Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

Abstract

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [https://github.com/tenpy/tenpy]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

arXiv comment38 pages, 13 figures. Preprint of the published version

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• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Tensor renormalization group approach to 2D classical lattice models
• The iTEBD algorithm beyond unitary evolution
• Corner Transfer Matrix Renormalization Group Method
• From density-matrix renormalization group to matrix product states
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Entropy scaling and simulability by Matrix Product States
• Entanglement spectrum in one-dimensional systems
• Tensor Network Renormalization
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Time-evolving a matrix product state with long-ranged interactions
• Scaling of entanglement support for Matrix Product States
• Minimally Entangled Typical Thermal State Algorithms
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Tensor network decompositions in the presence of a global symmetry
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• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Loop optimization for tensor network renormalization
• Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group
• Finite automata for caching in matrix product algorithms
• Finding matrix product state representations of highly-excited eigenstates of many-body localized Hamiltonians
• Tensor network states and algorithms in the presence of a global SU(2) symmetry
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Real-Space Parallel Density Matrix Renormalization Group
• Efficient variational diagonalization of fully many-body localized Hamiltonians
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
• Error estimates for extrapolations with matrix-product states
• Entanglement vs. gap for one-dimensional spin systems
• Light Cone Matrix Product
• Automated construction of $U(1)$-invariant matrix-product operators from graph representations
• Numerical Computation of Dynamically Important Excited States of Many-Body Systems

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