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We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is…
Renormalization-Group (RG) improvement has been frequently applied to capture the effect of quantum corrections on cosmological and black-hole spacetimes. This work utilizes an algebraically complete set of curvature invariants to establish…
We solve the problem of the spin quantum Hall transition on random networks using a mapping to classical percolation that focuses on the boundary of percolating clusters. Using tools of two-dimensional quantum gravity, we compute critical…
A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This ``Stochastic Renormalization Group'' (SRG) expresses statistical…
Using the renormalisation group (RG) we study two dimensional electromagnetic coulomb gas and extended Sine-Gordon theories invariant under the modular group SL(2,Z). The flow diagram is established from the scaling equations, and we derive…
Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ…
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential…
We investigate how additive weak noise (correlated as well as uncorrelated) modifies the parameters of the Gray-Scott (GS) reaction diffusion system by performing numerical simulations and applying a Renormalization Group (RG) analysis in…
We develop a perturbative renormalization-group method in real time to describe nonequilibrium properties of discrete quantum systems coupled linearly to an environment. We include energy broadening and dissipation and develop a…
The renormalization theory of the quantum Hall effect relies primarily on the non-perturbative concept of theta renormalization by instantons. Within the generalized non-linear sigma model approach initiated by Finkelstein we obtain the…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
Renormalization Group (RG) techniques have been successfully employed in quantum field theory and statistical physics. Here we apply RG methods to study the non-linear stages of structure formation in the Universe. Exact equations for the…
We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of…
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a modular symmetry group commuting with the renormalization group flow and hence mapping different phases of…
The theoretical description of transport in a wide class of novel materials is based upon quantum percolation and related random resistor network (RRN) models. We examine the localization properties of electronic states of diverse…
The fractional quantum Hall (FQH) effect gives rise to abundant topological phases, presenting an ultimate platform for studying the transport of edge states. Generic FQH edge contains multiple edge modes, commonly including the…
A theory of integer quantum Hall effect(QHE) in realistic systems based on von Neumann lattice is presented. We show that the momentum representation is quite useful and that the quantum Hall regime(QHR), which is defined by the propagator…
We show that the Wilsonian formulation of the renormalization group (RG) defines a quantum channel acting on the momentum-space density matrices of a quantum field theory. This information theoretical property of the RG allows us to derive…
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…
The phenomenological analysis of fully spin-polarized quantum Hall systems, based on holomorphic modular symmetries of the renormalization group (RG) flow, is generalized to more complicated situations where the spin or other "flavors" of…