Incollection,
Gauge Dependent Local Order Parameters of Quantum Disordered States : Characterization by Berry Connections
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Based on the symmetry breaking,
a characterization of phases by local order parameters
forms one of the basic notions in physics.
However it has now
become clear that some of interesting classes of phases
are not well described by the scheme.
Various kinds of quantum Hall states,
correlated electron systems with spin gap
and
quantum spin liquids such as frustrated spins and quantum dimer phases
can be in the classses.
These are quantum disordered states where strong quantum fluctuations
and their low dimensionality prevent from formation of local orders.
Although there are no classical
local order parameters to characterize these
quantum disordered phases, it is possible to define quantum
local order parameters which are relevant for the states1,2.
Classical order parameters
are
invariant for the
phase change
of the quantum state (generically unitary invariant) since any
observable which has its classical correspondent
is given by an expectation value of some hermite operator (trace over the states).
Since the phase change or the unitary transformation generically induces
gauge transformation in the corresponding Berry connection,
the classical observables are necessarily gauge invariants.
However there are other classes of
purely quantum objects which depend on
the gauge of the Berry connection3.
Berry phases are typical quantities which belong to these quantum classes.
This Berry phases
are gauge dependent but uniquely defined in modulo $2\pi$1-3.
Using the berry connections, quantum order parameters are
defined for some of the quantum disordered phases
and successfully characterize the states locally1,2,4.
When the system respects an
anti-unitary symmetry such as the time-reversal,
the Berry phases
as
the local order parameters are necessarily quantized as $0$ or $\pi$.
It is quite useful for the local identification of the phase.
Results for the
quantum dimer spins in one- and two-dimensions1,2
and the
translational invariant $t-J$ model
for the correlated electons systems4
are demonstrated.
In principle, these quantum order parameters
can be even measured by quantum interference experiments.
1) ``Quantized Berry Phases as Local Order Parameters of Quantum Liquids'',
Y. Hatsugai,J.\ Phys. \ Soc.\ Jpn.\ (Lett.) \ 75, 123601 (2006).\\
2) ``Quantized Berry phases for a local characterization of spin
liquids in frustrated spin systems'',
Y. Hatsugai,
J. Phys. Condens. Matter 19, 145209 (2007).\\
3) Y. Hatsugai, J.\ Phys. \ Soc.\ Jpn.\ 73,
2604-2607 (2004), \ 74, 1374-1377 (2005).\\
4) I. Maruyama and Y. Hatsugai, to be published.
