Entanglement and corner Hamiltonian spectra of integrable open spin chains

Abstract

Entanglement spectra (ES) for the critical SU(N) (2 <= N <= 4) spin chains and other integrable models of finite length are studied with the density matrix renormalization group method. For all models under investigation, the level spacings and the degeneracy structure of the ES are in excellent agreement with the spectra of the corner Hamiltonian, defined as the generator of the associated corner transfer matrix. The correspondence holds between the ES (n) at the n-th cut position from the edge of the spin model, and the corner Hamiltonian of length n, for all small values of n. The cut position dependence of the ES shows a period-N oscillatory behavior for a given SU(N) chain, reminiscent of the oscillatory part of the entanglement entropy observed in the past for the same models. Oscillations of the ES do not die out in the bulk of the chain, in contrast to the asymptotically vanishing oscillation of the entanglement entropy. Heuristic argument based on Young tableaux consideration can explain the period-N structure of the ES qualitatively.

References in corpus (16)

• Experimental quantum teleportation
• The density-matrix renormalization group in the age of matrix product states
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
• Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases
• Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders
• DMRG studies of critical SU(N) spin chains
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Rényi entanglement entropy of critical SU($N$) spin chains
• Entanglement analysis of isotropic spin-1 chains

Cited by in corpus (22)

• Integrable Floquet dynamics
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Entanglement Hamiltonian of Interacting Fermionic Models
• Properties of the entanglement Hamiltonian for finite free-fermion chains
• Universal Entanglement Spectra of Gapped One-dimensional Field Theories
• Entanglement Hamiltonians for non-critical quantum chains
• Entanglement Hamiltonian of quantum critical chains and conformal field theories
• Entanglement guided search for parent Hamiltonians
• Lattice Bisognano-Wichmann modular Hamiltonian in critical quantum spin chains
• Measuring von Neumann entanglement entropies without wave functions
• On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
• Spin-one bilinear-biquadratic model on a star lattice
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Gapless to gapless phase transitions in quantum spin chains
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Holographic encoding of universality in corner spectra
• Entanglement studies of interacting fermionic models
• Subsystem Evolution Speed as Indicator of Relaxation
• Edge-Edge Correlations without Edge-States: $\eta$-clustering State as Ground State of the Extended Attractive SU(3) Hubbard Chain
• Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain