Using density matrix renormalization group to study open quantum systems
b"This thesis is concerned with open quantum systems, and more specifically, quantum impurity models. By this we mean a small local quantum system in \\ncontact with a macroscopic non-interacting environment. This can be used \\nto model individual impurities in metals and quantum information systems where the influence from the surrounding\\nenvironment is not negligible. \\nThe numerical renormalization group (NRG) is the traditional method to study quantum impurity models. However its application\\nis limited when dealing with real-time dynamics and bosonic systems. In recent years\\nsome of NRG's techniques have been introduced to the density matrix renormalization group method (DMRG), which \\nitself is the most powerful numerical method to study one-dimensional quantum systems. The resulting\\nmethod shows great potential, and this thesis explores and extends \\nthe power of the NRG+DMRG combination in treating open quantum\\nsystems. \\n\\nWe focus mainly on two types of problem. The first is an open quantum system with a time-dependent\\nHamiltonian, which for example could be the theoretical description of various problems encountered in qubit manipulation.\\nWe combine NRG discretization and adaptive time-dependent DMRG (t-DMRG) to study the dissipative Landau-Zener problem. \\nWe also use this method to study the quantum decoherence process and \\nthe dynamical properties of the telegraph noise model. The results show that the NRG and t-DMRG combination is a fast, \\naccurate and versatile method for such problems. The second type of problem we study involves the quantum critical properties\\nof one- and two-bath spin-boson models. Unlike fermion and spin models, models with bosons are difficult to \\ntreat numerically as each boson basis has an infinite number of dimensions. \\nBy introducing the optimal boson basis into the variational matrix product state method\\n(VMPS), which is a variant of DMRG, we can deal with an effective local boson basis as large as $10^{10}$. This\\nis the crucial improvement over NRG which can only deal with at most a few dozen local basis states. With this powerful tool we have settled a controversy about the nature of the \\nquantum phase transition in a sub-Ohmic spin-boson model regarding quantum to classical mapping. \\nThere, NRG fails to yield the right result due to the highly truncated local boson basis. \\nWe also explore the phase diagram of the two-bath \\nspin-boson model and find a new critical phase. We demonstrate that NRG+VMPS with optimal boson basis represents a powerful\\nsetting to study quantum impurity models with a bosonic environment."