Correlation Functions and Coulomb Blockade of Interacting Fermions at Finite Temperature and Size

We present explicit expressions for the correlation functions of interacting fermions in one dimension which are valid for arbitrary system sizes and temperatures. The result applies to a number of very different strongly correlated systems, including mesoscopic quantum wires, quantum Hall edges, spin chains and quasi-one-dimensional metals. It is for example possible to calculate Coulomb blockade oscillations from our expression and determine their dependence on interaction strength and temperature. Numerical simulations show excellent agreement with the analytical results. 71.10.Pm, 71.27.+a, 73.23.Hk Typeset using REVTEX 1 Recently, there has been great interest in strongly correlated systems of all kinds, which is spurred by high temperature superconductivity, progress in mesoscopic physics, quantum Hall systems, and newly available materials which accurately display the characteristics of one-dimensional metals or spin chains. In the case of quasi-one-dimensional electron systems much progress can be made with the Luttinger liquid formalism [1] which is able to describe virtually any type of local interaction and can be solved by use of bosonization techniques [2,3]. Using these methods, it is well known how to calculate correlation functions in the infinite length or zero temperature limit and therefore determine the spectral properties [4] of a number of systems, like mesoscopic quantum wires, quantum Hall bars [5], quasi one-dimensional metals and spin chains [6,7] even in the presence of boundaries [8,9]. We now present explicit expressions for the correlation functions which are valid at arbitrary temperature, system size, and distances (as long as the lattice spacing is relatively small). These expressions can be used to calculate Coulomb blockade oscillations in mesoscopic systems as a function of the interaction strength and of temperature. Monte Carlo simulations of one of the simplest systems, namely interacting spinless fermions on a one-dimensional lattice, show excellent agreement with our result. As our model Hamiltonian we consider one-dimensional interacting fermions in the continuum limit