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

Abstract

This is the documentation for the tensor library QSpace (v4.0), 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 based on the semisimple 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 at 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 the type of operations that it can perform 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.

122 pages, 14 figures

References in corpus (27)

• The density-matrix renormalization group in the age of matrix product states
• The numerical renormalization group method for quantum impurity systems
• Real time evolution using the density matrix renormalization group
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
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• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Minimally Entangled Typical Thermal State Algorithms
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• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
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• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
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• Density matrix numerical renormalization group for non-Abelian symmetries
• Exact Diagonalization of Heisenberg SU(N) models
• Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization group
• SU(3) Anderson impurity model: A numerical renormalization group approach exploiting non-Abelian symmetries
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
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Cited by in corpus (11)

• Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
• Exploiting the Hermitian symmetry in tensor network algorithms
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• Oscillate and Renormalize: Fast Phonons Reshape the Kondo Effect in Flat Band Systems
• The Software Landscape for the Density Matrix Renormalization Group
• Back-action effects in charge detection
• Static impurity in a mesoscopic system of SU($N$) fermionic matter-waves
• Compressing local vertex functions from the multipoint numerical renormalization group using quantics tensor cross interpolation
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Critical spin models from holographic disorder
• Grassmann tensor networks