2007/01/03 by M. B. Hastings · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Conjecture #Density matrix #Entropy (arrow of time) #Ground state #Joint quantum entropy #Mathematics #Matrix product state #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.76.035114
published as Phys. Rev. B 76, 035114 (2007). · 7 pages, no figures
arxiv created 2007/01/03 · openalex publication_date 2007/07/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped one-dimensional local Hamiltonians such that the entropy is exponentially large in the correlation length, and we present strong evidence supporting a conjecture that there exist such systems with arbitrarily large entropy. However, we then show, under an assumption on the density of states which is believed to be satisfied by many physical systems such as the fractional quantum Hall effect, that an efficient matrix product state representation of the ground state exists in any dimension. Finally, we comment on the implications for numerical simulation.