Trebst Simon, Ardonne Eddy, Feiguin Adrian, Huse David A, Ludwig Andreas W W, Troyer Matthias
Microsoft Research, Station Q, University of California-Santa Barbara, CA 93106, USA.
Phys Rev Lett. 2008 Aug 1;101(5):050401. doi: 10.1103/PhysRevLett.101.050401. Epub 2008 Jul 30.
We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symmetry end points we numerically establish descriptions in terms of two-dimensional conformal field theories. A topological symmetry protects the critical phases and determines the nature of gapped phases.
我们表明，相互作用的斐波那契任意子链可以支持多种集体基态，范围从扩展的临界、无隙相到具有基态简并和准粒子激发的有隙相。特别地，我们通过将最近研究的两体任意子相互作用扩展到三体任意子交换，将马宗达-戈什哈密顿量推广到任意子自由度。两体和三体任意子相互作用之间的能量竞争导致了一个丰富的相图，其中包含多个临界相和有隙相。对于临界相及其更高对称性的端点，我们通过二维共形场论在数值上建立了描述。一种拓扑对称性保护临界相并决定有隙相的性质。
