Transport in a classical model of an one-dimensional Mott insulator: Influence of conservation laws

– We study numerically how conservation laws affect the optical conductivity σ(ω) of a slightly doped one-dimensional Mott insulator. We investigate a regime where the average distance between charge excitations is large compared to their thermal de Broglie wave length and a classical description is possible. Due to conservation laws, the dc-conductivity is infinite and the Drude weight D is finite even at finite temperatures. Our numerical results test and confirm exact theoretical predictions for D both for integrable and non-integrable models. Small deviations from integrability induce slowly decaying modes and, consequently, low-frequency peaks in σ(ω) which can be described by a memory matrix approach. Conservation laws and slowly decaying modes strongly affect transport properties [1]. The reason is that the presence of conserved quantities (e.g. momentum) can prohibit the complete decay of an electrical current J (in the absence of external fields). If a certain fraction Jc of J does not decay, the dc-conductivity is infinite and the optical conductivity σ(ω) is characterized by a finite Drude weight D on top of a regular contribution σreg(ω) even at finite temperature T , Reσ(ω) = 2πDδ(ω) + Reσreg(ω). In quasi one-dimensional (1D) systems conservation laws are especially important. Even in the presence of Umklapp scattering from a periodic potential, certain pseudo-momenta are approximately conserved [2]. Further, the low-energy properties of interacting electrons in one dimension are well described by integrable models like the Luttinger, Sine-Gordon or, equivalently, the massive Thirring model, which possess an infinite number of conservation laws. While generic models are not integrable, the integrability of their low-energy theories implies that their low-frequency, low-T optical conductivity can be strongly influenced by the presence of approximately conserved quantities [2, 3]. Quantitatively, the influence of conserved quantities (CQ) Pn on the conductivity can be understood in the following way. Any linear combination of the Pn is conserved: the Pn span a vector space. Components of J “perpendicular” to this space will decay. The component “parallel” to it, i.e. the projection Jc of J onto this space, is conserved and will give rise to an infinite conductivity. What is a physically meaningful definition of “perpendicular”? We define an operator B to be perpendicular to A, if 〈B〉 = 0 in a (linear-response) experiment