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We study the quantum anomalous Hall states in the $p$-orbital bands of the honeycomb optical lattices loaded with the single component fermions. Such an effect has not been realized in both condensed matter and cold atom systems yet. By…
We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the…
We consider renormalization group (RG) transformations for classical Ising-type lattice spin systems in the infinite volume limit. Formally, the RG maps a Hamiltonian H into a renormalized Hamiltonian H': exp(-H'(\sigma'))=\sum_\sigma…
Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating…
We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant…
In a quantum Hall system, the finite-wavevector Hall conductivity displays an intriguing dependence on the Hall viscosity, a coefficient that describes the non-dissipative response of the fluid to a velocity gradient. In this paper, we…
The quantum Hall effect hosts quantum phase transitions in which the localization length, that is the size of disorder-induced bulk localized states, is governed by universal scaling from percolation theory. However, this universal…
We make Kadanoff's block idea into a reliable three-dimensional (3D) real space renormalization group (RG) method. Kadanoff's idea, expressed in spin representation, offers a qualitative intuition for clarifying scaling behavior in…
The conventional duality analysis is employed to identify a location of a critical point on a uniform lattice without any disorder in its structure. In the present study, we deal with the random planar lattice, which consists of the…
The renormalization group (RG) in statistical physics focuses on ground-state properties of equilibrium systems. However, it is unclear how it should be generalized to nonunitary quantum dynamics caused by dissipation and measurement…
We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates…
Recent developments in the scaling theory of the integer quantum Hall effect are discussed. In particular, the influence of electron-electron interactions on the critical behavior are studied. It is further argued that recent experiments on…
Quantum transport properties in quantum Hall wires in the presence of spatially correlated random potential are investigated numerically. It is found that the potential correlation reduces the localization length associated with the edge…
We consider the dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias…
We discuss the averaging hypothesis tacitly assumed in standard cosmology. Our approach is implemented in a "3+1" formalism and invokes the coarse graining arguments, provided and supported by the real-space Renormalization Group (RG)…
This thesis is concerned with the development of a general method to compute renormalised local observables for quantum matter fields, in a given quantum state, on a rotating black hole spacetime. The rotating black hole may be surrounded…
The two-dimensional motion of a charged particle in a random potential and a transverse magnetic field is believed to be delocalized only at discrete energies $E_N$. In strong fields there is a small positive deviation of $E_N$ from the…
Using a new MBE growth technique, we fabricate a two-dimensional electron system which is bent around an atomically sharp 90 degree corner. In the quantum Hall regime under tilted magnetic fields, we can measure equilibration between both…
We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently…
We study the localization properties in the transition from a two-dimensional electron gas at zero magnetic field into an integer quantum Hall (QH) liquid. By carrying out a direct calculation of the localization length for a finite size…