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Quantum Spin Liquid in Quantum Spin Ice

In this project, we study the most general model for spins 1/2 on the pyrochlore lattice governed by nearest-neighbor exchange interactions, and show that the (ground state) phase diagram of our model contains the U(1) Quantum Spin Liquid described by Hermele, Fisher and Balents [Phys. Rev. B. 69 064404 (2004)]. We also exhibit and characterize a novel phase of matter, which we call U(1) Coulomb Ferromagnet. The latter is best seen to be a magnetized version of the U(1) Quantum Spin Liquid, and occupies a large part of the phase diagram of spin-1/2 pyrochlores.

We also make the connection with experiment by comparing our theory with inelastic neutron scattering data in high field of a single crystal of Yb2Ti2O7. The comparison is based on spin wave theory in high field and fits to the data remarkably well. Moreover the exchange coupling constants we get from our fits place Yb2Ti2O7 in a region where a so-called U(1) quantum spin liquid can be expected.

In the theory paper, we develop a novel non-perturbative slave particle approach and make use of a "gauge Mean Field Theory". In the "temperature paper" we extend this analysis to nonzero temperature. The "joint paper" describes the perturbative limit of our theory, the experiments, spin wave theory, and the fits.

Facts and FAQs

  • Yb2Ti2O7 is the first and only spin liquid candidate where the Hamiltonian is known quantitatively.
  • The Coulomb Ferromagnet (CFM) is a new phase of matter, so far never predicted. It contains all the exotic excitations of the U(1) Quantum Spin Liquids.
  • The U(1) Quantum Spin Liquid and Coulomb Ferromagnet described here are very promising in terms of future conclusive experimental discovery: many rare-earth pyrochlore materials (A2B2O7 and B-site spinels AB2X4) can be grown in large single crystals, high field inelastic neutron scattering can be performed, allowing to determine the Hamiltonian parameters, the theoretical understanding is detailed, many experiments can be performed...
  • The slave particle theory introduced here is quite different from the usual slave particle theories: here our spinons (slave bosons) have a very physical interpretation.

Check it out!

Random quantum spin ice paper

  • published in PRL: PRL 118, 087203 (23 Feb. 2017)
  • accepted by PRL (Jan. 2017)
  • arXiv: arXiv: 1604.04630 (Apr. 2016)
  • talk at ISSP (Sep. 2016)
  • talk at the KITP conference on Spin-Orbit Coupled Systems, Santa Barbara (Jul. 2015): video, pdf
  • talk at the APS March Meeting 2016, Baltimore (Mar. 2016): pdf
  • Condensed Matter Theory Seminar at Boston University (18 May 2016): pdf
  • post on Leon's webpage/blog: spinsandelectrons.com

Breathing paper

Temperature paper

Theory paper

  • published in PRL: PRL 108, 037202 (19 Jan. 2012)
  • arXiv: arXiv: 1110.2185 (11 Oct. 2011)
  • summary on Leon's web page: physics.ucsb.edu/~balents/projects
  • invited talk at the "Frustrated Magnetism in Brazil" IIP conference (Dec. 2011): pdf
  • Leon's invited talk on spin liquids at the "Frustrated Magnetism in Brazil" IIP conference, Natal (Dec. 2011): physics.ucsb.edu/~balents
  • contributed talk at the 2012 APS March Meeting, Boston (Feb. 2012): pdf
  • invited talk at the "Mott Physics beyond the Heisenberg Model" workshop at EPFL, Lausanne (Jun. 2012): pdf
  • there is a typo in the Supplemental Material: in Section IV.A., the classical energies Eqs. (68) and (70) are given per site and not per unit cell. We thank F. Bègue for noticing this.
  • the proof editors introduced a mistake in Eq. (6) of the main text: there is of course a \Phi missing in the first term of the right-hand-side (see the arXiv version for the correct equation).

Joint paper with experimental group

Bibtex (Click to Show/Hide)

Quantum Spin Liquids Review

title={Quantum spin liquids: a review},
author={Savary, Lucile and Balents, Leon},
journal={Reports on Progress in Physics},
publisher={IOP Publishing},

Random icing paper

title = {Disorder-Induced Quantum Spin Liquid in Spin Ice Pyrochlores},
author = {Savary, Lucile and Balents, Leon},
journal = {Phys. Rev. Lett.},
volume = {118},
issue = {8},
pages = {087203},
numpages = {5},
year = {2017},
month = {Feb},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.118.087203},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.118.087203}

Breathing paper

title = {Quantum spin ice on the breathing pyrochlore lattice},
author = {Savary, Lucile and Wang, Xiaoqun and Kee, Hae-Young and Kim, Yong Baek and Yu, Yue and Chen, Gang},
journal = {Phys. Rev. B},
volume = {94},
issue = {7},
pages = {075146},
numpages = {10},
year = {2016},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.94.075146},
url = {http://link.aps.org/doi/10.1103/PhysRevB.94.075146}

Temperature paper

title = {Spin liquid regimes at nonzero temperature in quantum spin ice},
author = {Savary, Lucile and Balents, Leon},
journal = {Phys. Rev. B},
volume = {87},
issue = {20},
pages = {205130},
numpages = {14},
year = {2013},
month = {May},
doi = {10.1103/PhysRevB.87.205130},
url = {http://link.aps.org/doi/10.1103/PhysRevB.87.205130},
publisher = {American Physical Society}

Theory paper

volume = {108},
journal = {Phys. Rev. Lett.},
month = {Jan},
numpages = {5},
author = {Savary, Lucile and Balents, Leon},
title = {Coulombic Quantum Liquids in Spin-$1/2$ Pyrochlores},
year = {2012},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.108.037202},
doi = {10.1103/PhysRevLett.108.037202},
issue = {3},
publisher = {American Physical Society},
pages = {037202}

Joint paper with experimental group

title = {Quantum Excitations in Quantum Spin Ice},
month = {Oct},
journal = {Phys. Rev. X},
doi = {10.1103/PhysRevX.1.021002},
author = {Ross, Kate A. and Savary, Lucile and Gaulin, Bruce D. and Balents, Leon},
year = {2011},
issue = {2},
url = {http://link.aps.org/doi/10.1103/PhysRevX.1.021002},
numpages = {10},
publisher = {American Physical Society},
pages = {021002},
volume = {1}