Mallayya Krishnanand, Rigol Marcos
Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Phys Rev E. 2017 Mar;95(3-1):033302. doi: 10.1103/PhysRevE.95.033302. Epub 2017 Mar 7.
We discuss the application of numerical linked cluster expansions (NLCEs) to study one dimensional lattice systems in thermal equilibrium and after quantum quenches from thermal equilibrium states. For the former, we calculate observables in the grand canonical ensemble, and for the latter we calculate observables in the diagonal ensemble. When converged, NLCEs provide results in the thermodynamic limit. We use two different NLCEs: a maximally connected expansion introduced in previous works and a site-based expansion. We compare the effectiveness of both NLCEs. The site-based NLCE is found to work best for systems in thermal equilibrium. However, in thermal equilibrium and after quantum quenches, the site-based NLCE can diverge when the maximally connected one converges. We relate this divergence to the exponentially large number of clusters in the site-based NLCE and the behavior of the weights of observables in those clusters. We discuss the effectiveness of resummations to cure the divergence. Our NLCE calculations are compared to exact diagonalization ones in lattices with periodic boundary conditions. NLCEs are found to outperform exact diagonalization in periodic systems for all quantities studied.
我们讨论数值链接簇展开（NLCEs）在研究处于热平衡以及从热平衡态进行量子猝灭后的一维晶格系统中的应用。对于前者，我们在巨正则系综中计算可观测量，而对于后者，我们在对角系综中计算可观测量。当收敛时，NLCEs在热力学极限下提供结果。我们使用两种不同的NLCEs：先前工作中引入的最大连通展开和基于格点的展开。我们比较了这两种NLCEs的有效性。发现基于格点的NLCE对于处于热平衡的系统效果最佳。然而，在热平衡以及量子猝灭之后，当最大连通的NLCE收敛时，基于格点的NLCE可能会发散。我们将这种发散与基于格点的NLCE中指数级大量的簇以及这些簇中可观测量权重的行为联系起来。我们讨论了用于消除发散的重求和的有效性。我们将NLCE计算结果与具有周期性边界条件的晶格中的精确对角化结果进行了比较。发现在周期性系统中，对于所有研究的量，NLCEs的表现优于精确对角化。
