Transverse fields to tune an Ising-nematic quantum phase transition

Akash V. Maharaj, Elliott W. Rosenberg, Alexander T. Hristov, Erez Berg, Rafael M. Fernandes, Ian R. Fisher, Steven A. Kivelson

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.

Original languageEnglish (US)
Pages (from-to)13430-13434
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number51
StatePublished - Dec 19 2017

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS. We acknowledge useful conversations with Maxwell C. Shapiro, Daniel Agterberg, and Andrey Chubukov. A.V.M., A.T.H., I.R.F., and S.A.K. were supported by the Department of Energy, Office of Basic Energy Sciences under Contract DE-AC02-76SF00515. A.T.H. also received support from the National Science Foundation Graduate Research Fellowship Program under Grant DGE-114747. E.W.R. was supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative through Grant GBMF4414. R.M.F. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award DE-SC0012336. E.B. was supported by the Israel Science Foundation under Grant 1291/12 and by the US-Israel Binational Science Foundation under Grant 2014209.


  • Condensed matter physics
  • Electronic nematicity
  • Quantum phase transitions
  • Strongly correlated electrons


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