Quantum phase transitions in semi-local quantum liquids

TL;DR

This work uses gauge-gravity duality to classify quantum critical points that lie beyond the Landau paradigm, identifying bifurcating, hybridized, and marginal types in finite-density systems with an IR SLQL phase described by AdS$_2\times\mathbb{R}^{d-1}$. It builds low-energy effective theories coupling a Landau-Ginsburg sector to the SLQL (hybridized QCP), or analyzes SLQL-to-confinement transitions (bifurcating QCP) and their marginal collisions, deriving static and dynamic susceptibilities, Efimov towers of bound states, and finite-temperature crossovers. The results reveal rich critical behavior including $\omega/T$ scaling in some regimes, a nondiverging static susceptibility at the bifurcation, and a holographic realization of Marginal Fermi Liquid-like spectra at the marginal QCP. These findings illuminate how nonquasiparticle SLQL dynamics can control quantum criticality and potentially connect to strange-metal phenomenology in correlated electron systems.

Abstract

We consider several types of quantum critical phenomena from finite-density gauge-gravity duality which to different degrees lie outside the Landau-Ginsburg-Wilson paradigm. These include: (1) a "bifurcating" critical point, for which the order parameter remains gapped at the critical point, and thus is not driven by soft order parameter fluctuations. Rather it appears to be driven by "confinement" which arises when two fixed points annihilate and lose conformality. On the condensed side, there is an infinite tower of condensed states and the nonlinear response of the tower exhibits an infinite spiral structure; (2) a "hybridized" critical point which can be described by a standard Landau-Ginsburg sector of order parameter fluctuations hybridized with a strongly coupled sector; (3) a "marginal" critical point which is obtained by tuning the above two critical points to occur together and whose bosonic fluctuation spectrum coincides with that postulated to underly the "Marginal Fermi Liquid" description of the optimally doped cuprates.

Figures (11)

• Figure 1: At a finite chemical potential, a CFT$_d$ flows in the IR to SLQL. On the gravity side this is realized geometrically via the flow of the AdS$_{d+1}$ near the boundary to AdS$_2 \times \mathbb{R}^{d-1}$ near the horizon.
• Figure 2: A cartoon picture: the system separates into domains of size $\xi \sim {1 \over \mu}$. Within each domain a conformal quantum mechanics governs dynamics in the time direction with a power law correlation (i.e. infinite relaxation time).
• Figure 3: Flow from CFT$_d^{\rm UV}$ to CFT$_d^{\rm IR}$ (the arrows denote flows to the IR). In the region between two fixed points, one can describe the system using either fixed point. To the left of the fixed point corresponding to CFT$_d^{\rm IR}$, the system develops a UV instability. To the right of CFT$_d^{\rm UV}$, the system develops an IR instability.
• Figure 4: The full phase diagram of the system for a neutral scalar. $C$ ($U$) denotes regions with (without) IR instabilities; $C$ stands for condensed, $U$ for uncondensed phase. The region with UV instability is filled with light blue. Top plot: phase diagram for the standard quantization. For $u < 0$, i.e. $m^2 R^2 < -{3 \over 2}$ the system is always unstable in the IR with $u=0$ the critical line for a bifurcating QCP. The vertical purple dashed line is at $u = {1 \over 24}$ corresponding to $m^2 R^2 = -{5 \over 4}$. There is no alternative quantization to the right of this line. The vertical black dashed line is at $u={1 \over 4}$ corresponding to $m^2 = 0$. The curve separating $C$ and $U$ approaches infinity when approaching this line. Bottom plot: phase diagram for the alternative quantization (for $\nu_{U} \in (0,1)$, hence the limited range in $u$ compared to the top plot, $u<{1\over 24}$). The ${\kappa}_->0$ part of the phase diagram can be obtained from the ${\kappa}_+<0$ part of the standard quantization phase diagram by using the relation \ref{['euive']}. In the vacuum, the system has an IR instability for ${\kappa}_- < 0$, i.e. with ${\kappa}_- =0$ the critical line. At a finite density the critical line is pushed into the region ${\kappa}_- > 0$.
• Figure 5: Comparison of the spacetime geometries (close to the critical point) corresponding to the condensed state of a neutral (left) and charged scalar (right). The vertical direction in the plot denotes the ${\mathbb{{R}}}^2$ directions. For AdS$_2$ the transverse directions has a constant size independent of radial coordinates, while for the Lifshitz geometry, the size of the transverse directions shrinks to zero in the interior. Close to the critical point, the IR scale at which the scalar condensate sets in is much smaller than the chemical potential and we expect an intermediate spacetime region described by the AdS$_2$ of the original black hole geometry.