Download H. Lee

Quantum state that never condenses
Dung-Hai Lee
U.C. Berkeley
Condense = develop some kind of order
As a solid develops order, some symmetry is
broken.
Spin rotational symmetry
is broken !
Ice crystal
Superfluid
Neutron star
Expanding universe
Examples of order
Metals do break any symmetry,
but they are not stable at zero temperature. Metals
always turn into some ordered states with symmetry
breaking as T  0.
Metals are characterized by the Fermi surface
Different types of Fermi surface instability lead to
different order.
Cooper instability 
superconductivity
Fermi surface nesting
instability  spin density
wave, or charge density wave
Landau’s paradigm
• Ordered state is characterized by the symmetry
that is broken.
• All ordered states originate from the metallic state
due to Fermi surface instability.
Metal
Superconductivity
Charge density wave
Spin density wave
Is it possible for a solid not to develop
any order at zero temperature ?
Insulators with integer filling factor are good candidates
Fermion band insulator
Boson Mott insulator
Mott insulator
Boson Mott insulator
Fermion Mott insulator
Insulating due to repulsion between particles.
Examples of electron band insulator
C, Si, Ge, GaAs, …
An example of electron Mott insulator
YBa2Cu3O6 – the parent compound of high temperature
superconductor
CuO2 sheet
An example of boson Mott insulator: optical lattice of neutral
atoms
Greiner et al, Nature 02
Why are we interested in insulators ?
Doping make them very useful !
Most of the time, doping make the particle
mobile, hence can conduct.
Doped band insulator
A Silicon chip
Doped Mott insulators
Doping Mott insulators has produced many materials with
interesting properties.
Doped YBa2Cu3O6
High Tc superconductors
Doped LaMnO3
Colossal magneto-resistive
materials
Is it possible that a solid remains
insulating after doping ?
Yes
An interesting fact: all insulators with fractional
filling factor break some kind of symmetry
hence exhibit some kind of order.
fermion
Antiferromagnet
Dimmerization
boson
Why is uncondensed insulator so rare at
fractional filling ?
Oshikawa’s theorem
If the system is insulating, and if the filling factor
= p/q, the ground state is q-fold degenerate.
Usually the required degeneracy is achieved by
long range order.
Can a fractional filled insulator exist without symmetry
breaking ?
Oshikawa PRL 2000
It is generally believed that featureless
insulators will have very unusual properties.
Such as fractional-charge excitations …
Anderson’s spin liquid idea
Resonating singlet patterns
+
+...
Spin liquid is a featureless insulator (at half filling)
with no long range order ! It has S=1/2 excitations
(spinons).
It exists in the parent state of high-temperature
superconductors.
Anderson, Science 1987
Condensed matter physicists have searched
for such insulators for 20 years.
The usual search guide line is “frustration”.
?
A new idea: symmetry protected
uncondensed quantum state
Filling factor =1/3
Melts crystal order but never changes the C-M position  preserve 3fold degeneracy.
The Quantum
effect
The fractional
quantumHall
Hall
effect
Rxx = VL /I; Rxy = VH /I
One example of this type of state is the fractional
quantum Hall liquid
Lee & Leinaas, PRL 2004
Another example is the quantum dimer liquid
Moessner & Sondhi, PRL, 2001
All existing models in the literature that exhibit
uncondensed quantum state conserve the
center-of-mass position and momentum.