TY - JOUR
T1 - Unparticles and anomalous dimensions in the cuprates
AU - Karch, Andreas
AU - Limtragool, Kridsanaphong
AU - Phillips, Philip W.
N1 - Publisher Copyright:
© The Authors.
PY - 2016/3
Y1 - 2016/3
N2 - Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and T −linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead to a unifying description of the observed scaling forms. We adopt the continuous mass formalism or multi band (flavor) formalism of the unparticle sector by letting various microscopic parameters be mass-dependent. In particular, we show that an effective mass that varies with the flavor index as well as a running band edge and lifetime capture the AC and DC transport phenomenology of the cuprates. A key consequence of the running mass is that the effective dynamical exponent can differ from the underlying bare critical exponent, thereby providing a mechanism for realizing the fractional values of the dynamical exponent required in a previous analysis [1]. We also predict that regardless of the bare dynamical exponent, z, a non-zero anomalous dimension for the current is required. Physically, the anomalous dimension arises because the charge depends on the flavor, mass or energy. The equivalent phenomenon in a d + 1 gravitational construction is the running of the charge along the radial direction. The nature of the superconducting instability in the presence of scale invariant stuff shows that the transition temperature is not necessarily a monotonic function of the pairing interaction.
AB - Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and T −linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead to a unifying description of the observed scaling forms. We adopt the continuous mass formalism or multi band (flavor) formalism of the unparticle sector by letting various microscopic parameters be mass-dependent. In particular, we show that an effective mass that varies with the flavor index as well as a running band edge and lifetime capture the AC and DC transport phenomenology of the cuprates. A key consequence of the running mass is that the effective dynamical exponent can differ from the underlying bare critical exponent, thereby providing a mechanism for realizing the fractional values of the dynamical exponent required in a previous analysis [1]. We also predict that regardless of the bare dynamical exponent, z, a non-zero anomalous dimension for the current is required. Physically, the anomalous dimension arises because the charge depends on the flavor, mass or energy. The equivalent phenomenon in a d + 1 gravitational construction is the running of the charge along the radial direction. The nature of the superconducting instability in the presence of scale invariant stuff shows that the transition temperature is not necessarily a monotonic function of the pairing interaction.
KW - Holography and condensed matter physics (AdS/CMT)
KW - Renormalization group
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U2 - 10.1007/JHEP03(2016)175
DO - 10.1007/JHEP03(2016)175
M3 - Article
AN - SCOPUS:85007579754
SN - 1126-6708
VL - 2016
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 3
M1 - 175
ER -