Department of Physics, University of California, Berkeley, 94720, USA.
Phys Rev Lett. 2011 Aug 5;107(6):067202. doi: 10.1103/PhysRevLett.107.067202. Epub 2011 Aug 3.
Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterizes their quantum structure. In particular we calculate the Renyi entropy S(2) on model wave functions obtained by Gutzwiller projection of a Fermi sea. Although the wave functions are not sign positive, S(2) can be calculated on relatively large systems (>324 spins) using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi sea state violates the boundary law, with S(2) enhanced by a logarithmic factor. This is an unusual result for a bosonic wave function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.
量子自旋液体是物质的一种相，其内部结构不能用局部序参量来描述。特别有趣的是临界自旋液体，其中强相互作用的激发控制着低能性质。在这里，我们计算了它们的二分量纠缠熵，这一熵描述了它们的量子结构。具体来说，我们计算了由费米海的 Gutzwiller 投影得到的模型波函数的 Renyi 熵 S(2)。尽管波函数不是正定的，但我们可以使用变分蒙特卡罗技术在相对较大的系统（>324 个自旋）上计算 S(2)。在三角晶格上，我们发现投影费米海态的纠缠熵违反了边界定律，其 S(2)被增强了一个对数因子。这对于玻色子波函数来说是一个不寻常的结果，反映了出emergent fermions 的存在。这些技术可以扩展到研究广泛的其他相。
