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Topological phases typically encode topology at the level of the single particle band structure. But a remarkable class of models shows that quantum anomalous Hall effects can be driven exclusively by interactions, while the parent…
The Hall and longitudinal conductivities of a recently studied holographic model of a quantum Hall ferromagnet are computed using the Karch-O'Bannon technique. In addition, the low temperature entropy of the model is determined. The…
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity…
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…
Unconventional fermions with high degeneracies in three dimensions beyond Weyl and Dirac fermions have sparked tremendous interest in condensed matter physics. Here, we study quantum Hall effects (QHEs) in a two-dimensional (2D)…
Kubo formula gives a linear response of a quantum system to external fields, which are classical and weak with respect to the energy of the system. In this work, we take the quantum nature of the external field into account, and define a…
Kondo lattice systems are recognized for potentially hosting a variety of rich topological phases. Several pioneering studies have demonstrated significant anomalous Hall and anomalous Nernst effects in these systems, attributed to the…
We present a mean field theory of composite fermion edge channel transport in the fractional and integer quantum Hall regimes. An expression relating the electro-chemical potentials of composite fermions at the edges of a sample to those of…
We have pointed out the possibility of quantum Hall effect or quantum patterns of transportation in a degenerate strongly magnetized quark matter, which might be expected inside a highly dense compact star. An anisotropic pattern of…
We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
The Hall conductivity of an electron gas on the surface of constant negative curvature (the Lobachevsky plane) in the presence of an orthogonal magnetic field is investigated. It is shown that the effect of the surface curvature is to…
We study two quantum mechanical systems on the noncommutative plane using a representation independent approach. First, in the context of the Landau problem, we obtain an explicit expression for the gauge transformation that connects the…
The quantum Hall effect in the three-dimensional anisotropic tight-binding electrons is investigated in the field-induced spin density wave phases with a magnetic field tilted to any direction. The Hall conductivity, $\sigma_{xy}$ and…
The disappearance of integer quantum Hall effect (IQHE) at strong disorder and weak magnetic field is studied in a lattice model. A generic sequence by which the IQHE plateaus disappear is revealed: higher IQHE plateaus always vanish…
The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
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…
This paper surveys some recent results on the theory of quantum linear systems and presents them within a unified framework. Quantum linear systems are a class of systems whose dynamics, which are described by the laws of quantum mechanics,…
The Hall viscosity, a non-dissipative transport coefficient analogous to Hall conductivity, is considered for quantum fluids in gapped or topological phases. The relation to mean orbital spin per particle discovered in previous work by one…