A grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation with fields for occupied and unoccupied sites, an effective field theory is derived in which a complex field corresponds with the order parameter of the condensate and a real field with the total density of bosons. Near the boundary between the normal and the superfluid phase, we obtain the Ginzburg-Landau functional for the superfluid order parameter. A mean-field calculation shows that the critical temperature
Tc increases with increasing density up to a maximum and decreases with further increasing density.
One of the most interesting directions in theoretical high-energy and condensed-matter physics is understanding dynamical properties of collective states of quantum field theories.The most elementary tool in this quest is retarded equilibrium correlators governing the linear response theory.In this article we examine tensor networks as a way of determining them in a fully ab initio way in a class of (1+1)-dimensional quantum field theories arising as infrared descriptions of quantum Ising chains.We show that, complemented with signal analysis using the Prony method, tensor network calculations for intermediate times provide a powerful way to explore the structure of singularities of the correlator in the complex frequency plane and to make predictions about the thermal response to perturbations in a class of nonintegrable interacting quantum field theories.