Heat equation approach to geometric changes of the torus Laughlin-state

摘要

We study the second quantized -or guiding center- description of the torusLaughlin state. Our main focus is the change of the guiding center degrees offreedom with the torus geometry, which we show to be generated by a two-bodyoperator. We demonstrate that this operator can be used to evolve the fulltorus Laughlin state at given modular parameter \tau\ from its simple(Slater-determinant) thin torus limit, thus giving rise to a new presentationof the torus Laughlin state in terms of its "root partition" and an exponentialof a two-body operator. This operator therefore generates in particular theadiabatic evolution between Laughlin states on regular tori and thequasi-one-dimensional thin torus limit. We make contact with the recentlyintroduced notion of a "Hall viscosity" for fractional quantum Hall states, towhich our two-body operator is naturally related, and which serves as ademonstration of our method to generate the Laughlin state on the torus.