# NMR relaxation in Ising spin chains

## Abstract

We examine the low frequency spin susceptibility of the paramagnetic phase of the quantum Ising chain in a transverse field at temperatures well below the energy gap. We find that the imaginary part is dominated by rare quantum processes in which the number of quasiparticles changes by an odd number. We obtain exact results for the NMR relaxation rate in the low temperature limit for the integrable model with nearest-neighbor Ising interactions, and derive exact universal scaling results applicable to generic Ising chains near the quantum critical point. These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system CoNb2O6.

- Authors:

- Publication Date:

- Research Org.:
- Energy Frontier Research Centers (EFRC) (United States). Institute for Quantum Matter (IQM); Johns Hopkins Univ., Baltimore, MD (United States)

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

- OSTI Identifier:
- 1566686

- DOE Contract Number:
- SC0019331

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 3; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- optics, thermal conductivity, defects, charge transport, superconductivity, magnetism and spin physics, quantum information science, materials and chemistry by design, synthesis (novel materials)

### Citation Formats

```
Steinberg, Julia, Armitage, N. P., Essler, Fabian H. L., and Sachdev, Subir.
```*NMR relaxation in Ising spin chains*. United States: N. p., 2019.
Web. doi:10.1103/physrevb.99.035156.

```
Steinberg, Julia, Armitage, N. P., Essler, Fabian H. L., & Sachdev, Subir.
```*NMR relaxation in Ising spin chains*. United States. doi:10.1103/physrevb.99.035156.

```
Steinberg, Julia, Armitage, N. P., Essler, Fabian H. L., and Sachdev, Subir. Tue .
"NMR relaxation in Ising spin chains". United States. doi:10.1103/physrevb.99.035156.
```

```
@article{osti_1566686,
```

title = {NMR relaxation in Ising spin chains},

author = {Steinberg, Julia and Armitage, N. P. and Essler, Fabian H. L. and Sachdev, Subir},

abstractNote = {We examine the low frequency spin susceptibility of the paramagnetic phase of the quantum Ising chain in a transverse field at temperatures well below the energy gap. We find that the imaginary part is dominated by rare quantum processes in which the number of quasiparticles changes by an odd number. We obtain exact results for the NMR relaxation rate in the low temperature limit for the integrable model with nearest-neighbor Ising interactions, and derive exact universal scaling results applicable to generic Ising chains near the quantum critical point. These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system CoNb2O6.},

doi = {10.1103/physrevb.99.035156},

journal = {Physical Review B},

issn = {2469-9950},

number = 3,

volume = 99,

place = {United States},

year = {2019},

month = {1}

}

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