Neutral order parameters in metallic criticality ind=2+1from a hairy electron star

Abstract

We use holography to study the spontaneous condensation of a neutral order parameter in a (2+1)-dimensional field theory at zero-temperature and finite density, dual to the electron star background of Hartnoll and Tavanfar. An appealing feature of this field theory is the emergence of an IR Lifshitz fixed-point with a finite dynamical critical exponent z, which is due to the strong interaction between critical bosonic degrees of freedom and a finite density of fermions (metallic quantum criticality). We show that under some circumstances the electron star background develops a neutral scalar hair whose holographic interpretation is that the boundary field theory undergoes a quantum phase transition, with a Berezinski-Kosterlitz-Thouless character, to a phase with a neutral order parameter. Including the backreaction of the bulk neutral scalar on the background, we argue that the two phases across the quantum critical point have different z, a novelty that exists in certain quantum phase transitions in condensed matter systems. We also analyze the system at finite temperature and find that the phase transition becomes, as expected, second-order. Embedding the neutral scalar into a higher form, a variety of interesting phases could potentially be realized for the boundary field theory. Examples which are of particular interest to condensed matter physics include an antiferromagnetic phase where a vector condenses and break the spin symmetry, a quadrupole nematic phase which involves the condensation of a symmetric traceless tensor breaking rotational symmetry, or different phases of a system with competing order parameters.

Dressing the electron star in a holographic superconductor

“…Below, we review these three models. Introducing more scalar fields can add features to these solutions, like partial fractionalization, as seen for example in [6,7,19].…”

“…Phases where a Fermi surface coexists with a superfluid have been considered in [18] in field theories that are relevant for condensed matter systems and for gaugegravity duality. In the holographic approach, a closely related system to the one we study here was considered by [19], with the difference that they have a neutral scalar in the bulk, so the phase transition is not to a superconductor but to antiferromagnetic or nematic phases, or other transitions characterized by a neutral order parameter. Another related work [7] considers also a competition between fractionalization and superconductivity, but with a bulk system consisting of a charged scalar and a neutral one (a dilaton).…”

Quantum phase transitions in semilocal quantum liquids

“…7. If we are studying a normalizable 52 Note at u ¼ 0, the two exponents in (D5) become degenerate and the independent solutions to the linear equation become ζ 1 2 and ζ 1 2 log ζ, respectively.…”

Fermionic response in a zero entropy state ofN=4super-Yang-Mills

“…The main difference, other than the introduction of a few factors of i, is that the formulation in terms of U ± involves X and Z in the coefficient of the first-order term (28), while the formulation in terms of ψ ± has Y and Z instead (154). Because the energy ω is contained in Y , this distinction is relevant when taking a small-ω limit.…”