2020/09/23 by Qi Hu, Hu, Qi, Adrián Franco Rubio +3 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2009.11383
openalex publication_date 2020/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Entanglement entropy and entanglement spectrum have been widely used to characterize quantum entanglement in extended many-body systems. Given a pure state of the system and a division into regions A and B, they can be obtained in terms of the Schmidt~ values, or eigenvalues λα of the reduced density matrix ρA for region A. In this paper we draw attention instead to the Schmidt~ vectors, or eigenvectors |vα⟩ of ρA. We consider the ground state of critical quantum spin chains whose low energy/long distance physics is described by an emergent conformal field theory (CFT). We show that the Schmidt vectors |vα⟩ display an emergent universal structure, corresponding to a realization of the Virasoro algebra of a boundary CFT (a chiral version of the original CFT). Indeed, we build weighted sums Hn of the lattice Hamiltonian density hj,j+1 over region A and show that the matrix elements ⟨ vαHn |vα'⟩ are universal, up to finite-size corrections. More concretely, these matrix elements are given by an analogous expression for Hn\tiny CFT = \frac 1 2 (Ln + L-n) in the boundary CFT, where Ln's are (one copy of) the Virasoro generators. We numerically confirm our results using the critical Ising quantum spin chain and other (free-fermion equivalent) models.