2013/09/09 by Iztok Pižorn, Iztok Pizorn, Frank Verstraete +2
Mathematics · Physics and Astronomy · #Bipartite graph #Boundary (topology) #Combinatorics #Eigenvalues and eigenvectors #Geometry #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Spectrum (functional analysis) #Tensor (intrinsic definition) #Tensor decomposition and applications #Tensor product #Tree (set theory) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.88.195102
published as Phys. Rev. B 88, 195102 (2013) · 16 pages, 16 figures (20 PDF figures)
arxiv created 2013/09/09 · openalex publication_date 2013/11/01 · arxiv updated 2013/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, namely how to extract the entanglement spectra in a bipartite splitting of a loopless tensor network across multiple links of the network, by constructing a matrix product operator for the reduced density operator and simulating its eigenstates. The entanglement spectra of 2\ifmmode×\else\texttimes\fiL, 3\ifmmode×\else\texttimes\fiL, and 4\ifmmode×\else\texttimes\fiL with either open or periodic boundary conditions on the rungs are studied using the presented methods, where it is found that the entanglement spectrum depends not only on the subsystem but also on the boundaries between the subsystems.