Efficient thermodynamics for strongly correlated fermions and bosons

对于可积系统，基态能量和激发态原则上是可计算的。尽管如此，热力学性质的计算本身仍然是一个挑战，因为必须考虑到所有的能级。传统上，可积系统配分函数的计算是通过所谓的热力学Bethe ansatz （TBA）来实现的，这是一种组合方法，通常会导致无限多个耦合的非线性积分方程。在以前的工作中，我们已经成功地将这种无限的方程组转化为有限多个方程的新方程组。与TBA方法相比，我们的替代配方有两个基本优势。首先，数值计算要快得多。其次，我们的方程具有更广泛的适用性，例如，用于计算有限温度相关长度和一般最近邻相关器。本项目的主要目标是找到一种系统的方法来推导所有可积晶格模型的非线性积分方程的有限系统，并提出数值求解它们的方法。这些技术将应用于有趣的系统，如多组分玻色或费米气体。

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.