# Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice

## Abstract

A spin- $1/2$ lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the $\mathbf{Q}=M$ point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.

- Authors:

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1497921

- Grant/Contract Number:
- FG02-06ER46305

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America

- Additional Journal Information:
- Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Volume: 116 Journal Issue: 12; Journal ID: ISSN 0027-8424

- Publisher:
- Proceedings of the National Academy of Sciences

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Zhu, W., Gong, Shou-shu, and Sheng, D. N.
```*Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice*. United States: N. p., 2019.
Web. doi:10.1073/pnas.1807840116.

```
Zhu, W., Gong, Shou-shu, & Sheng, D. N.
```*Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice*. United States. doi:10.1073/pnas.1807840116.

```
Zhu, W., Gong, Shou-shu, and Sheng, D. N. Mon .
"Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice". United States. doi:10.1073/pnas.1807840116.
```

```
@article{osti_1497921,
```

title = {Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice},

author = {Zhu, W. and Gong, Shou-shu and Sheng, D. N.},

abstractNote = {A spin- 1 / 2 lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the Q = M point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.},

doi = {10.1073/pnas.1807840116},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

issn = {0027-8424},

number = 12,

volume = 116,

place = {United States},

year = {2019},

month = {3}

}

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Web of Science

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