2009/08/31 by Silvano Garnerone, Thiago R. de Oliveira, Paolo Zanardi · 62 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Algorithm #Combinatorics #Computer science #Hilbert space #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Observable #Physics #Product (mathematics) #Property (philosophy) #Pure mathematics #Quantum Information and Cryptography #Quantum many-body systems #Quantum mechanics #Random matrix #Rank (graph theory) #Scaling #Set (abstract data type) #Space (punctuation) #State (computer science) #State space #Statistical physics #Statistics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreva.81.032336
published in Physical Review A 81(3) (American Physical Society) · 9 pages, 6 figures; accepted for publication in PRA
arxiv created 2010/03/03 · openalex publication_date 2010/03/29 · arxiv updated 2010/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recent results suggest that the use of ensembles in statistical mechanics may not be necessary for isolated systems, since typically the states of the Hilbert space would have properties similar to those of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are nonphysical and not good descriptions of realistic systems. Therefore, to better understand the actual power of typicality it is important to ask if it is also a property of a set of physically relevant states. Here we address this issue, studying if and how typicality emerges in the set of matrix product states. We show analytically that typicality occurs for the expectation value of subsystems' observables when the rank of the matrix product state scales polynomially with the size of the system with a power greater than 2. We illustrate this result numerically and present some indications that typicality may appear already for a linear scaling of the rank of the matrix product state.