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Matrix product purifications (MPPs) are a very efficient tool for thesimulation of strongly correlated quantum many-body systems at finitetemperatures. When a system features symmetries, these can be used to reducecomputation costs substantially. It is straightforward to compute an MPP of agrand-canonical ensemble, also when symmetries are exploited. This paperprovides and demonstrates methods for the efficient computation of MPPs ofcanonical ensembles under utilization of symmetries. Furthermore, we present ascheme for the evaluation of global quantum number distributions using matrixproduct density operators (MPDOs). We provide exact matrix productrepresentations for canonical infinite-temperature states, and discuss how theycan be constructed alternatively by applying matrix product operators tovacuum-type states or by using entangler Hamiltonians. A demonstration of thetechniques for Heisenberg spin-1/2 chains explains why the difference in theenergy densities of canonical and grand-canonical ensembles decays as 1/L.

Matrix product purifications for canonical ensembles and quantum number distributions