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Compressible quantum phases from conformal field theories in 2+1 dimensions

Subir Sachdev

TL;DR

This work analyzes how applying a chemical potential to 2+1D conformal field theories with a global U(1) charge yields compressible phases, including superfluids, solids, and Bose metals. It develops explicit $S$-duality mappings for the $XY$ model and the Abelian CP^{1} model, connecting electric and magnetic sectors and identifying monopole/dyon operators as order parameters for translational symmetry breaking. The authors then interpret these boundary theories holographically in AdS$_4$, proposing bulk duals that incorporate electric, magnetic, and dyonic degrees of freedom and verifying consistency via three-point correlators. The results illuminate how monopole/dyon physics governs density modulations and unit-cell scaling in compressible phases, and they pave the way for a holographic understanding of Bose metals and related non-Fermi liquid states in 2+1 dimensions.

Abstract

Conformal field theories (CFTs) with a globally conserved U(1) charge Q can be deformed into compressible phases by modifying their Hamiltonian, H, by a chemical potential H -> H - μQ. We study 2+1 dimensional CFTs upon which an explicit S duality mapping can be performed. We find that this construction leads naturally to compressible phases which are superfluids, solids, or non-Fermi liquids which are more appropriately called `Bose metals' in the present context. The Bose metal preserves all symmetries and has Fermi surfaces of gauge-charged fermions, even in cases where the parent CFT can be expressed solely by bosonic degrees of freedom. Monopole operators are identified as order parameters of the solid, and the product of their magnetic charge and Q determines the area of the unit cell. We discuss implications for holographic theories on asymptotically AdS4 spacetimes: S duality and monopole/dyon fields play important roles in this connection.

Compressible quantum phases from conformal field theories in 2+1 dimensions

TL;DR

This work analyzes how applying a chemical potential to 2+1D conformal field theories with a global U(1) charge yields compressible phases, including superfluids, solids, and Bose metals. It develops explicit -duality mappings for the model and the Abelian CP^{1} model, connecting electric and magnetic sectors and identifying monopole/dyon operators as order parameters for translational symmetry breaking. The authors then interpret these boundary theories holographically in AdS, proposing bulk duals that incorporate electric, magnetic, and dyonic degrees of freedom and verifying consistency via three-point correlators. The results illuminate how monopole/dyon physics governs density modulations and unit-cell scaling in compressible phases, and they pave the way for a holographic understanding of Bose metals and related non-Fermi liquid states in 2+1 dimensions.

Abstract

Conformal field theories (CFTs) with a globally conserved U(1) charge Q can be deformed into compressible phases by modifying their Hamiltonian, H, by a chemical potential H -> H - μQ. We study 2+1 dimensional CFTs upon which an explicit S duality mapping can be performed. We find that this construction leads naturally to compressible phases which are superfluids, solids, or non-Fermi liquids which are more appropriately called `Bose metals' in the present context. The Bose metal preserves all symmetries and has Fermi surfaces of gauge-charged fermions, even in cases where the parent CFT can be expressed solely by bosonic degrees of freedom. Monopole operators are identified as order parameters of the solid, and the product of their magnetic charge and Q determines the area of the unit cell. We discuss implications for holographic theories on asymptotically AdS4 spacetimes: S duality and monopole/dyon fields play important roles in this connection.

Paper Structure

This paper contains 17 sections, 80 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Conformal field theories
  3. $XY$ model
  4. $S$ duality
  5. Abelian $\mathbb{CP}^{N-1}$ model
  6. Doped conformal field theories
  7. $XY$ model
  8. Superfluid
  9. Solid
  10. Abelian $\mathbb{CP}^1$ model
  11. Bose metal
  12. Holography
  13. Conclusions
  14. Generalizations
  15. $S$ duality of the $XY$ model
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Connections between CFT3s and holography
  • Figure 2: 3-point correlators of the $XY$ model: ( a) the electric correlator $K$ in (\ref{['K1']}), ( b) the magnetic correlator $K_m$ in (\ref{['K4']}). The labels are the boundary $\rightarrow$ bulk fields.