# Log-rise of the resistivity in the holographic Kondo model

## Abstract

In this article, we study a single-channel Kondo effect using a recently developed [1–4] holographic large-$N$ technique. In order to obtain resistivity of this model, we introduce a probe field. The gravity dual of a localized fermionic impurity in $1 + 1$-dimensional host matter is constructed by embedding a localized two-dimensional Anti-de Sitter ($$\mathrm{AdS_2}$$)-brane in the bulk of three-dimensional $$\mathrm{AdS_3}$$. This helps us construct an impurity charge density which acts as a source to the bulk equation of motion of the probe gauge field. The functional form of the charge density is obtained independently by solving the equations of motion for the fields confined to the $$\mathrm{AdS_2}$$-brane. The asymptotic solution of the probe field is dictated by the impurity charge density, which in turn affects the current-current correlation functions and hence the resistivity. Our choice of parameters tunes the near-boundary impurity current to be marginal, resulting in a $$\mathrm{log}T$$ behavior in the UV resistivity, as is expected for the Kondo problem. The resistivity at the IR fixed point turns out to be zero, signaling a complete screening of the impurity.

- Authors:

- Publication Date:

- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Center for Emergent Superconductivity (CES); Brookhaven National Lab. (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1425525

- Alternate Identifier(s):
- OSTI ID: 1566380

- Grant/Contract Number:
- AC0298CH1088; AC02-98CH10886

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 6; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; phonons; thermal conductivity; energy storage (including batteries and capacitors); superconductivity; defects; spin dynamics

### Citation Formats

```
Padhi, Bikash, Tiwari, Apoorv, Setty, Chandan, and Phillips, Philip W. Log-rise of the resistivity in the holographic Kondo model. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.97.066012.
```

```
Padhi, Bikash, Tiwari, Apoorv, Setty, Chandan, & Phillips, Philip W. Log-rise of the resistivity in the holographic Kondo model. United States. doi:10.1103/PhysRevD.97.066012.
```

```
Padhi, Bikash, Tiwari, Apoorv, Setty, Chandan, and Phillips, Philip W. Mon .
"Log-rise of the resistivity in the holographic Kondo model". United States. doi:10.1103/PhysRevD.97.066012.
```

```
@article{osti_1425525,
```

title = {Log-rise of the resistivity in the holographic Kondo model},

author = {Padhi, Bikash and Tiwari, Apoorv and Setty, Chandan and Phillips, Philip W.},

abstractNote = {In this article, we study a single-channel Kondo effect using a recently developed [1–4] holographic large-$N$ technique. In order to obtain resistivity of this model, we introduce a probe field. The gravity dual of a localized fermionic impurity in $1 + 1$-dimensional host matter is constructed by embedding a localized two-dimensional Anti-de Sitter ($\mathrm{AdS_2}$)-brane in the bulk of three-dimensional $\mathrm{AdS_3}$. This helps us construct an impurity charge density which acts as a source to the bulk equation of motion of the probe gauge field. The functional form of the charge density is obtained independently by solving the equations of motion for the fields confined to the $\mathrm{AdS_2}$-brane. The asymptotic solution of the probe field is dictated by the impurity charge density, which in turn affects the current-current correlation functions and hence the resistivity. Our choice of parameters tunes the near-boundary impurity current to be marginal, resulting in a $\mathrm{log}T$ behavior in the UV resistivity, as is expected for the Kondo problem. The resistivity at the IR fixed point turns out to be zero, signaling a complete screening of the impurity.},

doi = {10.1103/PhysRevD.97.066012},

journal = {Physical Review D},

number = 6,

volume = 97,

place = {United States},

year = {2018},

month = {3}

}

DOI: 10.1103/PhysRevD.97.066012

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