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Ground-state ordering of the J1 - J2 model on the simple cubic and body-centered cubic lattices

Farnell, Damian, Richter, Johannes and Oliver, Goetze 2016. Ground-state ordering of the J1 - J2 model on the simple cubic and body-centered cubic lattices. Physical Review B 93 , 235123. 10.1103/PhysRevB.93.235123

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Abstract

The J1−J2 Heisenberg model is a “canonical” model in the field of quantum magnetism in order to study the interplay between frustration and quantum fluctuations as well as quantum phase transitions driven by frustration. Here we apply the coupled cluster method (CCM) to study the spin-half J1−J2 model with antiferromagnetic nearest-neighbor bonds J1>0 and next-nearest-neighbor bonds J2>0 for the simple cubic (sc) and body-centered cubic (bcc) lattices. In particular, we wish to study the ground-state ordering of these systems as a function of the frustration parameter p=z2J2/z1J1, where z1 (z2) is the number of nearest (next-nearest) neighbors. We wish to determine the positions of the phase transitions using the CCM and we aim to resolve the nature of the phase transition points. We consider the ground-state energy, order parameters, spin-spin correlation functions, as well as the spin stiffness in order to determine the ground-state phase diagrams of these models. We find a direct first-order phase transition at a value of p=0.528 from a state of nearest-neighbor Néel order to next-nearest-neighbor Néel order for the bcc lattice. For the sc lattice the situation is more subtle. CCM results for the energy, the order parameter, the spin-spin correlation functions, and the spin stiffness indicate that there is no direct first-order transition between ground-state phases with magnetic long-range order, rather it is more likely that two phases with antiferromagnetic long range are separated by a narrow region of a spin-liquid-like quantum phase around p=0.55. Thus the strong frustration present in the J1−J2 Heisenberg model on the sc lattice may open a window for an unconventional quantum ground state in this three-dimensional spin model.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Dentistry
Publisher: American Physical Society
ISSN: 2469-9950
Date of First Compliant Deposit: 17 June 2016
Date of Acceptance: 2 June 2016
Last Modified: 01 Feb 2018 06:09
URI: http://orca.cf.ac.uk/id/eprint/91845

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