Spin-gapped magnets with weak anisotropies I: Constraints on the phase of the condensate wave function

Abstract

We study the thermodynamic properties of dimerized spin-gapped quantum magnets with and without exchange anisotropy (EA) and Dzyaloshinsky-Moriya (DM) anisotropies within the mean-field approximation. For this, we obtain the thermodynamic potential Ω of a triplon gas taking into account the strength of DM interaction up to second order. The minimization of Ω with respect to self-energies yields the equation for X 1,2 = Σ n ± Σ an − µ, which define the dispersion of quasiparticleswhere k is the bare dispersion of triplons. The minimization of Ω with respect to magnitude ρ 0 and phase Θ of triplon condensate leads to the coupled equations. We discuss also the restrictions on ρ 0 and Θ imposed by these equations for systems. The requirement of dynamical stability conditions in equilibrium, as well as the Hugenholtz-Pines theorem, particularly for isotropic Bose condensate, impose certain conditions to the physical solutions of these equations. It is shown that the phase angle of a purely homogenous Bose-Einstein condensate (BEC) without any anisotropy may only take values Θ = πn (n=0,±1, ±2..) while that of BEC with even a tiny DM interaction results in Θ = π/2 + 2πn. In contrast to Hartree-Fock-Popov approximation, which allows arbitrary phase angle, our approach predicts that the phase angle may have only discrete values. The consequences of this phase-locking for interference of two Bose condensates and to their possible Josephson junction is studied. In such quantum magnets, the emergence of a triplon condensate leads to a finite staggered magnetization M ⊥ , whose direction in the xy-plane is related to the condensate phase Θ.The possible Kibble-Zurek mechanism in dimerized magnets and its influence on M ⊥ also discussed.

Effects of exchange and weak Dzyaloshinsky-Moriya anisotropies on thermodynamic characteristics of spin-gapped magnets

“…Firstly we show that even a tiny DM interaction changes the sign of anomalous density σ, which is negative for pure BEC, as it was proven in [22]. In fact, subtracting from Eq.…”

“…In our previous work [22], requiring positiveness of self-energies, X 1 and X 2 , we have found a boundary condition for the intensity of EA interaction as γ ≤ U |σ|. Now the question arises "Can a similar condition be found for the intensity of DM interaction γ ?…”

“…In our previous work [22] we have shown that the presence of H EA and D DM terms in the bosonic Hamiltonian with contact interaction may seriously modify the phase and the condensate fraction of BEC. Now we discuss their influence on some physical quantities .…”

“…Before studying the dependence of physical observables on the intensity of EA and DM interactions, by taking into account the locking of a condensate phase, we discuss the properties of equations for the self energies X 1,2 and the condensate fraction ρ 0 derived in our previous work [22] as follows:…”

“…In our previous work [22] we derived an explicit expression of Ω for homogenous system of bosons, described by the Hamiltonian (1.2). Minimization of thermodynamic potential with respect to the phase ξ and condensate fraction, ρ 0 , together with the requirement of dynamical stability of BEC led to following conclusions (see Table 1 of [22]).…”