1. PCE STAMP Physics & Astronomy UBC Vancouver Pacific Institute for Theoretical Physics QUANTUM GLASSES Talk given at 99 th Stat Mech meeting, Rutgers, 10 May 2008

2. This talk is NOT about “SEX and ASYMPTOTIC FREEDOM” SORRY !! Co-workers: M. Schechter (UBC Physics) I.S. Tupitsyn (PITP)

3. 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: H o =  j  j  j x +  ij V ij  i z  j 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 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 = H o (Q) + V(Q,x) + H env (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..

4. 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

5. 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?

6. 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 3 rd state by a gap 2 nd -order perturbation theory gives Dipolar interactions have nearest neighbour strength (1) LiHo x Y 1-x F 4 Q Ising (2) Fe-8 molecule

7. 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

8. 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 C V (T) ~ T (not ~T 3 ) Thermal conductivity K(T) ~ T 1.8 (not T 3 )

9. 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 0612571 M Schechter, PCE Stamp, /condmat 0801.4944 M 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’ coupling distinguishes between states which are produced by 180 o inversion (provided these are physically non-equivalent), ie., it couples directly to dipoles.

10. 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’ domains with correlation length Results for KBr:CN

11. 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?