CERTIFY-ED supplies a multi-oracle eigensolver, thirteen validation layers, and tamper-evident certificates to certify exact diagonalization results for quantum many-body models.
XDiag: Exact Diagonalization for Quantum Many-Body Systems
7 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Exact diagonalization (ED) is a cornerstone technique in quantum many-body physics, enabling precise solutions to the Schr\"odinger equation for interacting quantum systems. Despite its utility in studying ground states, excited states, and dynamical behaviors, the exponential growth of the Hilbert space with system size presents significant computational challenges. We introduce XDiag, an open-source software package designed to combine advanced and efficient algorithms for ED with and without symmetry-adapted bases with user-friendly interfaces. Implemented in C++ for computational efficiency and wrapped in Julia for ease of use, XDiag provides a comprehensive toolkit for ED calculations. Key features of XDiag include the first publicly accessible implementation of sublattice coding algorithms for large-scale spin system diagonalizations, efficient Lin table algorithms for symmetry lookups, and random-hashing techniques for distributed memory parallelization. The library supports various Hilbert space types (e.g., spin-1/2, electron, and t-J models), facilitates symmetry-adapted block calculations, and automates symmetry considerations. The package is complemented by extensive documentation, a user guide, reproducible benchmarks demonstrating near-linear scaling on thousands of CPU cores, and over 20 examples covering ground-state calculations, spectral functions, time evolution, and thermal states. By integrating high-performance computing with accessible scripting capabilities, XDiag allows researchers to perform state-of-the-art ED simulations and explore quantum many-body phenomena with unprecedented flexibility and efficiency.
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representative citing papers
In the Ising-like triangular antiferromagnet Er7TaO12, long-range magnetic order forms on cooling then melts into short-range correlations at lower temperature, realizing a spin analog of the Pomeranchuk effect.
Quantum fluctuations stabilize a chiral ferromagnet with orbital chirality and a chiral stripe phase in the presence of magnetization-non-conserving spin-orbit interactions, producing an enhanced thermal Hall effect.
A generalized coherent-state framework computes many-body density of states in irreducible sectors, supplies rigorous ground-state energy bounds, and identifies quantum and excited-state phase transitions in the LMG model and long-range Ising chains.
A block-procedural, hardware-adaptive matrix-free method for memory-efficient application of large quantum Hamiltonians on accelerators.
Polfed.jl provides an efficient implementation of polynomially filtered Lanczos diagonalization for mid-spectrum eigenpairs in quantum many-body systems, supporting larger sizes via on-the-fly polynomial transformations and GPU acceleration.
On-site repulsion monotonically suppresses current in ordered rings while extended interactions show filling-dependent enhancement or suppression, with disorder altering these trends at low fillings.
citing papers explorer
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CERTIFY-ED: A Multi-Layer Verification Framework for Exact Diagonalization of Quantum Many-Body Systems
CERTIFY-ED supplies a multi-oracle eigensolver, thirteen validation layers, and tamper-evident certificates to certify exact diagonalization results for quantum many-body models.
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Melting upon cooling in a quantum magnet
In the Ising-like triangular antiferromagnet Er7TaO12, long-range magnetic order forms on cooling then melts into short-range correlations at lower temperature, realizing a spin analog of the Pomeranchuk effect.
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Fluctuation-driven chiral ferromagnetism
Quantum fluctuations stabilize a chiral ferromagnet with orbital chirality and a chiral stripe phase in the presence of magnetization-non-conserving spin-orbit interactions, producing an enhanced thermal Hall effect.
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A Generalized Coherent State Framework for Many-Body Density of States
A generalized coherent-state framework computes many-body density of states in irreducible sectors, supplies rigorous ground-state energy bounds, and identifies quantum and excited-state phase transitions in the LMG model and long-range Ising chains.
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Memory-Scalable and Hardware-Adaptive Matrix-Free Quantum Simulation
A block-procedural, hardware-adaptive matrix-free method for memory-efficient application of large quantum Hamiltonians on accelerators.
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Computing eigenpairs of quantum many-body systems with Polfed.jl
Polfed.jl provides an efficient implementation of polynomially filtered Lanczos diagonalization for mid-spectrum eigenpairs in quantum many-body systems, supporting larger sizes via on-the-fly polynomial transformations and GPU acceleration.
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Exact and mean-field analysis of the role of Hubbard interactions on flux driven circular current in a quantum ring
On-site repulsion monotonically suppresses current in ordered rings while extended interactions show filling-dependent enhancement or suppression, with disorder altering these trends at low fillings.