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Adventures in Holographic Dimer Models

Shamit Kachru, Andreas Karch, Sho Yaida

TL;DR

The paper abstracts key features of holographic dimer models and shows how coupling a semi-holographic lattice of defect fermions to a free band alters the Fermi surface when dimers melt, yielding a transition between non-Fermi-liquid and conventional Fermi-liquid behavior. It then introduces double trace deformations to let dimer vibrations propagate as Bloch waves, deriving a determinant condition that yields an emergent band structure and demonstrating topology changes in a solvable toy model as the deformation strength is varied. Finally, it sketches a bottom-up holographic route to a Hubbard-like lattice model by incorporating a hopping term via bulk $U(2)$ gauge dynamics and IR brane physics, enabling parametric exploration of lattice phenomena in strongly coupled settings. The framework provides a tractable path to study lattice effects, heavy-fermion-like physics, and Hubbard-type dynamics within holography, with clear predictions for when and how Fermi surfaces reorganize and bands form. All mathematical results are expressed with explicit $\omega$, $k$, $\Delta$, and related quantities in $...$.

Abstract

We abstract the essential features of holographic dimer models, and develop several new applications of these models. First, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Second, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.

Adventures in Holographic Dimer Models

TL;DR

The paper abstracts key features of holographic dimer models and shows how coupling a semi-holographic lattice of defect fermions to a free band alters the Fermi surface when dimers melt, yielding a transition between non-Fermi-liquid and conventional Fermi-liquid behavior. It then introduces double trace deformations to let dimer vibrations propagate as Bloch waves, deriving a determinant condition that yields an emergent band structure and demonstrating topology changes in a solvable toy model as the deformation strength is varied. Finally, it sketches a bottom-up holographic route to a Hubbard-like lattice model by incorporating a hopping term via bulk gauge dynamics and IR brane physics, enabling parametric exploration of lattice phenomena in strongly coupled settings. The framework provides a tractable path to study lattice effects, heavy-fermion-like physics, and Hubbard-type dynamics within holography, with clear predictions for when and how Fermi surfaces reorganize and bands form. All mathematical results are expressed with explicit , , , and related quantities in .

Abstract

We abstract the essential features of holographic dimer models, and develop several new applications of these models. First, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Second, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.

Paper Structure

This paper contains 11 sections, 34 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Physics of a holographic dimer
  3. Undimerized phase: gapless spectrum
  4. Dimerized phase: gapped spectrum
  5. Semi-holographic phase transitions
  6. Double trace deformation: band structure of dimer vibrations
  7. Double trace deformation
  8. Band structure
  9. A simple toy model
  10. Towards a Holographic Hubbard Model
  11. Hypergeometric-ology

Figures (4)

  • Figure 1: (a)The high-temperature phase with $U(1)\times U(1)$ symmetry. (b)The low-temperature phase with $U(1) \times U(1) \to U(1)$ via brane recombination.
  • Figure 2: Dimerized configuration of interest. Note that we made the distance between $J=(2j+1)$th site and $J=(2j+2)$th site smaller than that between $J=(2j)$th site and $J=(2j+1)$th site, so that we have one unique dimerized configuration below the critical temperature.
  • Figure 3: Band structure of the global AdS$_2$ toy model for $\Delta=1$ and $h=0.05$ (top left panel), $h=0.82$ (top middle panel), $h=1$ (top right panel), $h=5$ (bottom left panel) and $h=50$ (bottom right panel).
  • Figure 4: (a)The high-temperature phase with two branes at each site, with lattice sites equally spaced. (b)A possible low-temperature configuration. (c)Another possible low-temperature configuration on which we will focus.