Excitation spectra of hard-core bosons on square and triangular lattices in superfluid phase

Abstract

Excitation spectra of hard-core bosons with nearest-and next-nearest-neighbor interactions on square and triangular lattices in the superfluid phase are studied using the spin-wave theory. We go beyond the standard linear spin-wave approximation calculating corrections due to spin-wave interaction. Account for the spinwave interaction considerably improves the quantitative description of the excitation spectra. The behavior of the spectra is analyzed in detail at different particle densities and relations between the interaction parameters. Particular attention is given to the spectrum minima with the aim to find out the conditions for instability of the superfluid phase. We show that for a triangular lattice at high enough next-nearest-neighbor repulsion there appears a true roton minimum inside the Brillouin zone located on the line connecting the zone center with the midpoint of the face of the zone boundary. The obtained analytical results are in excellent quantitative agreement with the numerical simulations known from literature.

Ground-state properties of quantum triangular ice

“…Figures (11) and (12) show the energy spectra of the Z 2 -invariant XXZ model in the CFM. As previously mentioned, the spectra have a similar behaviour to the U(1)invariant XXZ model 39,40 at the corners of the Brillouin zone and along RM except for the case of XY model. At the corners of the Brillouin zone, Q = (±4π 3, 0), the spectrum vanishes when J ′ z = J ±± − J z 2.…”

“…A related U(1)-invariant XXZ model in the superfluid phase has been studied previously on the triangular lattice, using series expansion methods 39 and spin wave theory. 40 The present model has not been studied in the ferromagnetic phase. The understanding of this phase might be applicable to many systems, since many magnetic materials are ferromagnets.…”

Quantum triangular ice in the easy-axis ferromagnetic phase

“…We also calculate the particle density and the non-divergent condensate fraction at k = 0. In contrast to the U(1)-invariant model, with a phonon dispersion near k = 0, 11,12 the spectrum of the Z 2 -invariant model exhibits a maxon dispersion near k = 0 with a gap of ∆ ∝ J ±± (J z + J z + J ±± ) at halffilling (h x,z = 0). We see that the gap does not vanish for J ±± = 0.…”

“…The sign of J ±± is immaterial by virtue of the unitary transformation S ± lm → ±iS ± lm . The crucial difference between the U(1)-invariant XXZ model [6][7][8][9][10][11][12] and Eq. ( 1) is that the ferromagnetic interaction in the former is easy-plane and has a unique sign for non-bipartite lattices, whereas in the latter, the ferromagnetic interaction is easy-axis and the sign is im-material, which results in a Z 2 -invariant Hamiltonian in the x-y plane.…”

“…A related U(1)-invariant XXZ model in the superfluid phase has been studied previously on the triangular lattice, using series expansion methods 11 and spin wave theory. 12 The present model has not been studied in the ferromagnetic phase. The study of this model has some physical relevance since many magnetic materials are ferromagnets.…”