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arXiv · 2306.01543

Existence of two distinct valence bond solid states in the dimerized frustrated ferromagnetic $J_1$-$J_1'$-$J_2$ chain

Jędrzej Wardyn·Satoshi Nishimoto·Cliò Efthimia Agrapidis
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Abstract

We study the frustrated and dimerized ferromagnetic-antiferromagnetic $J_1$-$J_1'$-$J_2$ 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 $J_1'/J_1$ and $J_2/|J_1|$ values. This phase diagram reveals a ferromagnetic phase and two distinct valence-bond-solid (VBS) phases. The first VBS phase, referred to as $\mathcal{D}_3$-VBS, is typified by the formation of valence bonds between third-neighbor spin-1/2's, persisting as a continuation from the $J_1'/J_1=1$ 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 $J_1'/J_1=0$ 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 LiCuSbO$_4$ is classified as the $\mathcal{D}_3$-VBS state. Collectively, these results mark a substantial stride forward in our comprehension of quantum phase transitions and topological states.

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Jędrzej Wardyn, Satoshi Nishimoto, Cliò Efthimia Agrapidis. 2023-11-09. Existence of two distinct valence bond solid states in the dimerized frustrated ferromagnetic $J_1$-$J_1'$-$J_2$ chain. https://doi.org/10.1103/physrevb.108.205111

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