# Unparticles and anomalous dimensions in the cuprates

## Abstract

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\cite{ Hartnoll:2015sea}. 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. We find that the nature of the superconducting instabilitymore »

- Authors:

- Univ. of Washington, Seattle, WA (United States)
- Univ. of Illinois, Chicago, IL (United States)

- Publication Date:

- Research Org.:
- Univ. of Washington, Seattle, WA (United States); Energy Frontier Research Centers (EFRC) (United States). Center for Emergent Superconductivity (CES)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1595196

- Grant/Contract Number:
- SC0011637

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 3; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Holography and condensed matter physics (AdS/CMT); Renormalization Group

### Citation Formats

```
Karch, Andreas, Limtragool, Kridsanaphong, and Phillips, Philip W. Unparticles and anomalous dimensions in the cuprates. United States: N. p., 2016.
Web. doi:10.1007/JHEP03(2016)175.
```

```
Karch, Andreas, Limtragool, Kridsanaphong, & Phillips, Philip W. Unparticles and anomalous dimensions in the cuprates. United States. doi:10.1007/JHEP03(2016)175.
```

```
Karch, Andreas, Limtragool, Kridsanaphong, and Phillips, Philip W. Fri .
"Unparticles and anomalous dimensions in the cuprates". United States. doi:10.1007/JHEP03(2016)175. https://www.osti.gov/servlets/purl/1595196.
```

```
@article{osti_1595196,
```

title = {Unparticles and anomalous dimensions in the cuprates},

author = {Karch, Andreas and Limtragool, Kridsanaphong and Phillips, Philip W.},

abstractNote = {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\cite{ Hartnoll:2015sea}. 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. We find that 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.},

doi = {10.1007/JHEP03(2016)175},

journal = {Journal of High Energy Physics (Online)},

number = 3,

volume = 2016,

place = {United States},

year = {2016},

month = {3}

}

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