Faculty of Physics, Vienna Center for Quantum Science and Technology, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
Phys Rev Lett. 2013 Jul 19;111(3):037202. doi: 10.1103/PhysRevLett.111.037202. Epub 2013 Jul 17.
We construct a class of projected entangled pair states which is exactly the resonating valence bond wave functions endowed with both short range and long range valence bonds. With an energetically preferred resonating valence bond pattern, the wave function is simplified to live in a one-parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin-1/2 J(1)-J(2) antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with an even or odd number of fluxes penetrating the cylinder and an even or odd number of spinons on the boundary. The energy splitting in different topological sectors is exponentially small with the cylinder perimeter. We find a power law decay of the dimer correlation function on a torus, and a lnL correction to the entanglement entropy, indicating a gapless spin-liquid phase at the optimum parameter.
我们构建了一类投影纠缠对态，它恰好是具有短程和长程价键的共振价键波函数。通过具有能量优势的共振价键模式，波函数简化为在一个参数变分空间中。我们调整这个变分参数，以最小化在正方晶格上受挫的自旋为 1/2 的 J(1)-J(2)反铁磁海森堡模型的能量。在圆柱几何中，我们能够构建四个拓扑区域，每个区域有偶数或奇数个磁通穿过圆柱，边界上有偶数或奇数个自旋子。不同拓扑区域之间的能量分裂随圆柱周长呈指数级减小。我们在环面上发现了二聚体相关函数的幂律衰减，以及对纠缠熵的 lnL 修正，这表明在最优参数下存在无能隙的自旋液体相。
