Post-matrix product state methods: To tangent space and beyond

2013/05/08 by Jutho Haegeman, Tobias J. Osborne, Frank Verstraete · 233 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Formalism (music) #Geometry #Manifold (fluid mechanics) #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Matrix product state #Numerical methods for differential equations #Physics #Physics of Superconductivity and Magnetism #Product (mathematics) #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Tangent #Tangent space #Theoretical physics #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.88.075133

published in Physical Review B 88(7) (American Physical Society) · 40 pages, 8 figures

arxiv created 2013/05/08 · openalex publication_date 2013/08/20 · arxiv updated 2013/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time evolution, excitations, and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well-defined quantum number. We present some illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post-matrix product methods.

Citations

• Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems
• Where are the black-hole entropy degrees of freedom?
• On the product of semi-groups of operators
• Efficient Simulation of One-Dimensional Quantum Many-Body Systems
• Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
• Density-matrix algorithms for quantum renormalization groups
• Dynamical correlation functions using the density matrix renormalization group
• Structure of a quantized vortex in boson systems
• Entanglement spectrum of a topological phase in one dimension
• Exact models for trimerization and tetramerization in spin chains
• Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• Density-Matrix Renormalization Group Methods for Momentum- and Frequency-Resolved Dynamical Correlation Functions
• Note on Exchange Phenomena in the Thomas Atom
• How robust is the entanglement entropy-area relation?
• The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods
• Chebyshev matrix product state approach for spectral functions
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
• Improving Vocabulary Knowledge and Reading Attitudes in 4th Grade Students Through Direct Vocabulary Instruction.
• Konfigurationsraum und zweite Quantelung

Cited by

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• Extracting average properties of disordered spin chains with translationally invariant tensor networks
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• Deformed Symmetry Structures and Quantum Many-body Scar Subspaces
• Emergent statistical bubble localization in aZ2lattice gauge theory
• Metrology of open quantum systems from emitted radiation
• Entanglement of exact excited states of Affleck-Kennedy-Lieb-Tasaki models: Exact results, many-body scars, and violation of the strong eigenstate thermalization hypothesis
• Kibble Zurek mechanism of topological defect formation in quantum field theory with matrix product states
• Real-time scattering of interacting quasiparticles in quantum spin chains
• Chebyshev expansion of spectral functions using restricted Boltzmann machines
• 461 Fe の高温における転位挙動の動的観察(レール・棒・線・焼入性・クラッド鋼・その他, 性質, 日本鉄鋼協会 第 98 回(秋季)講演大会)
• Path integral for spin-1 chain in the fluctuating matrix product state basis
• Variational optimization algorithms for uniform matrix product states

Related

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