In
this
presentation,
I
will
discuss
the
behavior
of
quantum
spin
chains
in
the
presence
of
a
uniform
Dzyaloshinskii-Moriya
(DM)
interaction
[1,2].
This
problem
is
analyzed
by
the
bosonization
technique.
Spin
chain
is
the
building
block
of
many
magnetic
materials,
such
as
K2CuSO4(Cl/Br)2 -
which
strongly
motivates
our
study.
DM
interaction, Dij \cdot (Si \times Sj),
originates
from
spin-orbit
coupling,
and
is
widely
present
in
real
materials.
Here Dij is
the
DM
vector
and Si is
a
spin
operator
on
site i.
Theories
of
these
systems
are
derived
and
described
for
both
individual
chain
[3]
and
weakly
coupled
chains
[4]
at
zero
and
finite
temperature,
and
in
the
presence
of
external
magnetic
field.
A
special
geometry
of
DM
interactions—staggered
between
chains,
but
uniform
within
a
given
chain—leads
to
a
peculiar
type
of
frustration
that
effectively
cancels
the
transverse
inter-chain
coupling
and
strongly
reduces
the
ordering
temperature.
By
taking
advantage
of
this
special
geometry
of
DM
interaction,
we
propose
to
construct
a
chiral
spin
liquid,
which
shares
some
basic
features
of
fractional
quantum
Hall
effect,
such
as
gapped
bulk
and
gapless
chiral
edge
states,
in
arrays
of
spin
chains.
[1]
I.
Dzyaloshinskii, J.
Phys.
Chem.
Solids 4,
241
(1958).
[2]
T.
Moriya, Phys.
Rev. 120,
91
(1960).
[3] Y.-H.
Chan,
W.
Jin,
O.
A.
Starykh,
and
H.-C.
Jiang, Phys.
Rev.
B 96,
214441
(2017).
[4]
W.
Jin
and
O.
A.
Starykh, Phys.
Rev.
B 95,
214404
(2017).