Excitation spectrum of a 2D long-range Bose liquid with a supersymmetry
by
Jenia Mozgunov(Landau Institute for Theoretical Physics)
→
Europe/Stockholm
132:028
132:028
Description
Specic model of a 2D Bose liquid with non-relativistic
supersymmetry [1, 2] is studied numerically by means of a
mapping to a classical Langevin dynamics [3, 4]. The model
contains dimensionless coupling constant . At small 1 this
model is very similar to the 2D Bose-lqiuid with pair-wise
logarithmic interaction and thus exibit superuid ground
state. At very large 35 the ground state nearly breaks
translational symmetry: equal-time density correlations in
the emergent ground state are equivalent to those of the
classical 2D crystal at nonzero temperature. We have
studied the excitation spectrum of this model in the whole
range of by means of the analysis of the dynamic structure
factor S(k, t) computed for the equivalent classical model,
like it was done in Ref. [5] for the model of quantum dimers
at the Rokshar-Kivelson point [6]. The spectrum !(q) we
found contains a plasmon gap !0 at q = 0 and a well-dened
roton minimum at q = q0 = 2 p n with minimal excitation
energy . The ratio /!0 decreases sharply with in the whole
range of the strongly coupled Bose liquid 1 < < 35, down
to very small values 10−2. However, we could not detect,
with our numerical accurace, a vanishing of the roton gap
before 2D crystallization transition takes place at = c
37.We thus conclude that the ground-state is of superuid
nature (at T = 0) in the whole range of < c (however, the
critical temperature Tc of superuid transition drops sharply
with ). In the crystalline state > c no well-dened low-
energy excitations corresponding to shear modes was
found, in agreement with theoretically expected spectrum
!(k) / k2 that suggests strongly decaying nature of the
corresponding quasiparticles.
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