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arXiv:0705.4361 · Acta Physica Polonica A

Frustration-Driven Quantum Phase Transition in the 1D Extended Anisotropic Heisenberg Model

Evgeny A. Plekhanov, Adolfo Avella, Francesco Paolo Mancini

Published Jan 1, 2008• 1 citation
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Abstract

By using density matrix renormalization group technique we study the 1D extended anisotropic Heisenberg model.We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions induced by frustration.By increasing the next-nearest-neighbor interaction, the ground state of the system changes smoothly from a completely polarized state to a next-nearest-neighbor correlated one.On the contrary, letting the in-plane interaction to be greater than the out-of-plane one, the ground state changes abruptly.

DOI
10.12693/aphyspola.113.429

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By using density matrix renormalization group technique we study the 1D extended anisotropic Heisenberg model.We find that starting from the ferromagnetic phase, the system undergoes two quantum phase transitions induced by frustration.By increasing the next-nearest-neighbor interaction, the ground state of the system changes smoothly from a completely polarized state to a next-nearest-neighbor correlated one.On the contrary, letting the in-plane interaction to be greater than the out-of-plane one, the ground state changes abruptly.
By using the density matrix renormalization group(DMRG) method,the author investigates the diagram of the one-dimensional frustrated anisotropic ferromagnetic S=1 Heisenberg spin model,in which the nearest neighboring interactions are anisotropic ferromagnetic and the next nearest neighboring exchanges are considerable anti-ferromagnetic.The ground state energy and both the in-plane and out-of-plane spin correlation functions are calculated.Apart from the ferromagnetic phase and the spin-fluid phase in the small frustration region,but in the large frustration region,it is identified that spin correlations decay with a short-range exponential law and an oscillating behavior.The result is different from the previous result for S=1/2.
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Abstract We have studied the ground state phases of the one-dimensional (1D) spin-1/2 anisotropic frustrated ferromagnetic model, using the numerical Lanczos method. We have focused on the quantum correlations as the concurrence and the quantum discord (QD) between the nearest neighbor (NN) and the next-nearest neighbor (NNN) spins. Numerical results show that the Tomonaga-Luttinger liquid (TLL), the even-parity dimer, and the vector chiral phases can be distinguished from each other using the long-distance quantum correlations. Specially, the critical points are explicitly detected in the first derivative of the concurrence between the nearest neighbor spins with respect to the frustration parameter.
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