String Theory, Quantum Phase Transitions, and the Emergent Fermi Liquid

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 in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed 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.

Holographic non-relativistic fermionic fixed point by the charged dilatonic black hole

“…We have investigated how the dual spectral function behaves at the non-relativistic as well as relativistic fermionic fixed point by working with the probe Dirac fermion 8 It is noteworthy that the probe sector does not always share the same thermodynamic behavior as the soup necessarily. Here the linear specific heat for the probe sector comes from the well known fact that the system consisting of the fermonic quasi-particle excitations has always the linear specific heat at low temperature [20].…”

“…The conventional boundary term to be chosen is the Lorentz covariant one, i.e., 8) whereby the variation of the full on-shell action reads 9) which apparently vanishes if the Dirichlet boundary condition is imposed on ψ + . This choice of boundary condition is usually referred to as the standard quantization for the Dirac field.…”

“…Speaking specifically, with the fermionic correlator, which can be extracted at the boundary holographically by evolving the bulk Dirac equation in the Reissner-Nordstrom AdS black hole with the ingoing boundary condition at the horizon, one can read off the Fermi surface with a rich spectrum of non-Fermi liquid behaviors [6,7,8,9,10,11,12,13]. However, as is well known, the Reissner-Nordstrom AdS black hole has a large ground state degeneracy, namely a finite entropy at zero temperature, which is somehow in tension with the third law of thermodynamics.…”

Fermi surfaces and gauge-gravity duality

“…The case µ 1 = µ 2 = µ 3 = 0, which leads to the extensively studied Reissner-Nordstrom black holes [1,2,[4][5][6][7], is connected to models very similar to those already considered. In this section we consider models inspired by the case µ 1 = µ 2 = 0, µ 3 = 0, which leads to some qualitatively different physics.…”

Holographic antiferromagnetic quantum criticality andAdS2scaling limit

“…In recent years, this duality has been extensively applied in condensed matter systems. Some remarkable progress has been made in this direction, including holographic superfluids (superconductors) [19,20] (for a recent review, see [21]), (non-) Fermi liquids [22][23][24] and so on. The models in the AdS/ CFT frame for ferromagnetism/paramagnetism and antiferromagnetism/paramagnetism phase transitions have also been proposed in [25,26].…”