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Transverse contraction methods are extremely promising tools for the efficient contraction of tensor networks associated with the time evolution of quantum many-body systems, allowing in some cases to circumvent the entanglement barrier…

Quantum Physics · Physics 2026-01-14 Stefano Carignano

Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…

Quantum Physics · Physics 2024-11-04 Ling Lin , Yongguan Ke , Li Zhang , Chaohong Lee

We show that the Z$_2$ invariant, which classifies the topological properties of time reversal invariant insulators, has deep relationship with the global anomaly. Although the second Chern number is the basic topological invariant…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 T. Fukui , T. Fujiwara , Y. Hatsugai

Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with…

Computational Geometry · Computer Science 2017-11-07 Francesco Furiani , Giulio Martella , Alberto Paoluzzi

We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…

Mesoscale and Nanoscale Physics · Physics 2021-09-28 Mikito Koshino , Hiroki Oka

Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete symmetries and are characterized by topological…

Quantum Gases · Physics 2019-05-29 M. Mochol-Grzelak , A. Dauphin , A. Celi , M. Lewenstein

We present Groebner.jl, a Julia package for computing Groebner bases with the F4 algorithm. Groebner.jl is an efficient, portable, and open-source software. Groebner.jl works over integers modulo a prime and over the rationals, supports…

Mathematical Software · Computer Science 2024-02-13 Alexander Demin , Shashi Gowda

We present two modules that expand functionalities of the all-electron full-potential density functional theory package WIEN2k for computation of the Chern and $Z_2$ topological invariants. Characterization of topological properties relies…

Computational Physics · Physics 2023-08-28 Andres F. Gomez-Bastidas , Oleg Rubel

Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of…

In this paper, we present Insertus.jl, the Julia package that can help the user generate a randomization sequence of a given length for a multi-arm trial with a pre-specified target allocation ratio and assess the operating characteristics…

Methodology · Statistics 2024-07-22 Yevgen Ryeznik , Oleksandr Sverdlov

Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in condensed phase. To facilitate effective development,…

Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…

Mesoscale and Nanoscale Physics · Physics 2024-01-17 Nicolas Baù , Antimo Marrazzo

We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software…

Mathematical Software · Computer Science 2018-05-31 Paul Breiding , Sascha Timme

We present Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi.jl is extensible, easy to use, and fast. We describe the main design choices…

Mathematical Software · Computer Science 2022-01-19 Hendrik Ranocha , Michael Schlottke-Lakemper , Andrew R. Winters , Erik Faulhaber , Jesse Chan , Gregor J. Gassner

We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…

Quantum Physics · Physics 2018-03-14 Sebastian Krämer , David Plankensteiner , Laurin Ostermann , Helmut Ritsch

HarmonicBalance.jl is a publicly available Julia package designed to simplify and solve systems of periodic time-dependent nonlinear ordinary differential equations. Time dependence of the system parameters is treated with the harmonic…

Mesoscale and Nanoscale Physics · Physics 2022-05-18 Jan Košata , Javier del Pino , Toni L. Heugel , Oded Zilberberg

Many-body topological quantum states host exotic quantum phenomena and lie at the forefront of developing next-generation quantum technologies. Recently emerged neural network wavefunction methods have established themselves as a powerful…

Strongly Correlated Electrons · Physics 2026-04-13 Haoxiang Chen , Yubing Qian , Weiluo Ren , Xiang Li , Ji Chen

We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining…

Algebraic Geometry · Mathematics 2018-08-17 Paul Breiding , Sara Kalisnik Verovsek , Bernd Sturmfels , Madeleine Weinstein

The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…

Mathematical Physics · Physics 2017-05-19 Domenico Monaco

MultiPrecisionArrays.jl is a Julia package. This package provides data structures and solvers for several variants of iterative refinement. It will become much more useful when half precision (aka Float16) is fully supported in LAPACK/BLAS.…

Numerical Analysis · Mathematics 2025-08-11 C. T. Kelley