermore, we constrain the optimizer to produce smooth geometries by applying image filtering and fabrication resolution constraints. We run the algorithm in various setups and find that it reliably produces geometries with increased topological gaps over large parameter ranges. The results are robust to variations in the optimization starting point and the presence of disorder, which suggests the optimizer is capable of finding global maxima.

  2 citations

• Deconfined quantum criticality in the long-range, anisotropic Heisenberg chain

  Anton Romen, Stefan Birnkammer, Michael Knap

  SciPost Phys. Core 7, 008 (2024) · published 22 February 2024 | Toggle abstract · pdf

  Deconfined quantum criticality describes continuous phase transitions that are not captured by the Landau-Ginzburg paradigm. Here, we investigate deconfined quantum critical points in the long-range, anisotropic Heisenberg chain. With matrix product state simulations, we show that the model undergoes a continuous phase transition from a valence bond solid to an antiferromagnet. We extract the critical exponents of the transition and connect them to an effective field theory obtained from bosonization techniques. We show that beyond stabilizing the valance bond order, the long-range interactions are irrelevant and the transition is well described by a double frequency sine-Gordon model. We propose how to realize and probe deconfined quantum criticality in our model with trapped-ion quantum simulators.

  2 citations

• Ab initio electron-lattice downfolding: Potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials

  Arne Schobert, Jan Berges, Erik G. C. P. van Loon, Michael A. Sentef, Sergey Brener, Mariana Rossi, Tim O. Wehling

  SciPost Phys. 16, 046 (2024) · published 9 February 2024 | Toggle abstract · pdf

  The interplay of electronic and nuclear degrees of freedom presents an outstanding problem in condensed matter physics and chemistry. Computational challenges arise especially for large systems, long time scales, in nonequilibrium, or in systems with strong correlations. In this work, we show how downfolding approaches facilitate complexity reduction on the electronic side and thereby boost the simulation of electronic properties and nuclear motion-in particular molecular dynamics (MD) simulations. Three different downfolding strategies based on constraining, unscreening, and combinations thereof are benchmarked against full density functional calculations for selected charge density wave (CDW) systems, namely 1H-TaS$_2$, 1T-TiSe$_2$, 1H-NbS$_2$, and a one-dimensional carbon chain. We find that the downfolded models can reproduce potential energy surfaces on supercells accurately and facilitate computational speedup in MD simulations by about five orders of magnitude in comparison to purely ab initio calculations. For monolayer 1H-TaS$_2$ we report classical and path integral replica exchange MD simulations, revealing the impact of thermal and quantum fluctuations on the CDW transition.

  2 citations

• Codebase release 0.1 for MatsubaraFunctions.jl

  Dominik Kiese, Anxiang Ge, Nepomuk Ritz, Jan von Delft, Nils Wentzell

  SciPost Phys. Codebases 24-r0.1 (2024) · published 11 January 2024 | Toggle abstract · src

  The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on introducing MatsubaraFunctions.jl, a Julia library that implements data structures for generalized n-point Green's functions on Matsubara frequency grids. The package's architecture prioritizes user-friendliness without compromising the development of efficient solvers for quantum field theories in equilibrium. Following a comprehensive introduction of the fundamental types, we delve into a thorough examination of key facets of the interface. This encompasses avenues for accessing Green's functions, techniques for extrapolation and interpolation, as well as the incorporation of symmetries and a variety of parallelization strategies. Examples of increasing complexity serve to demonstrate the practical utility of the library, supplemented by discussions on strategies for sidestepping impediments to optimal performance.

  2 citations

• MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language

  Dominik Kiese, Anxiang Ge, Nepomuk Ritz, Jan von Delft, Nils Wentzell

  SciPost Phys. Codebases 24 (2024) · published 11 January 2024 | Toggle abstract · pdf

  The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on introducing MatsubaraFunctions.jl, a Julia library that implements data structures for generalized n-point Green's functions on Matsubara frequency grids. The package's architecture prioritizes user-friendliness without compromising the development of efficient solvers for quantum field theories in equilibrium. Following a comprehensive introduction of the fundamental types, we delve into a thorough examination of key facets of the interface. This encompasses avenues for accessing Green's functions, techniques for extrapolation and interpolation, as well as the incorporation of symmetries and a variety of parallelization strategies. Examples of increasing complexity serve to demonstrate the practical utility of the library, supplemented by discussions on strategies for sidestepping impediments to optimal performance.

