Dynamical Properties of one dimensional Mott Insulators

At low energies the charge sector of one dimensional Mott insulators can be described in terms of a quantum Sine-Gordon model (SGM). Using exact results derived from integrability it is possible to determine dynamical properties like the frequency dependent optical conductivity. We compare the exact results to perturbation theory and renormalisation group calculations. We also discuss the application of our results to experiments on quasi-1D organic conductors. Lecture given by FHLE at the NATO ASI/EC summer school “New Theoretical Approaches to Strongly Correlated Systems”, Sir Isaac Newton Insitute for Mathematical Sciences, Cambridge April 2000 1 1D Mott insulators The Mott metal-insulator transition is a paradigm for the importance of electron-electron interactions in condensed matter systems. It occurs in a variety of actual materials and has attracted much attention over the last fifty years [1]. The underlying mechanism that drives the transition is by now well understood, but details on e.g. transport properties remain largely unknown in D = 2 and D = 3 due to the lack of nonperturbative methods for treating strongly correlated electron systems. The situation is more fortunate in two cases: D = ∞, where much progress has been made in recent years [2] and D = 1, where nonperturbative methods permit essentially a full solution of the problem. The 1D case is the one we will be concerned with here. A full characterization of the Mott insulating phase requires the knowledge of dynamical correlation functions. The frequency dependent optical conductivity σ(ω) is one of the most important examples from an experimental point of view. The behaviour of σ(ω) in the metallic regime is easily understood in terms of the Tomonaga-Luttinger theory [3, 4]. The situation in the Mott insulating phase is much more complicated due to the spectral gap that is dynamically generated by the electron-electron interactions. Here σ(ω) has until now only been studied by perturbative methods [5, 6], which break down in the most interesting regime of frequencies close to the optical gap. In these proceedings we use methods of integrable quantum field theory to determine σ(ω) in 1D Mott insulators for all frequencies much smaller than the bandwidth, which is the large scale in the field theory approach to the problem. Some of the results presented here have already appeared in [7]. The paradigm of a 1D Mott insulator is the Hubbard model H = −t ∑ l;σ ( cl,σcl+1,σ + h.c. )