A Numerically Exact Approach to Quantum Impurity Problems in Realistic Lattice Geometries

Abstract

We review a controlled numerical approach to quantum impurity problems in realistic geometries, consisting of exactly mapping the complete lattice Hamiltonian onto an equivalent one dimensional system through a unitary transformation. The resulting dimensional and entanglement reduction allows one to study the quantum many-body problem on arbitrary d-dimensional lattices using the density matrix renormalization group (DMRG) method. The real-space resolution allows one to position the impurities at the boundary or bulk of the sample and to study screening effects due to edge or surface modes. We describe how to generalize this approach to multi-impurity problems, discuss applications and possible extensions.

Non-perturbative treatment of giant atoms using chain transformations

“…This unitary transformation casts the field into the shape of a linear harmonic chain, which is particularly suited for numerical simulation. This methods were originally introduced and widely used in the study of open quantum systems (e.g., see [23][24][25]), but have also proven useful in quantum optics as seen, for example, in [15,[26][27][28]. We follow a similar numerical approach as [15], which allows us to go beyond the single-excitation subspace and numerically study system and bath observables using MPS [29,30].…”

Many-Body Effects in FeN4 Center Embedded in Graphene

“…Once all the parameters for the model are obtained, the problem can be recast and solved using the DMRG method. In order to do so, we mapped the problem onto an equivalent one-dimensional model by employing an exact canonical transformation, as presented in [88,89] and reviewed in detail in [90] and closely related to the chain mapping used in DMFT [35]. An outline of the method is as follows.…”

Local multiplet formation around a single vacancy in graphene: an effective Anderson model analysis based on the block-Lanczos DMRG method

“…For this purpose, we construct an effective Anderson model composed of the three-site two-orbital Hubbard model, which describes the local electronic states around the vacancy and thus serves as the impurity sites, and the surrounding π orbitals of carbon atoms forming the honeycomb lattice with the single vacancy. The Anderson model is solved by employing the density matrix renormalization group (DMRG) method [22,23] combining with the block-Lanczos technique [24][25][26][27], which gives the numerically accurate solution within controlled errors. With this numerical analysis, we can fully take into account the local multiplet structures as well as the coupling to the surrounding π electrons, which thus provides the valuable information complementary to the one-body type approximation used in the ab-initio DFT calculations.…”