The form of the entanglement Hamiltonian varies with the parameters of the original system. Whether there is a singularity is the key problem for demonstrating/negating the universality of the relation between the entanglement spectrum and edge energy spectrum. We carefully study the phase diagram of a 1D Ising entanglement Hamiltonian as an example to clarify the long-standing controversy of the general relation between the entanglement Hamiltonian and original Hamiltonian. Interestingly, even if the singularities indeed exist, the Li-Haldane-Poilblanc conjecture, i.e., the general relation between the entanglement spectrum and edge energy spectrum, seemingly still holds.
We present here the nonequilibrium dynamics of the recently studied quasiperiodic Ising model. The zero temperature phase diagram of this model mainly consists of three phases, where each of these three phases can have extended, localized, or critically delocalized low-energy excited states. We explore the nature of excitations in these different phases by studying the evolution of entanglement entropy after performing sudden quenches of different strengths to different phases. Our results on nonequilibrium dynamics of entanglement entropy are concurrent with the nature of excitations predicted in Chandran and Laumann [Phys. Rev. X 7, 031061 (2017)].
Searching for simple models that possess nontrivial controlling properties is one of the central tasks in the field of quantum technologies. In this work, we construct a quantum spin-
1/2 chain of finite size, termed as controllable spin wire (CSW), in which we have ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}^{z}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}^{z}$ (Ising) interactions with a transverse field in the bulk and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}^{x}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}^{z}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}^{z}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}^{z}$ couplings with a canted field on the boundaries. The Hamiltonians on the boundaries, dubbed as tuning Hamiltonians (TH's), bear the same form as the effective Hamiltonians emerging in the so-called ``quantum entanglement simulator'' that is originally proposed for mimicking infinite models. We show that tuning the TH's (parametrized by $\ensuremath{\alpha}$) can trigger nontrivial controlling of the bulk properties, including the degeneracy of energy/entanglement spectra, and the response to the magnetic field
hbulk in the bulk. A universal point dubbed as ${\ensuremath{\alpha}}^{s}$ emerges. For $\ensuremath{\alpha}>{\ensuremath{\alpha}}^{s}$, the ground-state diagram versus
hbulk consists of three ``phases,'' which are Ne\'eL and polarized phases, and an emergent pseudomagnet phase, distinguished by entanglement and magnetization. For $\ensuremath{\alpha}<{\ensuremath{\alpha}}^{s}$, the phase diagram changes completely, with no steplike behaviors to distinguish phases. Due to its controlling properties and simplicity, the CSW could potentially serve in future the experiments for developing quantum devices.