Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions

Aaram J. Kim, Philipp Werner, Evgeny Kozik

Arijit Haldar, Sumilan Banerjee, Vijay B. Shenoy

Some of the most interesting phenomena in condensed matter occur in high-temperature superconductors and heavy fermions, and arise from a parent non-Fermi-liquid background. Although the non-Fermi-liquid phase has metallic character, it is very different from typical metals in that the electronic excitations are not particlelike (no quasiparticles), and this has lead to these phases eluding a clear theoretical description. Here, the authors develop a model that provides a route to describe non-Fermi liquids realized in condensed matter systems. Building on the zero-dimensional Sachdev-Ye-Kitaev model that is inspired by connections between a non-Fermi liquid and black holes, the authors construct a model in a lattice system where the bands touch to give a divergent density of states (Lifshitz point). The resulting non-Fermi-liquid phases exhibit intriguing properties such as scaling symmetry, nontrivial power-law dependence of entropy on temperature, and fast information scrambling with rate linear in temperature, as well as dynamical transitions to more conventional phases with well-defined quasiparticles.

Subhro Bhattacharjee, Sung-Sik Lee, Yong Baek Kim

Jian-Pin Wu

We study the fermionic response including the bulk dipole coupling on the charged Lifshitz black brane from Einstein–Dilaton–Maxwell model. For fixed Lifshitz dynamical critical exponent z, by tuning the dipole coupling parameter p, we can realize the phase transitions from Fermi liquid, to marginal Fermi liquid, to non-Fermi liquid and finally to Mott insulator. The Lifshitz dynamical critical exponent z plays the role of making the phase transition point from Fermi liquid to non-Fermi liquid or to Mott insulator decrease with the increase of z for fixed dipole coupling p.

Xin Chen, Ruihua Fan, Yiming Chen +2 more

The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.