Publications

Order by: publication date number of citations

• Codebase release 1.0 for TeNPy

  Johannes Hauschild, Jakob Unfried, Sajant Anand, Bartholomew Andrews, Marcus Bintz, Umberto Borla, Stefan Divic, Markus Drescher, Jan Geiger, Martin Hefel, Kévin Hémery, Wilhelm Kadow, Jack Kemp, Nico Kirchner, Vincent S. Liu, Gunnar Möller, Daniel Parker, Michael Rader, Anton Romen, Samuel Scalet, Leon Schoonderwoerd, Maximilian Schulz, Tomohiro Soejima, Philipp Thoma, Yantao Wu, Philip Zechmann, Ludwig Zweng, Roger S. K. Mong, Michael P. Zaletel, Frank Pollmann

  SciPost Phys. Codebases 41-r1.0 (2024) · published 26 November 2024 | Toggle abstract · src

  TeNPy (short for 'Tensor Network Python') is a python library for the simulation of strongly correlated quantum systems with tensor networks. The philosophy of this library is to achieve a balance of readability and usability for new-comers, while at the same time providing powerful algorithms for experts. The focus is on MPS algorithms for 1D and 2D lattices, such as DMRG ground state search, as well as dynamics using TEBD, TDVP, or MPO evolution. This article is a companion to the recent version 1.0 release of TeNPy and gives a brief overview of the package.

  3 citations

• Comparative microscopic study of entropies and their production

  Philipp Strasberg, Joseph Schindler

  SciPost Phys. 17, 143 (2024) · published 25 November 2024 | Toggle abstract · pdf

  We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on Boltzmann, Gibbs or canonical entropy). This is done for the archetypal nonequilibrium setup of two systems exchanging energy, modeled here with random matrix theory, based on numerical integration of the Schrödinger equation. We consider three types of pure initial states (local energy eigenstates, decorrelated and entangled microcanonical states) and three classes of systems: (A) two normal systems, (B) a normal and a negative temperature system and (C) a normal and a negative heat capacity system. We find: (1) All types of initial states give rise to the same macroscopic dynamics. (2) Entanglement and diagonal entropy sensitively depend on the microstate, in contrast to all other entropies. (3) For class B and C, Gibbs-volume entropies can violate the second law and the associated temperature becomes meaningless. (4) For class C, Boltzmann-surface entropies can violate the second law and the associated temperature becomes meaningless. (5) Canonical entropy has a tendency to remain almost constant. (6) For a Haar random initial state, entanglement or diagonal entropy behave similar or identical to coarse-grained-observational entropy.

  2 citations

• Efficient higher-order matrix product operators for time evolution

  Maarten Van Damme, Jutho Haegeman, Ian McCulloch, Laurens Vanderstraeten

  SciPost Phys. 17, 135 (2024) · published 15 November 2024 | Toggle abstract · pdf

  We introduce a systematic construction of higher-order matrix product operator (MPO) approximations of the time evolution operator for generic (short and long range) one-dimensional Hamiltonians. We demonstrate the utility of our construction, by showing an order of magnitude speedup in simulation cost compared to conventional first-order MPO time evolution schemes.

  5 citations

• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries

  Andreas Weichselbaum

  SciPost Phys. Codebases 40 (2024) · published 14 November 2024 | Toggle abstract · pdf

  This is the documentation for the tensor library QSpace (v4.0) that provides a toolbox to exploit 'quantum symmetry spaces' in tensor network states in the quantum many-body context. QSpace permits arbitrary combinations of symmetries including the Abelian symmetries $\mathbb{Z}_n$ and $U(1)$, as well as all non-Abelian symmetries represented by the simple classical Lie algebras: $A_n$, $B_n$, $C_n$, and $D_n$, or respectively, the special unitary group SU($n$), the odd orthogonal group SO($2n+1$), the symplectic group Sp($2n$), and the even orthogonal group SO($2n$). The code (C++ embedded via the MEX interface into Matlab) is available open-source as of QSpace v4.0 on bitbucket (https://bitbucket.org/qspace4u) under the Apache 2.0 license. QSpace is designed as a bottom-up approach for non-Abelian symmetries. It starts from the defining representation and the respective Lie algebra. By explicitly computing and tabulating generalized Clebsch-Gordan coefficient tensors, QSpace is versatile in its operations across all symmetries. At the level of an application, much of the symmetry-related details are hidden within the QSpace C++ core libraries. Hence when developing tensor network algorithms with QSpace, these can be coded (nearly) as if there are no symmetries at all, despite being able to fully exploit general non-Abelian symmetries.

