Semi-local quantum liquids

TL;DR

Gauge/gravity duality applied to finite-density systems reveals a universal semi-local quantum liquid (SLQL) as an intermediate-energy phase, described by the IR geometry $AdS2×R^2$ that exhibits time-direction scaling and a finite entropy density. The SLQL provides a deconfined, fractionalized description with momentum-dependent scaling $δ_k$ and ω/T spectral scaling, preceding various low-energy orders such as superconductivity, AFM-like states, or heavy-fermion Fermi liquids. Lower-energy phases arise via bound-state formation of operators in the SLQL: fermionic bound states yield dense Fermi surfaces of heavy fermions, while scalar bound states condense into Bose-Einstein condensates; backreaction can resolve the SLQL into a Lifshitz IR geometry with a large dynamical exponent $z$. The results suggest connections to strange metal behavior in cuprates and heavy-electron systems, and offer a unifying holographic mechanism for intermediate-energy physics.

Abstract

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.

Figures (7)

• Figure 1: Heuristic visualization of semi-local quantum liquid phase; system splits into many different weakly correlated domains, each of which is governed by a conformal quantum mechanics.
• Figure 2: The semi-local quantum liquid phase is a useful description at intermediate scales; many different UV theories (i.e. those with gravity duals described by a Maxwell-Einstein sector) flow to it, and at low energies it settles into one of many different ground states.
• Figure 3: In the AdS$_2 \times {\mathbb{{R}}}^2$ region of the extremal black hole geometry, at each point in the bulk there is a local three-dimensional Fermi surface with Fermi momentum $k_o$, which upon projection to the boundary theory would result in a Fermi disc, in which there are gapless excitations at each point in the interior of a disc in the two-dimensional momentum space.
• Figure 4: Two different geometries: on the top, the AdS$_2 \times \mathbb{R}^2$ describing the SLQL phase; on the bottom, its resolution into a Lifshitz geometry with a finite $z$ given by \ref{['zexp']}. The horizon direction represents the $y$ direction, while the vertical direction represents the transverse ${\mathbb{{R}}}^2$ (i.e. $x_1, x_2$ directions). In the plot for the Lifshitz geometry it should be understood that the tip lies at an infinite proper distance away. When $z$ is large as in \ref{['zexp']}, there is a large range of $y$ for which the Lifshitz geometry resembles that of AdS$_2 \times \mathbb{R}^2$. Also note that $e^{-y}$ translates into the boundary theory energy scale.
• Figure 5: Taking into account the quantization condition \ref{['roro']}, we find instead a set of discrete states in the bulk in which radial motion is quantized. This results in a family of concentric Fermi surfaces in the boundary theory, which resolves the Fermi disk of Fig. \ref{['fig:bal']}.