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We develop a time-dependent real-space renormalization-group approach which can be applied to Hamiltonians with time-dependent random terms. To illustrate the renormalization-group analysis, we focus on the quantum Ising Hamiltonian with random site- and time-dependent (adiabatic) transverse-field and nearest-neighbour exchange couplings. We demonstrate how the method works in detail, by calculating the off-critical flows and recovering the ground state properties of the Hamiltonian such as magnetization and correlation functions. The adiabatic time allows us to traverse the parameter space, remaining near-to the ground state which is broadened if the rate of change of the Hamiltonian is finite. The quantum critical point, or points, depend on time through the time-dependence of the parameters of the Hamiltonian. We, furthermore, make connections with Kibble-Zurek dynamics and provide a scaling argument for the density of defects as we adiabatically pass through the critical point of the system.
We introduce a real time version of the functional renormalization group which allows to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a nonequilibrium i
We construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. We find that the current vertex develop
We develop a renormalization group approach for analyzing Frohlich polarons and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement wit
We revisit perturbative RG analysis in the replicated Landau-Ginzburg description of the Random Field Ising Model near the upper critical dimension 6. Working in a field basis with manifest vicinity to a weakly-coupled Parisi-Sourlas supersymmetric f
The pseudofermion functional renormalization group (pf-FRG) is one of the few numerical approaches that has been demonstrated to quantitatively determine the ordering tendencies of frustrated quantum magnets in two and three spatial dimensions. The a