  14 citations

• Codebase release 4.0 for QSpace

  Andreas Weichselbaum

  SciPost Phys. Codebases 40-r4.0 (2024) · published 14 November 2024 | Toggle abstract · src

  This is the documentation for the tensor library QSpace (v4.0) that provides a toolbox to exploit 'quantum symmetry spaces' in tensor network states in the quantum many-body context. QSpace permits arbitrary combinations of symmetries including the Abelian symmetries $\mathbb{Z}_n$ and $U(1)$, as well as all non-Abelian symmetries represented by the simple classical Lie algebras: $A_n$, $B_n$, $C_n$, and $D_n$, or respectively, the special unitary group SU($n$), the odd orthogonal group SO($2n+1$), the symplectic group Sp($2n$), and the even orthogonal group SO($2n$). The code (C++ embedded via the MEX interface into Matlab) is available (https://bitbucket.org/qspace4u) under the Apache 2.0 license. QSpace is designed as a bottom-up approach for non-Abelian symmetries. It starts from the defining representation and the respective Lie algebra. By explicitly computing and tabulating generalized Clebsch-Gordan coefficient tensors, QSpace is versatile in its operations across all symmetries. At the level of an application, much of the symmetry-related details are hidden within the QSpace C++ core libraries. Hence when developing tensor network algorithms with QSpace, these can be coded (nearly) as if there are no symmetries at all, despite being able to fully exploit general non-Abelian symmetries.

  4 citations

• SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions

  James Neuhaus, Nathan S. Nichols, Debshikha Banerjee, Benjamin Cohen-Stead, Thomas A. Maier, Adrian Del Maestro, Steven Johnston

  SciPost Phys. Codebases 39 (2024) · published 12 November 2024 | Toggle abstract · pdf

  We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package's output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

  3 citations

• Codebase release r1.1 for SmoQyDEAC.jl

  James Neuhaus, Nathan S. Nichols, Debshikha Banerjee, Benjamin Cohen-Stead, Thomas A. Maier, Adrian Del Maestro, Steven Johnston

  SciPost Phys. Codebases 39-r1.1 (2024) · published 12 November 2024 | Toggle abstract · src

  We introduce the SmoQyDEAC.jl package, a Julia implementation of the Differential Evolution Analytic Continuation (DEAC) algorithm [N. S. Nichols et al., Phys. Rev. E 106, 025312 (2022)] for analytically continuing noisy imaginary time correlation functions to the real frequency axis. Our implementation supports fermionic and bosonic correlation functions on either the imaginary time or Matsubara frequency axes, and treatment of the covariance error in the input data. This paper presents an overview of the DEAC algorithm and the features implemented in the SmoQyDEAC.jl package. It also provides detailed benchmarks of the package's output against the popular maximum entropy and stochastic analytic continuation methods. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDEAC.jl or installed using the Julia package manager. The online documentation, including examples, can be accessed at https://smoqysuite.github.io/SmoQyDEAC.jl/stable/.

  1 citation

• QArray: A GPU-accelerated constant capacitance model simulator for large quantum dot arrays

  Barnaby van Straaten, Joseph Hickie, Lucas Schorling, Jonas Schuff, Federico Fedele, Natalia Ares

  SciPost Phys. Codebases 35 (2024) · published 21 October 2024 | Toggle abstract · pdf

  Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a $100 × 100$ pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.

  4 citations

• Codebase release 1.3 for QArray

  Barnaby van Straaten, Joseph Hickie, Lucas Schorling, Jonas Schuff, Federico Fedele, Natalia Ares

  SciPost Phys. Codebases 35-r1.3 (2024) · published 21 October 2024 | Toggle abstract · src

  Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a $100 × 100$ pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.

  3 citations

• Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices

  J. A. Koziol, G. Morigi, K. P. Schmidt

  SciPost Phys. 17, 111 (2024) · published 10 October 2024 | Toggle abstract · pdf

  We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil's staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.

  5 citations