| الوصف: |
We study the frustrated and dimerized ferromagnetic-antiferromagnetic J1-J′1-J2 chain using the density-matrix renormalization group (DMRG) method. Based on numerical calculations of the second derivative of energy, spin gap, spin-spin correlations, string order parameter (SOP), and entanglement spectrum (ES), we obtain the ground-state phase diagram for a wide range of J′1/J1 and J2/|J1| values. This phase diagram reveals a ferromagnetic phase and two distinct valence-bond-solid (VBS) phases. The first VBS phase, referred to as D3-VBS, is typified by the formation of valence bonds between third-neighbor spin-1/2’s, persisting as a continuation from the J′1/J1 = 1 limit. Alternatively, the second VBS phase, referred to as mixed-VBS, exhibits a coexistence of both second- and third-neighbor valence bonds, interpreted as a continuation from the J′1/J1 = 0 case. Remarkably, both VBS states are identified as being of Haldane-type, marked by a finite SOP and 2-fold ES degeneracy. Unexpectedly, our analysis uncovers a significant enhancement of the valence bond stability at the boundary of the two VBS phases. This study provides the first empirical demonstration of a nontrivial quantum phase transition between different topological VBS states in spin-1/2 chains. Moreover, we find that the ground state of the relevant quasi-one-dimensional material LiCuSbO4 is classified as the D3-VBS state. Collectively, these results mark a substantial stride forward in our comprehension of quantum phase transitions and topological states. ; This work was supported by Narodowe Centrum Nauki (NCN, Poland) under Project Nos. 2021/40/C/ST3/00177. This research was carried out with the support of the Interdisciplinary Center for Mathematical and Computational Modeling at the University of Warsaw (ICM UW) under grants No. G81-4 and No. G93-1613. This project is funded by the German Research Foundation (DFG) via the projects A05 of the Collaborative Research Center SFB 1143 (project-id 247310070). |