Getting the same answer from complementary numerical methods
Developing reliable numerical methods that can give meaningful and useful results for lattice models [e.g. the Hubbard, Heisenberg, and t-J models] of strongly correlated electrons is a challenging and tedious task. An important outcome is when complementary methods (including analytical methods) give the same result! There is a nice Physical Review E article by Marcos Rigol , Tyler Bryant, and Rajiv Singh which considers the application of a new numerical linked cluster algorithm (NLC) method to the t-J model. To put nicely things in context they state In spite of its simplicity, understanding finite-temperature thermodynamic properties of the t-J model has proven to be a very challenging task. Quantum Monte Carlo simulations suffer from severe sign problems, which become a major difficulty at low temperatures. The two general approaches that have been commonly used to study this model are [exact diagonalisation] ED and [high temperature expansions] HTE. ED studies in which one f