2008/02/29 by Dao‐Xin Yao, Dao-Xin Yao, Yen Lee Loh +3 · 2 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.78.024428
published as Phys. Rev. B 78, 024428 (2008) · 12 pages, 12 figures
arxiv created 2008/05/16 · openalex publication_date 2008/07/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The recently fabricated two-dimensional magnetic materials Cu9X2(cpa)6\ensuremath⋅xH2O (cpa=2-carboxypentonic acid and X=F,Cl,Br) have copper sites which form a triangular kagome lattice (TKL), formed by introducing small triangles (``a-trimers'') inside of each kagome triangle (``b-trimer''). We show that in the limit where spins residing on b-trimers have Ising character, quantum fluctuations of XXZ spins residing on the a-trimers can be exactly accounted for in the absence of applied field. This is accomplished through a mapping to the kagome Ising model, for which exact analytic solutions exist. We derive the complete finite-temperature phase diagram for this XXZ-Ising model, including the residual zero-temperature entropies of the seven ground-state phases. Whereas the disordered (spin liquid) ground state of the pure Ising TKL model has macroscopic residual entropy ln 72=4.2767… per unit cell, the introduction of transverse (quantum) couplings between neighboring a-spins reduces this entropy to 2.5258… per unit cell. In the presence of applied magnetic field, we map the TKL XXZ-Ising model to the kagome Ising model with three-spin interactions and derive the ground-state phase diagram. A small (or even infinitesimal) field leads to a new phase that corresponds to a nonintersecting loop gas on the kagome lattice, with entropy 1.4053… per unit cell and a mean magnetization for the b-spins of 0.12(1) per site. In addition, we find that for moderate applied field, there is a critical spin liquid phase that maps to close-packed dimers on the honeycomb lattice, which survives even when the a-spins are in the Heisenberg limit.