Figure 4
From: Exact dimer phase with anisotropic interaction for one dimensional magnets
(a) Dimer and (b) magnetization orders at \(\theta = \pi /7\) from density matrix renormalization group (DMRG) method with open boundary condition (OBC). The numerical determined boundary is \(z_{\text {ex}} = -0.29283\), while the exact boundary from Eq. (13) is \(z_c = -0.29285\). (c) The cut EE (see definition in the inset) as a function of z at \(\theta = \pi /7\). At the phase boundary, the EE exhibits a sharp peak. (d) A typical result for oscillating of EE due to singlet dimer state. (e) Excitation gaps \(\delta E_{n1}\) from z-FM to exact dimer phase. (f) The enlarged excitation gaps near the critical point. Data are obtained for \(L= 16\) from exact diagonalization (ED) with PBC. (g) The degeneracy of the GSs at the phase boundary as a function of L and \(\theta\), which scales as \(\mathcal {O}(L/2)\). (h) The degeneracy of the GSs of H(1, 0, 0) with scaling of \(\mathcal {O}(2^{L/2})\).
