Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice

Abstract

We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the s = 1/2 next-next-nearest neighbor Heisenberg antiferromagnet on the square lattice, with additional 4-spin ring exchange from higher order terms in the Hubbard expansion. We have varied the ratio between Hubbard model parameters, t/U , to obtain different relative strengths of the exchange parameters, while keeping electrons localized. The Hubbard model parameters have been parametrized via an effective ring exchange coupling, Jr, which have been varied between 0 J and 1.5 J. We find that ring exchange induces a quantum phase transition from the (π, π) ordered Neèl state to a (π/2, π/2) ordered state. This quantum critical point is reduced by quantum fluctuations from its mean field value of Jr/J = 2 to a value of ∼ 1.1. At the quantum critical point, the dynamical correlation function shows a pseudo-continuum at q-values between the two competing ordering vectors. arXiv:1812.04277v1 [cond-mat.str-el] 11 Dec 2018 A a b d c e f B i j k l J J J J r

Fractional spin excitations in the infinite-layer cuprate CaCuO$_2$

“…However, their observation in layered cuprates had remained somehow not conclusive so far [10] and our results can support the assignment of the magnon anomaly close to the X point to fractional spin excitations also in other cuprates. More in general, we demonstrate that multi-spin couplings play a non-marginal role in determining the short-wavelength physics of the magnetic excitations, as indeed proposed by several theories [14,21,57].…”

“…The presence of spinons in the spectrum of the Heisenberg AF with strong multi-spin couplings (of which the ring exchange is an example) has been predicted some years ago and is now well established [20][21][22]32]. Interestingly, a recent exact diagonalization study [57] performed on the EHM Hamiltonian has shown that, at J c /J ≈ 1 the excitation spectrum at ( 1 /2, 0) breaks into a continuum of states very close in energy, similarly to what has been calculated for Neél-RVB and Neél-VBS transitions [20,[28][29][30][31].…”

Possible Quantum Paramagnetism in Compressed Sr2IrO4

“…It remains to be seen whether realistic Hamiltonians for exchange correlations between J eff = 1 2 moments at high pressure can stabilize a quantum paramagnetic phase. In particular, the role of J r in Sr-214 needs to be experimentally and theoretically clarified as such exchange may also lead to quantum criticality [71,72]. Measuring the spectrum of magnetic excitations of Sr-214 at high pressure remains critical; not only to determine changes in the exchange constants, but also to verify if the isotropic Heisenberg model remains a valid approximation.…”

Coexistence of spontaneous dimerization and magnetic order in a transverse-field Ising ladder with four-spin interactions

“…While nearest-neighbor exchange is often the dominant interaction in Mott insulating materials, longerrange and multi-spin interactions may play an impor-tant role, particularly in the vicinity of a metal-insulator transition 23,24 . In fact, the ring exchange interaction has been invoked to reproduce the dispersion relation observed in inelastic neutron scattering experiments on cuprates such as La 2 CuO 4 and La 6 Ca 8 Cu 24 O 41 [25][26][27][28] . More recently, four-spin interactions have been argued to stabilize a chiral spin liquid on the triangular lattice 29 .…”