[Paper Review] Fermions and the AdS/CFT correspondence: quantum phase transitions and the emergent Fermi-liquid

Mihailo Čubrović, Jan Zaanen+1 more|arXiv (Cornell University)|Apr 13, 2009

Physics of Superconductivity and Magnetism1 references31 citations

TL;DR

This paper applies the AdS/CFT correspondence to model fermionic quantum critical points in strongly correlated electron systems, showing that increasing fermion density away from a relativistic critical point leads to the emergence of a Fermi-liquid state with all characteristic features. The gravitational dual description successfully captures the transition from quantum criticality to Fermi-liquid behavior in strongly renormalized fermions.

ABSTRACT

A central problem in quantum condensed matter physics is the critical theory governing the zero temperature quantum phase transition between strongly renormalized Fermi-liquids as found in heavy fermion intermetallics and possibly high Tc superconductors. We present here results showing that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to relate fermionic quantum critical fields to a gravitational problem, we compute the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi-liquid.

Motivation & Objective

• To understand the quantum critical theory governing the zero-temperature phase transition between strongly renormalized Fermi-liquids and non-Fermi-liquid states in heavy fermion materials.
• To investigate whether string theory, via the AdS/CFT correspondence, can describe fermionic quantum critical states with non-Fermi liquid behavior.
• To compute spectral functions of fermions in the field theory dual to a gravitational system, capturing the emergence of Fermi-liquid features.

Proposed method

• Employ the Anti-de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to map a strongly interacting fermionic quantum field theory to a gravitational background in higher dimensions.
• Construct a gravitational dual with fermionic fields in the bulk, coupled to a background geometry that captures quantum critical behavior.
• Compute the retarded two-point correlation functions and spectral functions of the fermionic operators in the boundary field theory.
• Vary the fermion density in the field theory by tuning parameters in the gravitational dual, simulating the approach to and departure from the quantum critical point.
• Analyze the spectral function's structure to identify the emergence of a Fermi surface and quasiparticle peaks characteristic of a Fermi liquid.
• Use the AdS/CFT dictionary to relate bulk fermion dynamics to the boundary field theory's low-energy excitations.

Experimental results

Research questions

• RQ1 Can the AdS/CFT correspondence describe the quantum critical point separating strongly renormalized Fermi-liquids from non-Fermi liquid states in correlated electron systems?
• RQ2 How does the spectral function of fermions evolve as the system is tuned away from the quantum critical point via increased fermion density?
• RQ3 What features in the spectral function signal the emergence of a Fermi-liquid state in the gravitational dual description?
• RQ4 To what extent does the gravitational model reproduce the key characteristics of a Fermi liquid, such as a well-defined Fermi surface and quasiparticle peaks?
• RQ5 Does the AdS/CFT framework capture the crossover from relativistic quantum criticality to non-relativistic Fermi-liquid behavior?

Key findings

• The spectral functions computed via the AdS/CFT correspondence show the emergence of a sharp quasiparticle peak at low energy and momentum, signaling the formation of a Fermi surface.
• As fermion density increases beyond the critical point, the system transitions from non-Fermi liquid behavior to a state with all hallmarks of a Fermi liquid.
• The quasiparticle residue and Fermi momentum are dynamically generated in the gravitational dual, consistent with Fermi-liquid theory.
• The structure of the spectral function evolves continuously from a broad, incoherent peak at criticality to a sharp peak at finite momentum, indicating coherent quasiparticles.
• The model successfully realizes the crossover from relativistic quantum criticality to a non-relativistic Fermi-liquid state within a unified string-theoretic framework.