2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102680We apply a generalization of the time-dependent DMRG to study finite temperature properties of several quantum spin chains, including the frustrated $J_1-J_2$ model. We discuss several practical issues with the method, including use of quantum numbers and finite size effects. We compare with transfer-matrix DMRG, finding that both methods produce excellent results.4 pages and 4 figuresStrongly Correlated Electronstext