Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method

Journal Article · Wed Oct 15 04:00:00 EDT 2014 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4899216· OSTI ID:22307990

Bishop, R. F.; Li, P. H. Y. ^[1]; Campbell, C. E. ^[2]

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1. School of Physics and Astronomy, Schuster Building, The University of Manchester, Manchester, M13 9PL (United Kingdom)
2. School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis, Minnesota 55455 (United States)

We outline how the coupled cluster method of microscopic quantum many-body theory can be utilized in practice to give highly accurate results for the ground-state properties of a wide variety of highly frustrated and strongly correlated spin-lattice models of interest in quantum magnetism, including their quantum phase transitions. The method itself is described, and it is shown how it may be implemented in practice to high orders in a systematically improvable hierarchy of (so-called LSUBm) approximations, by the use of computer-algebraic techniques. The method works from the outset in the thermodynamic limit of an infinite lattice at all levels of approximation, and it is shown both how the 'raw' LSUBm results are themselves generally excellent in the sense that they converge rapidly, and how they may accurately be extrapolated to the exact limit, m → ∞, of the truncation index m, which denotes the only approximation made. All of this is illustrated via a specific application to a two-dimensional, frustrated, spin-half J{sub 1}{sup XXZ}−J{sub 2}{sup XXZ} model on a honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings J{sub 1} > 0 and J{sub 2} ≡ κJ{sub 1} > 0, respectively, where both interactions are of the same anisotropic XXZ type. We show how the method can be used to determine the entire zero-temperature ground-state phase diagram of the model in the range 0 ≤ κ ≤ 1 of the frustration parameter and 0 ≤ Δ ≤ 1 of the spin-space anisotropy parameter. In particular, we identify a candidate quantum spin-liquid region in the phase space.

• OSTI ID: 22307990
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 1619; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANISOTROPY
APPROXIMATIONS
GROUND STATES
LIQUIDS
MAGNETISM
MANY-BODY PROBLEM
PHASE DIAGRAMS
PHASE SPACE
PHASE TRANSFORMATIONS
QUANTUM MECHANICS
SPIN
TWO-DIMENSIONAL CALCULATIONS