  2 citations

• Charge order and antiferromagnetism in twisted bilayer graphene from the variational cluster approximation

  B. Pahlevanzadeh, P. Sahebsara, D. Sénéchal

  SciPost Phys. 13, 040 (2022) · published 30 August 2022 | Toggle abstract · pdf

  We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek, relevant to a twist angle of $1.30^\circ$, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion $U$ is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.

  2 citations

• Residual matrix product state for machine learning

  Ye-Ming Meng, Jing Zhang, Peng Zhang, Chao Gao, Shi-Ju Ran

  SciPost Phys. 14, 142 (2023) · published 2 June 2023 | Toggle abstract · pdf

  Tensor network, which originates from quantum physics, is emerging as an efficient tool for classical and quantum machine learning. Nevertheless, there still exists a considerable accuracy gap between tensor network and the sophisticated neural network models for classical machine learning. In this work, we combine the ideas of matrix product state (MPS), the simplest tensor network structure, and residual neural network and propose the residual matrix product state (ResMPS). The ResMPS can be treated as a network where its layers map the "hidden" features to the outputs (e.g., classifications), and the variational parameters of the layers are the functions of the features of the samples (e.g., pixels of images). This is different from neural network, where the layers map feed-forwardly the features to the output. The ResMPS can equip with the non-linear activations and dropout layers, and outperforms the state-of-the-art tensor network models in terms of efficiency, stability, and expression power. Besides, ResMPS is interpretable from the perspective of polynomial expansion, where the factorization and exponential machines naturally emerge. Our work contributes to connecting and hybridizing neural and tensor networks, which is crucial to further enhance our understanding of the working mechanisms and improve the performance of both models.

  2 citations

• Codebase release 2.2 for Pyqcm

  Théo N. Dionne, Alexandre Foley, Moïse Rousseau, David Sénéchal

  SciPost Phys. Codebases 23-r2.2 (2023) · published 20 December 2023 | Toggle abstract · src

  Pyqcm is a Python/C++ library that implements a few quantum cluster methods with an exact diagonalization impurity solver. Quantum cluster methods are used in the study of strongly correlated electrons to provide an approximate solution to Hubbard-like models. The methods covered by this library are Cluster Perturbation Theory (CPT), the Variational Cluster Approach (VCA) and Cellular (or Cluster) Dynamical Mean Field Theory (CDMFT). The impurity solver (the technique used to compute the cluster's interacting Green function) is exact diagonalization from sparse matrices, using the Lanczos algorithm and variants thereof. The core library is written in C++ for performance, but the interface is in Python, for ease of use and inter-operability with the numerical Python ecosystem. The library is distributed under the GPL license.

  2 citations

• Pressure-dependent structural and electronic instabilities in LaSb$_2$

  Theodore I. Weinberger, Christian K. de Podesta, Jiasheng Chen, Stephen A. Hodgson, F. Malte Grosche

  SciPost Phys. Proc. 11, 018 (2023) · published 6 June 2023 | Toggle abstract · pdf

  LaSb$_2$ exhibits a large, non-saturating, linear magnetoresistance at low temperatures, defying the expectations of Fermi liquid theory. This is thought to be caused by charge density wave order emerging below an abrupt, hysteretic anomaly in the resistivity at $\sim$ 355 K. We find that, under hydrostatic pressure, this anomaly becomes much more pronounced, develops strong hysteresis, and shifts rapidly towards lower temperatures. The anomaly is fully suppressed by only 6 kbar. Moreover, we observe a second transition anomaly at lower temperature, which likewise disappears under pressure. These findings are discussed in the context of a structural transition recently discovered in the sister material CeSb$_2$ and of density functional theory calculations, which indicate that the SmSb$_2$-type structure adopted by LaSb$_2$ at ambient conditions is unstable at moderate applied pressures.

  2 citations

• Competition between frustration and spin dimensionality in the classical antiferromagnetic $n$-vector model with arbitrary $n$

  Nikolaos P. Konstantinidis

  SciPost Phys. Core 6, 042 (2023) · published 8 June 2023 | Toggle abstract · pdf

  A new method to characterize the strength of magnetic frustration is proposed by calculating the minimum dimensionality of the absolute ground states of the classical nearest-neighbor antiferromagnetic $n$-vector model with arbitrary $n$. Platonic solids in three and four dimensions and Archimedean solids have lowest-energy configurations in a number of spin dimensions equal to their real-space dimensionality. Fullerene molecules and geodesic icosahedra can produce ground states in as many as five spin dimensions. Frustration is also characterized by the maximum value of the round-state energy when the exchange interactions are allowed to vary.

  2 citations