2. Once the theoretical considerations for quantum criticality in the transverse field Ising model became known, the search began for a real material to display this QPT. By changing the orbital basis, it is easy to see that Φ1 is associated with breaking the equivalence between the two diagonals x±y and corresponds to a nematic order parameter with B2g (xy) symmetry, which breaks tetragonal symmetry but preserves diagonal mirror symmetries. The corresponding multipole moments and associated conjugate fields are shown in the third and fourth rows for each pseudospin component. A small fossil reptile related to dinosaurs and pterosaurs suggests a miniaturized origin for some of the largest animals to live on Earth. designed research; A.V.M., E.W.R., A.T.H., E.B., R.M.F., I.R.F., and S.A.K. ↵1A.V.M., E.W.R., A.T.H., E.B., R.M.F., I.R.F., and S.A.K. Because each operator alone would result in a ground state with distinct symmetries, the two operators must not commute. Of course, changing the value of any term in the microscopic Hamiltonian that does not explicitly break a relevant symmetry will generally result in a shift in Tc. R.M.F. 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. For these elements, quadrupole–quadrupole (QQ) interactions can exceed spin–spin interactions. We focus on an insulating tetragonal system with an odd number of sites. Shown is a schematic representation of the three types of order possible for a non-Kramers Eg doublet in a tetragonal system, corresponding to three components of a pseudospin representation. In summary, our work introduces a powerful tuning parameter for electronic Ising-nematic order: strain that breaks different symmetries than the nematic order. The second row illustrates the polarization of local (Wannier) orbitals for a model comprising orbitals with xz and yz symmetry. Transverse strain provides a way to tune through the nematic phase diagram, to access the quantum critical regime, and potentially to realize new phenomena. Image credit: Rosenzweig lab, Weizmann Institute of Science. Identifying appropriate means to tune systems through a continuous nematic quantum phase transition is therefore of considerable importance. By this argument, we can establish the rough topology of the phase diagram for those doublet-based nematic states without the formal correspondence to the transverse field Ising model: The zero transverse strain, low-temperature nematic state will be destroyed by quantum fluctuations at large enough strains, while the intervening region will have a phase boundary (and possibly novel intermediate phases) that are determined by the microscopic details of the specific system. The transverse eld Ising model (TFIM) was rst introduced by de Gennes in 1963  as a pseudo spin model to describe the tunneling of protons in ferroelectric crystalls. 4 and 6 (with h2=0), Eq. A 1.4-million-year-old handaxe made from hippopotamus bone expands the known technological repertoire of early human ancestors. In this case, an x2−y2 nematic order parameter must involve at least nearest neighbor sites:Φ3(R→)≡∑R→′f(R→−R→′)[cσ,R→†cσ,R→′+H.C. A.T.H. More importantly, while the commutation relations of the nematic operators are moderately complicated, they commute when averaged over sites.[Φ3(R→),∑R→′Φ1(R→′)]=0. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The one-dimensional Ising model with a transverse field is solved exactly by transforming the set of Pauli operators to a new set of Fermi operators. Pairs of states represent opposite signs/polarization of the Ising pseudospins The longitudinal component Φ3 corresponds to orbital polarization with an x2−y2 (B1g) symmetry; Φ1 corresponds to an orbital polarization with an xy (B2g) symmetry; and Φ2 corresponds to an orbital magnetic moment. performed research; A.V.M., E.W.R., and A.T.H. in the post Ground state degeneracy: Spin vs Fermionic language; in particular, the discussion below the answer lists some references where the derivation is carried out.. NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. first the infinite algorithm, and then doing sweeps for convergence with the finite algorithm. Reviewers: C.H., Max Planck Institute for Chemical Physics of Solids; and M.V., Technische Universität Dresden. Consequently, εxy and Hz are appropriate transverse fields to tune the ferroquadrupolar transition to a quantum critical point. If there is a (non-Kramers) orbital doublet that transforms according to a 2D representation (E, Eg, or Eu) of the tetragonal point group, then there is a local pseudospin-1/2 associated with each unit cell of the crystal. where τ is the imaginary time and () is the Berry connection associated with a monopole in “nematic space” of topological charge q. was supported by the Gordon and Betty Moore Foundation Emergent Phenomena in Quantum Systems Initiative through Grant GBMF4414. This site writes the Hamiltonian in terms of spin operators as you can see, but still states that the critical point occurs at h/J = 1, which is not correct. Ising model in a transverse field: I. Thus, strain can prove a valuable tuning parameter even without the correspondence to the transverse field Ising model. This Eg doublet may be formally identified with a pseudospin-1/2, and so shear strain εxy acts as a transverse field and reduces the spontaneous quadrupole moment ⟨O^22⟩ by inducing quantum fluctuations between the eigenstates |ψ1⟩ and |ψ2⟩. The authors declare no conflict of interest. Though this formal identification with the transverse field Ising model is not universal for all electronic Ising-nematic order, we emphasize that it elucidates an underlying mechanism that is relevant wherever electronic degrees of freedom in the high-temperature tetragonal phase belong to a doublet representation. The open access journal for physics New Jou rnal of Ph ys ics Quantum simulation of the transverse Ising model with trapped ions K Kim1,5,6, S Korenblit1, R Islam1, E E Edwards1, M-S Chang1,7, C Noh2,8, H Carmichael2, G-D Lin3,9, L-M Duan3, C C Joseph Wang4, J K Freericks4 and C Monroe1 1 Joint Quantum Institute, University of Maryland Department of Physics and Further insight into the dichotomy between the quantum properties of degenerate and single-band nematic systems comes from the effective field theory of the pseudospin Φ→. 2 imply that a pseudospin with a well-defined value of Φ1 or Φ2 must be highly uncertain in Φ3. Image credit: Stephanie Gamez (University of California San Diego, La Jolla, CA). For example, shear strain does not only couple to =0 ferroquadrupolar order but εxy may also act as a transverse field for antiferroquadrupolar order by promoting quantum fluctuations between components of each local pseudospin. In the iron-based superconductors, electronic nematic phases are unambiguously present (1⇓⇓⇓⇓–6), and the maximum superconducting transition temperature often correlates with the location of a putative quantum critical point with a nematic character.
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