Topological order parameters of the spin-12dimerized Heisenberg ladder in magnetic field

Abstract

Topological properties of the spin-1/2 dimerized Heisenberg ladder are investigated, focusing on the plateau phase in the magnetic field whose magnetization is half of the saturation value. Although the applied magnetic field removes most of the symmetries of the system, there is a symmetry-protected topological phase supported by the spatial inversion symmetry. The Z 2 Berry phase associated with a symmetry-respecting boundary and quantized into 0 and π is used as a symmetry-protected topological order parameter. Edge states are also analyzed to confirm the bulk-edge correspondence. In addition, a symmetry-breaking boundary is considered. Then, we observe a different type of quantization of the Berry phase, i.e., a quantization into ±π/2 of the Berry phase. In this case, the bulk-edge correspondence is also different, namely, there emerge "polarized" edge states for the case with ±π/2 quantization. We also evaluate the entanglement entropy by the infinite time-evolving block decimation (iTEBD) to complement the Berry-phase-based arguments. Further, a different type of the topological order parameter is extracted from the matrix product state representation of the ground state given by the iTEBD.

Rigorous decoupling between edge states in frustrated spin chains and ladders

“…In recent years, the investigation of the topological properties spin-1/2 ladders has been a very active field of research. 26,27 It has long been known that some topologically non-trivial states can be revealed by the presence of localized edge states that appear in two-leg ladders with diagonal edges but are absent in the case of vertical edges 28,29 . In this section we consider the antiferromagnetic spin-1/2 ladder with an additional next-nearestneighbor interaction along the legs (see Fig.3) that induces incommensurate correlations.…”

Appreciating the heterogeneity in the unity of Africa: A socio‐ecological perspective on Africa's geographies

“…The description of Africa as a single mass often obscures this diversity and rich resourcefulness of the continent. From a geopolitical perspective, the continental economic blocks also tend to straddle the alliances Africa has with Western and Eastern economic superpowers, particularly China as the emerging Eastern power (Harris ; Kariyado and Hatsugai ). The traditional superpowers of Europe and America have been joined by the emerging superpowers of Brazil, China, India, South Eastern Asian countries, and arguably South Africa.…”

Signature of a quantum dimensional transition in the spin- 12 antiferromagnetic Heisenberg model on a square lattice and space reduction in the matrix product state

“…Variants of DMRG such as infinite time evolving block decimation (iTEBD) method were applied to the case of N = 2 [29], yielding results conflicting with that by the infinite quasi-1D entanglement perturbation theory (iqEPT) [30], and so on [31], but not for larger N because of the rapid increase of the number of density matrix elements needed for a sufficient accuracy. Tensor network state (TNS) [32,33] based methods such as the infinite projected entangled pair state (iPEPS) [34,35], illustrated in Fig.2 (a) and natively designed for an infinite 2D system, still do not show sufficient efficiency to tackle the tensor's bond index size greater than a few dozens [35,36].…”