Master’s thesis work

Towards my master’s research project (can be found here), I performed an analytical non-perturbative renormalization group analysis of an extended single impurity Anderson model (SIAM). The standard SIAM involves a correlated impurity site embedded in a conduction bath, the two being coupled through a single-particle hopping. The analysis includes a derivation of the unitary renormalization group (URG) equations for the couplings, as well as computation of physical properties. The URG is a recent many-body technique developed in Refs [1-4], and is applies unitary transformations on the Hamiltonian to decouple high energy modes, leading to a low-energy effective Hamiltonian. We apply the URG on a generalized version of the SIAM with explicit spin-exchange and charge isospin-exchange couplings. We find strong-coupling fixed points for both the spin and isospin couplings. We characterise the fixed-point by studying the ground state wavefunctions and thermodynamic quantities like the magnetic susceptibility and the specific heat. We extract an effective Hamiltonian for the cloud of electrons that screen the impurity. This effective Hamiltonian is found to contain both Fermi liquid as well as four-Fermion off-diagonal interaction terms. We show that the flow to the strong-coupling fixed point involves a change in the topological Luttinger volume by 1. We finally calculate the mutual information and correlations along the RG flow between impurity and a Kondo cloud electron, as well as between two members of the Kondo cloud. Both the measures increase towards the strong-coupling fixed point, showing that the flow towards low energies is accompanied by a substantial increase in the entanglement content.

References