Transcript Slide 1

PCE STAMP
QUANTUM GLASSES
Talk given at 99th Stat Mech meeting, Rutgers, 10 May 2008
Physics & Astronomy
UBC
Vancouver
Pacific Institute
for
Theoretical Physics
This talk is NOT about
“SEX and ASYMPTOTIC FREEDOM”
SORRY !!
Co-workers:
M. Schechter
I.S. Tupitsyn
(UBC Physics)
(PITP)
WHAT IS A QUANTUM GLASS?
The quantum glass is usually introduced as a system where a set of frustrating
Interactions (which try to freeze the system in a glass state) competes with
x +
quantum fluctuations – for example:
V z z
Ho = Sj Dj t j
However this is not enough to properly understand the
system – it will give results which badly misrepresent
its true behaviour of a real physical system. This is
because the dynamics at low T depends essentially on
what sort of environment the glassy variables couple
to. The question of how to treat the environment must
not be treated lightly.
Quite generally we are interested in
= Ho(Q) +
H
However there are two kinds of environment:
OSCILLATOR BATH:
where
and
SPIN BATH:
where
and
Defects, TLS,
dislocations,
Nuclear & PM spins,
Charge fluctuators..
Sij
ij
ti tj
V(Q,x) + Henv(x)
A NOTE on the FORMAL NATURE of the PROBLEM
We want the density matrix
Easy for oscillator baths (it is how Feynman set up field theory). But for a spin bath it
is harder:
where
&
Considerable success has been achieved for some problems –
eg., a qubit coupled to a spin bath, or a set of dipolar interacting
qubits coupled to a spin bath.
The most important problem is to find the decoherence rates
for experiments on real systems. This has been very
successful recently. A general feature of the results is that
one can have extremely strong decoherence with almost no
dissipation – the spin bath is almost invisible in energy
relaxation, but causes massive Decoherence (largely
PRECESSIONAL DECOHERENCE)
Precessional
decoherence
QUANTUM SPIN GLASSES
A much better description is
The naïve description of a QSG is
Where the interactions are often
anisotropic dipolar
The usual ‘quantum
critical’ scenario
where we couple to a nuclear spin bath,
and to a phonon oscillator bath
What we now have
KEY QUESTIONS
(1) What controls the phase
diagram now?
(2) What drives dynamics?
Some experimental examples
NUCLEAR SPIN BATH in MAGNETIC SYSTEMS
(1) LiHoxY1-xF4
Q Ising
The single spin has
and
a 1-spin crystal-field Hamiltonian
In zero field there is a low-energy doublet, which we call
This is separated from a 3rd state
by a gap
2nd-order perturbation theory gives
Dipolar interactions have nearest neighbour strength
(2) Fe-8 molecule
LiHo SYSTEM: THEORY
M Schechter, PCE Stamp, PRL 95, 267208 (2005)
“
“ J Phys CM19, 145218 (2007)
“
“
/condmat 0801.2889
However the real Hamiltonian is quite different
A full treatment also
includes the transverse
dipolar interactions. The
thermodynamics &
Quantum phase
transition depend
essentially on the
nuclear spins. This has
been very successful in
treating the LiHo system
Fe-8 SYSTEM: THEORY
A full theory
of the dynamics
now exists
The hyperfine couplings of all 213 nuclear
spins are well known (as are spin-phonon
and dipolar couplings). Theory works
quantitatively on real systems, even in
predictions of decoherence rates.
AMORPHOUS GLASSES:
LOW-T UNIVERSAL PROPERTIES
There are some remarkable universalities in
the acoustic properties at low T (below ~ 3K)
The dissipation in,
eg., torsional
oscillator expts, is
similar in almost all
amorphous systems. Below
1-3 K, Q ~ 600. Likewise for the ratio of the
phonon mfp to the phonon thermal wavelength.
One has a
~ 1/150
‘universal ratio’
The Berret-Meissner ratio
between longitudinal and
transverse sound velocities
follows a straight line, with
slope ~ 1.58
Thermal conductivity K(T) ~ T1.8
(not T3)
Specific Ht CV(T) ~ T (not ~T3)
INTERACTIONS in DIPOLAR & AMORPHOUS GLASSES
Consider first dilute defects in a
crystal:
M Schechter, PCE Stamp, /condmat 0612571
M Schechter, PCE Stamp, /condmat 0801.4944
M Schechter, PCE Stamp, submitted to Nature
where
The strain interactions take the form
with a linear coupling
and a non-linear ‘gradient’ coupling
The key point here is that the linear coupling is to that part of
defect field which is distinguished by the phonon field (eg.,
the rotational modes at left). However the ‘gradient’ coupling
distinguishes between states which are produced by 180o
inversion (provided these are physically non-equivalent), ie., it
couples directly to dipoles.
KEY QUESTIONS
(1) Why no glass transition?
There is also an interaction d.E between
(2) What is responsible for
the electric dipole moments of the defects
the universal properties?
and the electric field
LOWEST-ORDER INTERACTIONS BETWEEN DEFECTS
If we write:
(1) ‘dipole-dipole’ Ising term
then:
where if
then
(2) ‘Monopole-dipole’ Random Field Term
where
HIGH-E HAMILTONIAN
where
and
We then get ‘Imry-Ma’ domains
with correlation length
Results for
KBr:CN
EFFECT of NON-LINEAR DEFECT-PHONON COUPLING
This generates a more complicated effective Hamiltonian:
With interaction
The interaction is much smaller:
with
However it leads to a smaller random field which now acts on linear
tunneling defects, of size:
But this leads to a density of states for these defects given by
And thence to an effective universal ratio:
Can this be the explanation of the universal low-T properties?