https://doi.org/10.1007/s100510050287
Quantum rotors with regular frustration and the quantum Lifshitz point
1
Saha Institute of Nuclear Physics,
1/AF Bidhannagar, Calcutta-700064, India
2
Indian Association for the Cultivation of Science,
Jadavpur, Calcutta-700032, India
Corresponding author: a adutta@hp2.saha.ernet.in
Received:
23
December
1997
Revised:
6
January
1998
Accepted:
7
January
1998
Published online: 15 May 1998
We have discussed the zero-temperature quantum phase transition in
n-component quantum rotor Hamiltonian in the presence of regular
frustration in the interaction. The phase diagram consists
of ferromagnetic, helical
and quantum paramagnetic phase, where the ferro-para and the helical-para
phase boundary meets at a multicritical point called a (d,m) quantum
Lifshitz point where (d,m) indicates that the m of the d spatial
dimensions incorporate frustration. We have studied the Hamiltonian
in the vicinity
of the quantum Lifshitz point in the spherical limit and also studied the
renormalisation group flow behaviour
using standard momentum space renormalisation
technique (for finite n). In the spherical limit ()
one finds that
the helical phase
does not exist in the presence of any nonvanishing
quantum fluctuation for m =d though
the quantum Lifshitz point exists for all d > 1+m/2,
and the upper critical dimensionality
is given by
. The scaling behaviour in the neighbourhood of
a quantum Lifshitz point in d dimensions is consistent with the
behaviour near the classical Lifshitz point in (d+z) dimensions.
The dynamical exponent of the quantum
Hamiltonian z is unity in the case of anisotropic Lifshitz point
(d>m)
whereas z=2 in the case of isotropic Lifshitz point (d=m).
We have evaluated all the
exponents using the renormalisation flow equations along-with the
scaling relations near the quantum Lifshitz point. We have also obtained
the exponents in the spherical limit (
).
It has also been shown that the exponents in the spherical model are
all related to those of the corresponding Gaussian model by
Fisher renormalisation.
PACS: 05.30.-d – Quantum statistical mechanics / 75.10.Jm – Quantized spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998