Heisenberg antiferromagnet on the Husimi lattice

• Published in: arXiv.org
• Main Authors: Liao, H J, Xie, Z Y, Chen, J, Han, X J, Xie, H D, Normand, B, Xiang, T
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.03.2016
• Subjects: Antiferromagnetism; Broken symmetry; Entanglement; Ground state; Heisenberg theory; Numerical methods; Physics - Strongly Correlated Electrons; Solid state; Spin liquid; Statistical models; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1510.08655

We perform a systematic study of the antiferromagnetic Heisenberg model on the Husimi lattice using numerical tensor-network methods based on Projected Entangled Simplex States (PESS). The nature of the ground state varies strongly with the spin quantum number, \(S\). For \(S = 1/2\), it is an algebraic (gapless) quantum spin liquid. For \(S = 1\), it is a gapped, non-magnetic state with spontaneous breaking of triangle symmetry (a trimerized simplex-solid state). For \(S = 2\), it is a simplex-solid state with a spin gap and no symmetry-breaking; both integer-spin simplex-solid states are characterized by specific degeneracies in the entanglement spectrum. For \(S = 3/2\), and indeed for all spin values \(S \ge 5/2\), the ground states have \(120\)-degree antiferromagnetic order. In a finite magnetic field, we find that, irrespective of the value of \(S\), there is always a plateau in the magnetization at \(m = 1/3\).