Entanglement, combinatorics and finite-size effects in spin chains

2008/08/31 by Bernard Nienhuis, Massimo Campostrini, Pasquale Calabrese · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Degeneracy (biology) #Density matrix #Eigenvalues and eigenvectors #Entropy (arrow of time) #Ground state #Hamiltonian (control theory) #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Neural Networks and Reservoir Computing #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Scaling #Spins #Squashed entanglement #Statistical physics #cond-mat.stat-mech #cond-mat.str-el #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/1742-5468/2009/02/p02063

published as J. Stat. Mech. (2009) P02063 · 5 pages, 4 figures, one mathematica file attached

arxiv created 2009/02/26 · openalex publication_date 2009/02/26 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05

Abstract

We carry out a systematic study of the exact block entanglement in the XXZ spin chain at Δ = −1/2. We present the first analytic expressions for reduced density matrices for n spins in a chain of length L (for n ≤6 and arbitrary but odd L ) for a truly interacting model. The entanglement entropy and the moments of the reduced density matrix and its spectrum are then easily derived. We explicitly construct the 'entanglement Hamiltonian' as the logarithm of this matrix. Exploiting the degeneracy of the ground state, we find the scaling behavior of the entanglement of the zero-temperature mixed state.

Citations

• Spin chains and combinatorics
• Density matrices for finite segments of Heisenberg chains of arbitrary length
• Renyi entropy of the XY spin chain
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Calculation of reduced density matrices from correlation functions
• Entanglement and boundary critical phenomena
• Matrix product states represent ground states faithfully
• Entanglement spectrum in one-dimensional systems
• Density-matrix spectra of solvable fermionic systems
• Scaling of entanglement support for matrix product states
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Entanglement in many-body systems

Cited by

• Entanglement entropy of two disjoint blocks in critical Ising models
• On entanglement Hamiltonians of an interval in massless harmonic chains