相关论文: Particle-Vortex Duality and the Modular Group: App…

We derive the implications of particle-vortex duality for the electromagnetic response of Quantum Hall systems beyond the linear-response regime. This provides a first theoretical explanation of the remarkable duality which has been…

We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain…

At low temperatures the phase diagram for the quantum Hall effect has a powerful symmetry arising from the Law of Corresponding States. This symmetry gives rise to an infinite order discrete group which is a generalisation of…

We discuss the possible origin of the duality observed in the quantum Hall current-voltage characteristics. We clarify the difference between "particle-vortex" (complex modular) duality, which acts on the full transport tensor, and…

In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for rotating fermion…

As discovered in the quantum Hall effect, a very effective way for strongly-repulsive electrons to minimize their potential energy is to aquire non-zero relative angular momentum. We pursue this mechanism for interacting two-dimensional…

In this paper we study particle-vortex duality and the effect of theta terms from the point of view of AdS/CMT constructions. We can construct the duality in 2+1 dimensional field theories with or without a Chern-Simons term, and derive an…

We consider a theory of a two-component Dirac fermion localized on a (2+1) dimensional brane coupled to a (3+1) dimensional bulk. Using the fermionic particle-vortex duality, we show that the theory has a strong-weak duality that maps the…

The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but…

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of…

Experiments studying renormalization group flows in the quantum Hall system provide significant evidence for the existence of an emergent holomorphic modular symmetry $\Gamma_0(2)$. We briefly review this evidence and show that, for the…

There is considerable experimental evidence for the existence in Quantum Hall systems of an approximate emergent discrete symmetry, $\Gamma_0(2) \subset SL(2,Z)$. The evidence consists of the robustness of the tests of a suite a predictions…

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the…

We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting…

Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson paradigm have led to a number of field theories, potentially important for certain two-dimensional magnetic insulating systems, where criticality is not very well…

The edge states of a sample displaying the quantum Hall effect (QHE) can be described by a 1+1 dimensional (conformal) field theory of $d$ massless scalar fields taking values on a $d$-dimensional torus. It is known from the work of…

The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…

I analyze non-local symmetries of finite-size Euclidean 3D lattice Chern-Simons models in the presence of an external magnetic field and non-zero average current. It is shown that under very general assumptions the particle-vortex duality…

We provide evidence for conjectural dualities between nonrelativistic Chern-Simons-matter theories and theories of (fractional, nonAbelian) quantum Hall fluids in $2+1$ dimensions. At low temperatures, the dynamics of nonrelativistic…

The parallel roles of modular symmetry in ${\cal N}=2$ supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac's electric -- magnetic…