Abstract
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}12 ferromagnetic (J_1J1) Heisenberg chain with next-nearest-neighbor antiferromagnetic (J_2J2) interactions. On the basis of density-matrix renormalization group calculations we show the existence of a finite spin gap at J_2/|J_1|>1/4J2/|J1|>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.
Highlights
The one-dimensional quantum world of spin-chain systems connects some of the most advanced concepts from many-body physics, such as integrability and symmetry-protected topological order [1], with the measurable physical properties of real materials
We studied the frustrated FM J1-J2 chain using the density-matrix renormalization group (DMRG) technique
1 4 from a state to a third-neighbor state with the AKLT-like topological hidden order. This provides a simple realization of coexistence of spontaneous symmetry breaking and topological order, or rather, topological order caused by spontaneous symmetry breaking
Summary
The one-dimensional quantum world of spin-chain systems connects some of the most advanced concepts from many-body physics, such as integrability and symmetry-protected topological order [1], with the measurable physical properties of real materials. An example is the presence of the Haldane phase [2] in spin-1 chains, which is a topological ground state protected by global Z2 × Z2 symmetry [3, 4]. One of the simplest systems that shares both these features – geometric frustration and one-dimensionality – is the so-called J1-J2 chain, the Hamiltonian of which is given by. This chain system can be represented as a zigzag ladder [Fig. 1(a)] or a diagonal ladder [Fig. 1(b)-(d)]. Multi-magnons bound state [13] and multipolar ordering [14] under magnetic field have been established both theoretically and experimentally in this context
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