Building on earlier work in the high energy and condensed matter communities, we present
a web of dualities in 2+ 1 dimensions that generalize the known particle/vortex duality. Some …

We show how particle-vortex duality in d= 2+ 1 dimensions arises as part of an intricate web
of relationships between different field theories. The starting point is “bosonization,” a …

Coupled-wire constructions use bosonization to analytically tackle the strong interactions
underlying fractional topological states of matter. We give an introduction to this technique …

We introduce exactly solvable gapless quantum systems in d dimensions that support
symmetry-protected topological (SPT) edge modes. Our construction leads to long-range …

We study bosonization in 2+ 1 dimensions using mirror symmetry, a duality that relates pairs
of supersymmetric theories. Upon breaking supersymmetry in a controlled way, we …

We study composite Fermi liquid (CFL) states in the lowest Landau level (LLL) limit at a
generic filling ν= 1 n. We begin with the old observation that, in compressible states, the …

We study the interplay of particle-hole symmetry and fermion-vortex duality in
multicomponent half-filled Landau levels, such as quantum Hall gallium arsenide bilayers …

The Monte Carlo method is very useful for studying various model states proposed for the
fractional quantum Hall systems. In this paper, we introduce a lattice Monte Carlo method …

We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-
pair angular momentum. These wave functions are parameter-free and can be efficiently …

Motivated by the appearance of a “reflection symmetry” in transport experiments and the
absence of statistical periodicity in relativistic quantum field theories, we propose a series of …