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Quantum magnetism in ultracold alkali and alkaline-earth fermion systems with symplectic symmetry

Quantum magnetism in ultracold alkali and alkaline-earth fermion systems with symplectic symmetry We numerically study the quantum magnetism of ultracold alkali and alkaline-earth fermion systems with large hyperfine spin F = 3 2 , which are characterized by a generic S p ( N ) symmetry with N = 4 . The methods of exact diagonalization (ED) and density matrix renormalization group are employed for the large size one-dimensional (1D) systems, and the ED method is applied to a two-dimensional (2D) square lattice on small sizes. We focus on the magnetic exchange models in the Mott-insulating state at quarter-filling. Both 1D and 2D systems exhibit rich phase diagrams depending on the ratio between the spin exchanges J 0 and J 2 in the bond spin singlet and quintet channels, respectively. In one dimension, the ground states exhibit a long-range-ordered dimerization with a finite spin gap at J 0 / J 2 > 1 and a gapless spin-liquid state at J 0 / J 2 ⩽ 1 , respectively. In the former and latter cases, the correlation functions exhibit the two-site and four-site periodicities, respectively. In two-dimensions, various spin-correlation functions are calculated up to the size of 4 × 4 . The Néel-type spin correlation dominates at large values of J 0 / J 2 , while a 2 × 2 plaquette correlation is prominent at small values of this ratio. Between them, a columnar spin-Peierls dimerization correlation peaks. We infer the competition among the plaquette ordering, the dimer ordering, and the Néel ordering in the 2D system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Quantum magnetism in ultracold alkali and alkaline-earth fermion systems with symplectic symmetry

Hung, Hsiang-Hsuan; Wang, Yupeng; Wu, Congjun
Physical Review B , Volume 84 (5) – Aug 1, 2011
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References (3)

Publisher
American Physical Society (APS)
Copyright
Copyright © 2011 The American Physical Society
ISSN
1098-0121
eISSN
1550-235X
DOI
10.1103/PhysRevB.84.054406
Publisher site
See Article on Publisher Site

Abstract

We numerically study the quantum magnetism of ultracold alkali and alkaline-earth fermion systems with large hyperfine spin F = 3 2 , which are characterized by a generic S p ( N ) symmetry with N = 4 . The methods of exact diagonalization (ED) and density matrix renormalization group are employed for the large size one-dimensional (1D) systems, and the ED method is applied to a two-dimensional (2D) square lattice on small sizes. We focus on the magnetic exchange models in the Mott-insulating state at quarter-filling. Both 1D and 2D systems exhibit rich phase diagrams depending on the ratio between the spin exchanges J 0 and J 2 in the bond spin singlet and quintet channels, respectively. In one dimension, the ground states exhibit a long-range-ordered dimerization with a finite spin gap at J 0 / J 2 > 1 and a gapless spin-liquid state at J 0 / J 2 ⩽ 1 , respectively. In the former and latter cases, the correlation functions exhibit the two-site and four-site periodicities, respectively. In two-dimensions, various spin-correlation functions are calculated up to the size of 4 × 4 . The Néel-type spin correlation dominates at large values of J 0 / J 2 , while a 2 × 2 plaquette correlation is prominent at small values of this ratio. Between them, a columnar spin-Peierls dimerization correlation peaks. We infer the competition among the plaquette ordering, the dimer ordering, and the Néel ordering in the 2D system.

Journal

Physical Review B – American Physical Society (APS)

Published: Aug 1, 2011

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