Magnetization jumps in 1D valence bond solids

Munehisa Matsumoto

Anders W. Sandvik

Hui Shao, Wenan Guo, Anders W. Sandvik

Adam Iaizzi, Anders W. Sandvik

A Valence bond solid (VBS) is a nonmagnetic, long-range ordered state of a quantum spin system where local spin singlets are formed in some regular pattern. We here study the competition between VBS order and a fully polarized ferromagnetic state as function of an external magnetic field in a one-dimensional extended Heisenberg model—the J-Q 2 model— using stochastic series expansion (SSE) quantum Monte Carlo simulations with directed loop updates. We discuss the ground state phase diagram.

George Theodorou, Morrel H. Cohen

Cliò Efthimia Agrapidis, Stefan-Ludwig Drechsler, Jeroen van den Brink +1 more

Frustrated one-dimensional (1D) magnets are known as ideal playgrounds for new exotic quantum phenomena to emerge. We consider an elementary frustrated 1D system: the spin- \frac{1}{2} 1 2 ferromagnetic ( J_1 J 1 ) Heisenberg chain with next-nearest-neighbor antiferromagnetic ( J_2 J 2 ) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at J_2/|J_1|>1/4 J 2 / | J 1 | > 1 / 4 and we find the ground state in this region to be a valence bond solid (VBS) with spin-singlet dimerization between third-neighbor sites. The VBS is the consequence of spontaneous symmetry breaking through order by disorder. Quite interestingly, this VBS state has a Affleck-Kennedy-Lieb-Tasaki-type topological order. This is the first example of a frustrated spin chain in which quantum fluctuations induce gapped topological order.