Efficient thermodynamics for strongly correlated fermions and bosons

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For integrable systems the ground-state energy and excitations are computable in principle. Still, the calculation of thermodynamical properties remains a challenge of its own as all energy levels have to be taken into account. Traditionally the computation of the partition function of integrable systems is achieved by means of the so-called thermodynamic Bethe ansatz (TBA) which is a combinatorial approach typically leading to infinitely many coupled non-linear integral equations. In previous work we have succeeded to transform such infinite systems of equations into a new system of finitely many equations. Our alternative formulation has two essential advantages over the TBA approach. First, the numerical computations are much faster. And second, our equations have a much wider range of applicability as, for instance, to the computation of finite temperature correlation lengths and general nearest-neighbour correlators.The main objective of this project is to find a systematic way how to derive such finite systems of non-linear integral equations for all integrable lattice models and to advance methods for solving them numerically. These techniques shall be applied to interesting systems like multicomponent Bose or Fermi gases.