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The integer quantum Hall effect can be observed in a two-dimensional conductor penetrated by a perpendicular magnetic field and with edges connecting the current carrying contacts. Its signature is a state of quantized Hall and…
The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist in principle in the phase transitions involving symmetry protected topological phase, however, examples of such kinds of transition in physical…
We investigate the ground-state properties of a disorderd Ising model with uniform transverse field on the Bethe lattice, focusing on the quantum phase transition from a paramagnetic to a glassy phase that is induced by reducing the…
We study the metal-insulator transition on a three dimensional quantum percolation model by analyzing energy level statistics. The quantum percolation threshold $\pq$, which is larger than the classical percolation threshold $\pc$, becomes…
A nonconventional renormalization-group (RG) treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their…
A mapping is developed between the quantum Hall plateau transition and two-dimensional self-interacting lattice polymers. This mapping is exact in the classical percolation limit of the plateau transition, and diffusive behavior at the…
The Renormalization Group (RG) is one of the central and modern techniques in quantum field theory. Indeed, quantum field theories can be understood as flows between fixed points of the RG flow, which represent Conformal Field Theories…
The square lattice with central forces between nearest neighbors is isostatic with a subextensive number of floppy modes. It can be made rigid by the random addition of next-nearest neighbor bonds. This constitutes a rigidity percolation…
Hall coefficient implies the mechanism for reconstruction of a Fermi surface, distinguishing competing scenarios for Mott criticality such as electron fractionalization, dynamical mean-field theory, and metal-insulator transition driven by…
The paper describes an explicit variational modification of the standard RSRG method and its application to quantum spin lattice systems. The modified approach is applied to exactly solvable ITF, XX and isotropic Heisenberg models. Better…
We analysis the quantum Hall effect exhibited by a system of particles moving in a higher dimensional space. This can be done by considering particles on the Bergman ball {\bb{B}_{\rho}^d} of radius \rho in the presence of an external…
A polymer folding model on the square lattice is constructed with attractive contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a dynamical random lattice, with freely fluctuating co-ordination number at each vertex,…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
Statistics of level spacing and magnetization are studied for the phase diagram of the integer quantum Hall effect in a 2D finite lattice model with Anderson disorder.
We study a quantum network percolation model which is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We show dynamical localization for parameters corresponding to edges of Landau…
We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the {\it integer} quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be…
We investigate the integer quantum Hall system in a two dimensional lattice model with spatially correlated disorder by using the efficient method to calculate the Chern number proposed by Fukui \textit{et al}. Distribution of charge…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point…
We introduce a general corner transfer matrix renormalization group algorithm tailored to projected entangled-pair states on the triangular lattice. By integrating automatic differentiation, our approach enables direct variational energy…