Shi-Ju Ran,^1,2,* Cheng Peng,³ Gang Su,^3,4 and Maciej Lewenstein^2,5

¹Department of Physics, Capital Normal University, Beijing 100048, China

²ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

³School of Physical Sciences, University of Chinese Academy of Sciences, P. O. Box 4588, Beijing 100049, China

⁴Kavli Institute for Theoretical Sciences, and CAS Center for Excellence in Topological Quantum Compuatation, University of Chinese Academy of Sciences, Beijing 100190, China

⁵ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain

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 ${\hat{S}}^z{\hat{S}}^z$ (Ising) interactions with a transverse field in the bulk and ${\hat{S}}^x{\hat{S}}^z$ and ${\hat{S}}^z{\hat{S}}^z$ 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 $\alpha$) can trigger nontrivial controlling of the bulk properties, including the degeneracy of energy/entanglement spectra, and the response to the magnetic field $h_{bulk}$ in the bulk. A universal point dubbed as ${\alpha }^s$ emerges. For $\alpha >{\alpha }^s$, the ground-state diagram versus $h_{bulk}$ consists of three “phases,” which are NeéL and polarized phases, and an emergent pseudomagnet phase, distinguished by entanglement and magnetization. For $\alpha <{\alpha }^s$, 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.