Energy twisted boundary condition

Thermal transport in condensed matter systems is traditionally formulated as a response to a background gravitational field. In this work, we seek a twisted boundary condition formalism for thermal transport in analog to the U(1) twisted boundary condition for electrical transport. We started by implementing the energy twisted boundary condition in CFT. Then using the transfer matrix method, we obtained the thermal Meissner stiffness of the Ising model and disordered Fermion model with energy twisted boundary condition. We also identified boost deformation for integrable systems as a similar formalism as energy twisted boundary condition and computed linear and nonlinear Drude weight for XXZ model.