PCE STAMP

Physics & AstronomyUBCVancouver

Pacific Institute for Theoretical Physics

QUANTUM GLASSESTalk given at 99th Stat Mech meeting, Rutgers, 10 May 2008

This talk is NOT about

“SEX and ASYMPTOTIC FREEDOM”

SORRY !!

Co-workers: M. Schechter (UBC Physics) I.S. Tupitsyn (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 quantum fluctuations – for example: Ho = j j j

x + ij Vij izj

z

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 onwhat sort of environment the glassy variables coupleto. The question of how to treat the environment must not be treated lightly. Quite generally we are interested in = Ho(Q) + V(Q,x) + Henv(x)H

However there are two kinds of environment:OSCILLATOR BATH:

SPIN BATH:

where and

where

and

Defects, TLS, dislocations,Nuclear & PM spins,Charge fluctuators..

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 ratesfor 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

The naïve description of a QSG is

Where the interactions are often anisotropic dipolar

A much better description is

where we couple to a nuclear spin bath, and to a phonon oscillator bath

The usual ‘quantum critical’ scenario What we now have Some experimental examples

KEY QUESTIONS(1) What controls the phase

diagram now?(2) What drives dynamics?

NUCLEAR SPIN BATH in MAGNETIC SYSTEMS

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

(1) LiHoxY1-xF4 Q Ising

(2) Fe-8 molecule

LiHo SYSTEM: THEORY

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

M Schechter, PCE Stamp, PRL 95, 267208 (2005) “ “ J Phys CM19, 145218 (2007) “ “ /condmat 0801.2889

Fe-8 SYSTEM: THEORY

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.

A full theory of the dynamics now exists

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 ‘universal ratio’

The Berret-Meissner ratio between longitudinal and transverse sound velocities follows a straight line, with slope ~ 1.58

~ 1/150

Specific Ht CV(T) ~ T (not ~T3)

Thermal conductivity K(T) ~ T1.8

(not T3)

INTERACTIONS in DIPOLAR & AMORPHOUS GLASSES

Consider first dilute defects in a crystal:

where

The strain interactions take the form

with a linear coupling

and a non-linear ‘gradient’ coupling

There is also an interaction d.E between the electric dipole moments of the defects and the electric field

M Schechter, PCE Stamp, /condmat 0612571M Schechter, PCE Stamp, /condmat 0801.4944M Schechter, PCE Stamp, submitted to Nature

KEY QUESTIONS(1) Why no glass transition?(2) What is responsible for the universal properties?

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’ couplingdistinguishes between states which are produced by 180o inversion (provided these are physically non-equivalent), ie., it couples directly to dipoles.

LOWEST-ORDER INTERACTIONS BETWEEN DEFECTS

(1) ‘dipole-dipole’ Ising term If we write:

then:

where if

then

(2) ‘Monopole-dipole’ Random Field Term

where

HIGH-E HAMILTONIAN

where and

We then get ‘Imry-Ma’ domainswith 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?