Fractionalization of holographic Fermi surfaces

TL;DR

The paper addresses how zero-temperature, finite-density phases in holographic theories organize when the bulk electric flux can be sourced by either bulk fermions, an extremal horizon, or both. By coupling a charged fluid of fermions to an Einstein-Maxwell-dilaton theory, they realize transitions between mesonic, fully fractionalized, and partially fractionalized phases, with the onset of fractionalization potentially continuous or first-order. A continuous transition is controlled by an emergent IR Lifshitz fixed point with dynamical exponent $z>1$, while complex scaling dimensions can preempt it with a first-order transition. The resulting phase diagram, parameterized by the UV dilaton coupling $\phi_0$ and chemical potential $\hat\mu$, exhibits Lifshitz-mediated crossovers and charge fractionation $\hat Q_{\text{frac.}}/\hat Q$, offering a concrete holographic platform for FL/FL$^*$/NFL-like behavior and the study of order parameters distinguishing fractionalized from mesonic phases.

Abstract

Zero temperature states of matter are holographically described by a spacetime with an asymptotic electric flux. This flux can be sourced either by explicit charged matter fields in the bulk, by an extremal black hole horizon, or by a combination of the two. We refer to these as mesonic, fully fractionalized and partially fractionalized phases of matter, respectively. By coupling a charged fluid of fermions to an asymptotically AdS_4 Einstein-Maxwell-dilaton theory, we exhibit quantum phase transitions between all three of these phases. The onset of fractionalization can be either a first order or continuous phase transition. In the latter case, at the quantum critical point the theory displays an emergent Lifshitz scaling symmetry in the IR.

Figures (7)

• Figure 1: Phase diagram. By tuning a relevant coupling in the relativistic UV theory at fixed nonzero chemical potential, the charge density ranges from fully fractionalized to fully mesonic. The fractionalization transition is controlled by an IR fixed point with dynamical critical exponent $z>1$. The IR critical point is sometimes preempted by a first order phase transition.
• Figure 2: Maximal mass $\hat{m}_\text{max.}$ as a function of $\hat{\beta}$. The Lifshitz solution requires $\hat{m} < \hat{m}_\text{max.}$.
• Figure 3: Contour plot of the dynamical critical exponent $z$ (left) and dimension $[g_{\mathcal{O}}]$ of the irrelevant operator (right) as a function of $\{\hat{\beta}, \hat{m} \}$.
• Figure 4: Contour plot of the real (left) and imaginary (right) parts of the scaling dimension $[g_{\mathcal{O}}]$ of the relevant operator as a function of $\{\hat{\beta}, \hat{m} \}$. A nonzero imaginary part indicates an instability of the Lifshitz solution, leading to a first order phase transistion.
• Figure 5: Free energy $\hat{\Omega}$ as a function of the relevant coupling $\phi_0$ for $\{\hat{m}, \hat{\beta}\} =\{0.1, 20 \}$ (left) and $\{\hat{m}, \hat{\beta}\} = \{0.5, 10 \}$ (right). Dashed blue lines indicate a mesonic phase while the solid red lines indicate a partially fractionalized phase. The black dot denotes the location of the Lifshitz fixed point. The left plot exhibits a continuous fractionalization transition, while the right plot exhibits a first order transition.