Imaginary boost deformation of integrable models

Some integrable models in 1+1 dimension preserve Lorentz symmetry. We treat the Lorentz boost operator as a generator and deform the Hamiltonian with an imaginary parameter. The complex energy spectrum of the boosted non-Hermitian Hamiltonian emerges from infinity. We compute the energy spectrums and winding numbers for the free Fermion model, XXZ model, and Calogero Sutherland model. Non-Hermitian skin effect is observed on single-particle and two-particle energy spectrums. We also discuss the relation between boost deformation and Lorentz transformation on lattice systems and transport properties generated by the boost deformation.