Dynamical structure factor S(ω, k) of quantum Ising chain coupled to Bosonic dissipative bath

Using the methods of Quantum Monte Carlo simulation + Numerical analytic continuation,
I will demostrate that, the dissipative environment will smear the sharp ε(k) spectrum of the well known transverse field Ising chain.
For large enough dissipation, the gap will be closed, and the quasi-particle picture is no longer available.