Variational coupled-cluster study of plasmonlike excitations in quantum antiferromagnets

Abstract

We extend recently proposed variational coupled-cluster method to describe excitation states of quantum antiferromagnetic bipartite lattices. We reproduce the spin-wave excitations (i.e., magnons with spin ±1). In addition, we obtain a new, spin-zero excitation (magnon-density waves) which has been missing in all existing spin-wave theories. Within our approximation, this magnon-densitywave excitation has a nonzero energy gap in a cubic lattice and is gapless in a square lattice, similar to those of charge-density-wave excitations (plasmons) in quantum electron gases.PACS numbers: 31.15. Dv, 75.10.Jm, 75.30.Ds, 75.50.Ee From many-body physics view, energy spectra of lowlying excitation states of a quantum many-body interacting system are mainly determined by the correlations included in its ground state. Feynman's description of the phonon-roton excitations in a Helium-4 quantum liquid is a well-known example [1,2]. For the ground state properties, the method of correlated basis functions (CBF) has produced satisfactory results. Combining with Feynman's excitation theory, we therefore have an analytical, systematic method capable of describing most states of the Helium-4 quantum liquid at low temperature [2].The coupled-cluster method (CCM) [3,4,5] is another successful microscopic many-body theory which has produced many most competitive results for the ground state properties of many atoms, molecules, electron gas, and quantum spin systems [6]. In the traditional CCM, however, the bra and ket states are not hermitian to one another [7]. We recently extended the CCM to a variational formalism [8,9], in which bra and ket states are hermitian to one another. In our analysis, a close relation with the CBF method was found and exploited by using diagrammatic techniques. In application to quantum antiferromagnets, our calculations in a simple approximation reproduced the ground state properties of the spin-wave theory (SWT) [10]. Improvements over SWT by higherorder calculations were also obtained [9]. Here we extend this variational method to describe excitation states. Inspired by the close relation to the CBF method, we are able to obtain the energy spectra of quasiparticle-densitywave excitations by following Feynman, as well as the usual quasiparticle excitation spectra as in the traditional CCM. For the antiferromagnetic models, these quasiparticle excitations correspond to the well known spin-wave excitations (magnons) with spin ±1; the new, spin-zero excitations are identified as magnon-density-wave excitations whose energy spectra share some characteristics with that of charge-density-wave excitations (plasmons) in quantum electron gases [11]. We like to emphasize that these spin-zero excitations have been missing in all spinwave theories, including the more recently modified spinwave theories [12,13,14]. Magnon-density fluctuations in Heisenberg ferromagnets at low temperature were investigated in the sixties by calculating the longitudinal susceptibility [15,16]. Calculations for the longitudinal spin ...

Excited states of quantum many-body interacting systems: a variational coupled-cluster description

“…(This is slightly different to that reported in Ref. 12 where detailed calculations in this region had no been were done.) This gap is about the same as the largest magnon energy, ǫ q = sz at q = (π/2, π/2, π/2) from Eq.…”

“…A brief report of some preliminary results has been published [12]. We investigate two different types of excitation states using two approaches.…”

The Effects of Three Magnons Interactions in the Magnon-Density Waves of Triangular Spin Lattices

“…The logarithmic behavior of the structure factor and the energy spectrum of the triangular lattice model is similar to that of the square lattice model investigated earlier [39,42,46,47]. We have identified these gapless modes of the 2D models as quasi-gapped modes because any finite size effect or anisotropy will induce a large energy gap when compared with the counterparts of the spin-wave spectrum.…”

“…For a generic quantum spin-s antiferromagnetic Hamiltonian system with a Néel order, a microscopic theory of the longitudinal modes has been proposed [39]. In this theory the longitudinal excitations are identified as the collective modes of the magnon-density waves, and the corresponding wave functions are constructed by employing the magnon-density operator S z in similar fashion to Feynman's theory on the low-lying excited states of the helium-4 superfluid where the particle density operator is used [40].…”

Longitudinal Excitations in Bipartite and Hexagonal Antiferromagnetic Spin Lattices

“…Our theoretical investigation of the longitudinal modes in quantum antiferromagnets is based on a microscopic theory for a generic spin-s Hamiltonian system [23]. We identify the longitudinal excitation states in a quantum antiferromagnet with a Néel-like order as the collective modes of the magnondensity waves, which represent the fluctuations in the magnitude of the long-range order and are supported by the interactions between magnons.…”