Numerical Investigations Of Boson Impurity Models

The coupling between quantum emitters and photons in structured baths is a representative model in quantum optics for studying many problems.It is not only the basic arena for studying many interesting phenomena,but also can be used to simulate strongly correlated many-body systems and perform quantum information tasks.Numerical calculations play an essential role in understanding these models,such as exact diagonalization,density matrix renormalization group,etc.In the exact diagonalization of multiple photon systems,the dimension of the Hamiltonian matrix grows exponentially with the number of lattice sites,which severely limits the maximal system size that can be reached.Density matrix renormalization group has almost solved the problem of exponential growth in onedimensional system,but its direct application in two and three dimensions are highly constrained.For certain parameter regimes,it is usually necessary to consider very large system to achieve a comprehensive understanding.To deal with these complicated cases,we propose a truncated Hilbert space method.It can deal with arbitrary spatial dimension and multiple quantum emitters,and allows us to use moderate computational resources to study very large systems,while retaining sufficiently high accuracy.We first perform calculations in one-dimensional systems to confirm the efficiency of our method by comparing the ground state energy and its scaling relation with those reported in the literature.The power of our truncated Hilbert space method is further demonstrated by studying several aspects of twodimensional systems?This work paves the way toward more in-depth studies of quantum emitter models.