Exact degenerate ground states for the F-AF spin chain with bond alternation

Abstract

We investigate the $J_1$-$J_2$ spin chain consisting of spins with magnitude $\frac{1}{2}$. The nearest-neighbor and the next-nearest-neighbor exchange interactions are ferromagnetic and antiferromagnetic, respectively, and induce strong frustration. Both these interactions involve the bond alternation. We find exact solutions for all the degenerate ground states on the phase boundary of the ferromagnetic phase. The degeneracy remains irrespective of two parameters representing the bond alternation. The exact solutions are of closed forms for no bond alternation and of recursion formulae in general. The exact solutions are applicable to the $\Delta$ chain as a special case.

arXiv comment4 pages, 2 figures

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Cited by in corpus (9)

• Delta chain with ferromagnetic and antiferromagnetic interactions at the critical point
• The J1-J2 Heisenberg model at and close to its z=4 quantum critical point
• Topological Phases of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain with Frustrated Next-Nearest-Neighbour Interaction
• Magnetic crossover and complex excitation spectrum of the ferromagnetic/antiferromagnetic spin-1/2 chain system alpha-TeVO4
• Factorized ground state for a general class of ferrimagnets
• Entanglement and level crossings in frustrated ferromagnetic rings
• Discrete symmetries and Lieb-Schultz-Mattis theorem
• Scaling Property of the F-AF Spin Chain Near the Exactly Solvable Point
• Topological Phases of Spin-1/2 Ferromagnetic--Antiferromagnetic Alternating Heisenberg Chains with Alternating Next-Nearest-Neighbour Interaction