Abstract
In strictly one-dimensional systems, repulsive interactions tend to reduce particle mobility on a lattice. Therefore, the Drude weight, controlling the divergence at zero-frequency of optical conductivities in perfect conductors, is lower than in non-interacting cases. We show that this is not the case when extending to quasi one-dimensional ladder systems. Relying on bosonization, perturbative and matrix product states (MPS) calculations, we show that nearest-neighbor interactions and magnetic fluxes provide a bias between back- and forward-scattering processes, leading to linear corrections to the Drude weight in the interaction strength. As a consequence, Drude weights counter-intuitively increase (decrease) with repulsive (attractive) interactions. Our findings are relevant for the efficient tuning of Drude weights in the framework of ultracold atoms trapped in optical lattices and equally affect topological edge states in condensed matter systems.
Highlights
The seminal work by Kohn [1] established the Drude weight as a crucial quantity to describe the conduction properties of strongly correlated quantum systems
We show that the increase of Drude weight by local repulsive interactions at zero temperature is a more general feature of quasi-1D interacting systems thread by a transverse magnetic flux χ, see Fig. 1
The arguments leading to the identity (5), namely the commutation rule (4), do not generally apply in the presence of orbital effects in quasi-1D systems and, in this paper, we show a very simple mechanism leading to a modification of the Drude weight in quantum ladders, which is linear in the interaction amplitudes and, remarkably, is positive in presence of typical intrachain repulsive terms
Summary
The seminal work by Kohn [1] established the Drude weight as a crucial quantity to describe the conduction properties of strongly correlated quantum systems. The currents driven by either displacing the confining potential [56] or tilting the system [57] reproduce those generated persistently by a flux penetrating a ring geometry in an adiabatic approximation [46], accessing Drude weights with open boundary conditions It is important, both on the experimental and fundamental level, to understand and develop physical intuition concerning the effects of strong correlations on the Drude weight. A more fundamental understanding is derived from the effective low-energy Luttinger liquid theory of interacting quantum ladders, showing that nearest-neighbor interactions and magnetic fluxes provide a bias between backand forward-scattering processes.
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