# 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:
- 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},

number = 12,

volume = 116,

place = {United States},

year = {2019},

month = {3}

}

DOI: 10.1073/pnas.1807840116

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Works referenced in this record:

##
Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagome Compound ${\mathrm{ZnCu}}_{3}(\mathrm{OH}{)}_{6}{\mathrm{Cl}}_{2}$

journal, July 2008

- Zorko, A.; Nellutla, S.; van Tol, J.
- Physical Review Letters, Vol. 101, Issue 2

##
A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics

journal, January 1958

- Dzyaloshinsky, I.
- Journal of Physics and Chemistry of Solids, Vol. 4, Issue 4

##
Thermodynamic properties of a spin-1/2 spin-liquid state in a κ-type organic salt

journal, April 2008

- Yamashita, Satoshi; Nakazawa, Yasuhiro; Oguni, Masaharu
- Nature Physics, Vol. 4, Issue 6

##
Structure factors of the kagome-lattice Heisenberg antiferromagnets at finite temperatures

journal, January 2018

- Sherman, Nicholas E.; Singh, Rajiv R. P.
- Physical Review B, Vol. 97, Issue 1

##
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group

journal, March 2012

- Stoudenmire, E. M.; White, Steven R.
- Annual Review of Condensed Matter Physics, Vol. 3, Issue 1

##
Quantum spin liquids: a review

journal, November 2016

- Savary, Lucile; Balents, Leon
- Reports on Progress in Physics, Vol. 80, Issue 1

##
Schwinger-boson approach to the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions: Phase diagram and dynamical structure factors

journal, February 2010

- Messio, L.; Cépas, O.; Lhuillier, C.
- Physical Review B, Vol. 81, Issue 6

##
Quantum Magnetism in the Paratacamite Family: Towards an Ideal Kagomé Lattice

journal, February 2007

- Mendels, P.; Bert, F.; de Vries, M. A.
- Physical Review Letters, Vol. 98, Issue 7

##
Equivalence of the resonating-valence-bond and fractional quantum Hall states

journal, November 1987

- Kalmeyer, V.; Laughlin, R. B.
- Physical Review Letters, Vol. 59, Issue 18

##
Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet

journal, April 2011

- Yan, S.; Huse, D. A.; White, S. R.
- Science, Vol. 332, Issue 6034

##
Identifying topological order by entanglement entropy

journal, November 2012

- Jiang, Hong-Chen; Wang, Zhenghan; Balents, Leon
- Nature Physics, Vol. 8, Issue 12

##
Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet

journal, January 2014

- Iqbal, Yasir; Poilblanc, Didier; Becca, Federico
- Physical Review B, Vol. 89, Issue 2

##
Quantum spin liquids in the absence of spin-rotation symmetry: Application to herbertsmithite

journal, December 2013

- Dodds, Tyler; Bhattacharjee, Subhro; Kim, Yong Baek
- Physical Review B, Vol. 88, Issue 22

##
Vacuum degeneracy of chiral spin states in compactified space

journal, October 1989

- Wen, X. G.
- Physical Review B, Vol. 40, Issue 10

##
Projected wave function study of ${\mathbb{Z}}_{2}$ spin liquids on the kagome lattice for the spin- $\frac{1}{2}$ quantum Heisenberg antiferromagnet

journal, July 2011

- Iqbal, Yasir; Becca, Federico; Poilblanc, Didier
- Physical Review B, Vol. 84, Issue 2

##
Static and dynamical spin correlations of the $S=\frac{1}{2}$ random-bond antiferromagnetic Heisenberg model on the triangular and kagome lattices

journal, October 2015

- Shimokawa, Tokuro; Watanabe, Ken; Kawamura, Hikaru
- Physical Review B, Vol. 92, Issue 13

##
Density matrix formulation for quantum renormalization groups

journal, November 1992

- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19

##
*Colloquium* : Herbertsmithite and the search for the quantum spin liquid

journal, December 2016

- Norman, M. R.
- Reviews of Modern Physics, Vol. 88, Issue 4

##
Chiral Spin Liquid on a Kagome Antiferromagnet Induced by the Dzyaloshinskii-Moriya Interaction

journal, June 2017

- Messio, Laura; Bieri, Samuel; Lhuillier, Claire
- Physical Review Letters, Vol. 118, Issue 26

##
Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces

journal, May 1990

- Wen, X. G.; Niu, Q.
- Physical Review B, Vol. 41, Issue 13

##
Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet

journal, November 2015

- Fu, M.; Imai, T.; Han, T. -H.
- Science, Vol. 350, Issue 6261

##
Large- *N* expansion for frustrated quantum antiferromagnets

journal, April 1991

- Read, N.; Sachdev, Subir
- Physical Review Letters, Vol. 66, Issue 13

##
Spin structure factors of chiral quantum spin liquids on the kagome lattice

journal, September 2016

- Halimeh, Jad C.; Punk, Matthias
- Physical Review B, Vol. 94, Issue 10

##
Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons

journal, June 1992

- Sachdev, Subir
- Physical Review B, Vol. 45, Issue 21

##
Gapless Spin-Liquid Ground State in the $S=1/2$ Kagome Antiferromagnet

journal, March 2017

- Liao, H. J.; Xie, Z. Y.; Chen, J.
- Physical Review Letters, Vol. 118, Issue 13

