Numerical renormalization approach to two-dimensional quantum antiferromagnets with valence-bond-solid type ground state

Jennifer Chayes, Lincoln Chayes, Steven Allan Kivelson

Kedar Damle, Fabien Alet, Sumiran Pujari +2 more

Yasuhiro Hieida, Kouichi Okunishi, Yasuhiro Akutsu

We study the ground-state properties of two-dimensional quantum spin systems having the valence-bond-solid (VBS) type ground states. The `product-of-tensors' form of the ground-state wavefunction of the system is utilized to associate it with an equivalent classical lattice statistical model which can be treated by the transfer-matrix method. For diagonalization of the transfer matrix, we employ the product-wavefunction renormalization group method, which is a variant of the density-matrix renormalization group method. We obtain the correlation length and the sublattice magnetization accurately. For the anisotropically `deformed' S = 3/2 VBS model on the honeycomb lattice, we find that the correlation length as a function of the deformation parameter behaves very much as that in the S = 3/2 VBS chain.

Subir Sachdev A, Kwon Park

Jędrzej Wardyn, Satoshi Nishimoto, Cliò Efthimia Agrapidis

We study the frustrated and dimerized ferromagnetic-antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{1}^{\ensuremath{'}}\text{\ensuremath{-}}{J}_{2}$ chain using the density-matrix renormalization group 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 ${J}_{1}^{\ensuremath{'}}/{J}_{1}$ 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 ${J}_{1}^{\ensuremath{'}}/{J}_{1}=1$ 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 ${J}_{1}^{\ensuremath{'}}/{J}_{1}=0$ case. Remarkably, both VBS states are identified as being of Haldane type, marked by a finite SOP and twofold 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 an 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 ${\mathrm{LiCuSbO}}_{4}$ 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.

Ian K. Affleck, Tom Kennedy, Élliott H. Lieb +1 more