| Popis: |
There has been much work in the recent past in developing the idea of quantum geometry to characterize and understand the structure of many-particle states. For mean-field states, the quantum geometry has been defined and analysed in terms of the quantum distances between two points in the space of single particle spectral parameters (the Brillioun zone for periodic systems) and the geometric phase associated with any loop in this space. These definitions are in terms of single-particle wavefunctions. In recent work, we had proposed a formalism to define quantum distances between two points in the spectral parameter space for any correlated many-body state. In this paper we argue that, for correlated states, the application of the theory of optimal transport to analyse the geometry is a powerful approach. This technique enables us to define geometric quantities which are averaged over the entire spectral parameter space. We present explicit results for a well studied model, the one dimensional t-V model, which exhibits a metal-insulator transition, as evidence for our hypothesis. |
