Holographic anyonic superfluidity

Abstract

Starting with a holographic construction for a fractional quantum Hall state based on the D3-D7' system, we explore alternative quantization conditions for the bulk gauge fields. This gives a description of a quantum Hall state with various filling fractions. For a particular alternative quantization of the bulk gauge fields, we obtain a holographic anyon fluid in a vanishing background magnetic field. We show that this system is a superfluid, exhibiting the relevant gapless excitation.

Pinning of holographic sliding stripes

“…For a particular ratio of charge density to magnetic field, the D7-brane can take a Minkowski embedding, which is holographically dual to a gapped, quantum Hall phase [32,[45][46][47]. However, we will concentrate in this paper on the generic black hole embedding, which is dual to a gapless quantum fluid.…”

“…Generalizing the model by an SLð2; ZÞ transformation [46,47,[59][60][61][62] 14 allows us to address the transport of striped anyonic fluids [67], which are notoriously difficult to tackle with perturbative methods.…”

A strongly coupled anyon material

“…Let us call the corresponding solutions V (1) and V (2) and use them to define a matrix P (r, ω, k 1 ) by…”

“…This approach is novel because the field theories in question are strongly coupled and quite distinct from the "usual" field theories of condensed matter. An example of standard condensed matter phenomenology that has been garnering interest in holography [1][2][3] is anyon physics in (2 + 1)-dimensions. We continue the study of [2] which considers the low energy physics of a strongly coupled anyonic material in a magentic field by examining the same material in the absence of a magnetic field.…”

Flux and Hall states in ABJM with dynamical flavors

“…In a four-dimensional bulk, the gauge field can take Dirichlet, Neumann, or mixed boundary conditions in the UV, and these choices correspond to different boundary CFTs dual to strongly coupled anyon fluids in dynamical gauge fields. In particular, by changing the quantization as in [66][67][68], this ABJM system could be turned from a quantum Hall fluid into an anyon superfluid. …”