Entanglement spectrum of the degenerative ground state of Heisenberg ladders in a time-dependent magnetic field

Abstract

We investigate of the relationship between the entanglement and subsystem Hamiltonians in the perturbative regime of strong coupling between subsystems. One of the two conditions that guarantees the proportionality between these Hamiltonians obtained by using the nondegenerate perturbation theory within the first order is that the unperturbed ground state has a trivial entanglement Hamiltonian. Furthermore, we study the entanglement Hamiltonian of the Heisenberg ladders in a time-dependent magnetic field using the degenerate perturbation theory, where couplings between legs are considered as a perturbation. In this case, when the ground state is two-fold degenerate, and the entanglement Hamiltonian is proportional to the Hamiltonian of a chain within first-order perturbation theory, even then also the unperturbed ground state has a nontrivial entanglement spectrum.

1 figure, Refs. added, minor changes

References in corpus (5)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Entanglement spectra between coupled Tomonaga-Luttinger liquids: Applications to ladder systems and topological phases
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
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Cited by in corpus (3)

• Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• Distribution of entanglement Hamiltonian spectrum in free fermion models