##
Quantum phase transition induced by Dzyaloshinskii-Moriya interactions in the kagome antiferromagnet

journal, October 2008

- Cépas, O.; Fong, C. M.; Leung, P. W.
- Physical Review B, Vol. 78, Issue 14

##
Spin Dynamics of the Spin- $1/2$ Kagome Lattice Antiferromagnet ${\mathrm{ZnCu}}_{3}(\mathrm{OH}{)}_{6}{\mathrm{Cl}}_{2}$

journal, March 2007

- Helton, J. S.; Matan, K.; Shores, M. P.
- Physical Review Letters, Vol. 98, Issue 10

##
First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

journal, May 1998

- Waldtmann, C.; Everts, H. -U.; Bernu, B.
- The European Physical Journal B, Vol. 2, Issue 4

##
Dynamical correlation functions using the density matrix renormalization group

journal, July 1999

- Kühner, Till D.; White, Steven R.
- Physical Review B, Vol. 60, Issue 1

##
Kagome Antiferromagnet: A Chiral Topological Spin Liquid?

journal, May 2012

- Messio, Laura; Bernu, Bernard; Lhuillier, Claire
- Physical Review Letters, Vol. 108, Issue 20

##
Entanglement signatures of emergent Dirac fermions: Kagome spin liquid and quantum criticality

journal, November 2018

- Zhu, Wei; Chen, Xiao; He, Yin-Chen
- Science Advances, Vol. 4, Issue 11

##
Dirac structure, RVB, and Goldstone modes in the *kagomé* antiferromagnet

journal, December 2000

- Hastings, M. B.
- Physical Review B, Vol. 63, Issue 1

##
Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice

journal, March 2014

- Punk, Matthias; Chowdhury, Debanjan; Sachdev, Subir
- Nature Physics, Vol. 10, Issue 4

##
Projected-Wave-Function Study of the Spin- $1/2$ Heisenberg Model on the Kagomé Lattice

journal, March 2007

- Ran, Ying; Hermele, Michael; Lee, Patrick A.
- Physical Review Letters, Vol. 98, Issue 11

##
Mean-field theory of spin-liquid states with finite energy gap and topological orders

journal, August 1991

- Wen, X. G.
- Physical Review B, Vol. 44, Issue 6

##
Quantum criticality of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions

journal, April 2010

- Huh, Yejin; Fritz, Lars; Sachdev, Subir
- Physical Review B, Vol. 81, Issue 14

##
Gapless spin-liquid phase in the kagome spin- $\frac{1}{2}$ Heisenberg antiferromagnet

journal, February 2013

- Iqbal, Yasir; Becca, Federico; Sorella, Sandro
- Physical Review B, Vol. 87, Issue 6

##
Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice

journal, February 2015

- Gong, Shou-Shu; Zhu, Wei; Balents, Leon
- Physical Review B, Vol. 91, Issue 7

##
Properties of an algebraic spin liquid on the kagome lattice

journal, June 2008

- Hermele, Michael; Ran, Ying; Lee, Patrick A.
- Physical Review B, Vol. 77, Issue 22

##
Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor $\kappa \mathrm{\text{\u2212}}(\mathrm{ET}{)}_{2}{\mathrm{Cu}}_{2}(\mathrm{CN}{)}_{3}$

journal, October 2005

- Kurosaki, Y.; Shimizu, Y.; Miyagawa, K.
- Physical Review Letters, Vol. 95, Issue 17

##
Dynamical density-matrix renormalization-group method

journal, July 2002

- Jeckelmann, Eric
- Physical Review B, Vol. 66, Issue 4

##
Gapped spin liquid with ${\mathbb{Z}}_{2}$ topological order for the kagome Heisenberg model

journal, June 2017

- Mei, Jia-Wei; Chen, Ji-Yao; He, Huan
- Physical Review B, Vol. 95, Issue 23

##
Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet

journal, December 2012

- Han, Tian-Heng; Helton, Joel S.; Chu, Shaoyan
- Nature, Vol. 492, Issue 7429

##
Phase diagram of the ${J}_{1}\text{\u2212}{J}_{2}$ Heisenberg model on the kagome lattice

journal, March 2015

- Kolley, F.; Depenbrock, S.; McCulloch, I. P.
- Physical Review B, Vol. 91, Issue 10

##
Anisotropic Superexchange Interaction and Weak Ferromagnetism

journal, October 1960

- Moriya, Tôru
- Physical Review, Vol. 120, Issue 1

##
Doping a Mott insulator: Physics of high-temperature superconductivity

journal, January 2006

- Lee, Patrick A.; Nagaosa, Naoto; Wen, Xiao-Gang
- Reviews of Modern Physics, Vol. 78, Issue 1

##
Density Matrix Renormalization Group Numerical Study of the Kagome Antiferromagnet

journal, September 2008

- Jiang, H. C.; Weng, Z. Y.; Sheng, D. N.
- Physical Review Letters, Vol. 101, Issue 11

##
Refining the Spin Hamiltonian in the Spin- $\frac{1}{2}$ Kagome Lattice Antiferromagnet ${\mathrm{ZnCu}}_{3}(\mathrm{OH}{)}_{6}{\mathrm{Cl}}_{2}$ Using Single Crystals

journal, April 2012

- Han, Tianheng; Chu, Shaoyan; Lee, Young S.
- Physical Review Letters, Vol. 108, Issue 15

##
Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice

journal, September 2003

- Shimizu, Y.; Miyagawa, K.; Kanoda, K.
- Physical Review Letters, Vol. 91, Issue 10

##
Nature of the Spin-Liquid Ground State of the $S=1/2$ Heisenberg Model on the Kagome Lattice

journal, August 2012

- Depenbrock, Stefan; McCulloch, Ian P.; Schollwöck, Ulrich
- Physical Review Letters, Vol. 109, Issue 6