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Physics Letters B

The charged Lifshitz black brane geometry and the bulk dipole coupling

Jian-Pin Wu

Published Nov 22, 2013• 16 citations
Publisher

Abstract

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.

DOI
10.1016/j.physletb.2013.11.040

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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.
A class of strongly interacting many-body fermionic systems in 2+12+12+1-dimensional nonrelativistic conformal field theory is examined via the gauge-gravity duality correspondence. The five-dimensional charged black hole with asymptotic Schr\"odinger isometry in the bulk gravity side introduces parameters of background density and finite particle number into the boundary field theory. We propose the holographic dictionary, and realize a quantum phase transition of this fermionic liquid with fixed particle number by tuning the background density $\ensuremath{\beta}$ at zero temperature. On the larger $\ensuremath{\beta}$ side, we find the signal of a sharp quasiparticle pole on the spectral function $A(k,\ensuremath{\omega})$, indicating a well-defined Fermi surface. On the smaller $\ensuremath{\beta}$ side, we find only a hump with no sharp peak for $A(k,\ensuremath{\omega})$, indicating the disappearance of the Fermi surface. The dynamical exponent zzz of quasiparticle dispersion goes from being Fermi-liquid-like $z\ensuremath{\simeq}1$ scaling at larger $\ensuremath{\beta}$ to a non-Fermi-liquid scaling $z\ensuremath{\simeq}3/2$ at smaller $\ensuremath{\beta}$. By comparing the structure of Green's function with Landau Fermi liquid theory and Senthil's scaling ansatz, we further investigate the behavior of this quantum phase transition.
Abstract In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction- or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken Z2 inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent z ≃ 2, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.
In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction- or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken Z2Z_2Z2​ inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent z≃2z \simeq 2z≃2, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.
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.
We show that the competition between the fermi liquidity and the gap generation, which is the physics of the Hubbard model, can be realized in a canonical holographic model of a fermion with bulk mass and a dipole interaction. The bulk mass near 1/2 tends to protect the fermi liquidity while large dipole coupling attempts to generate the mass gap so that the model is equipped with the basic mechanism of the Mott transition and expected to play the role of Hubbard model in holographic context. In fact, the spectral densities of the holographic model agree with the dynamical mean field theory (DMFT) calculation in two features: the 'three peaks' and 'the transfer' of the degree of freedom from the quasi-particle peak to the side peak. The phase diagram of our holographic model contains six phases including bad metals and pseudo-gap as well as the Fermi liquid and Mott insulator, and a line connecting the last two defines a Holographic version of Hubbard model. The experimental data for spectral densities of Vanadium Oxide materials seem to be well fit by our theory.
We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.