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Quantum Spin Glasses & Spin Liquids

Quantum Spin Glasses & Spin Liquids.  QUANTUM RELAXATION Ising Magnet in a Transverse Magnetic Field (1) Aging in the Spin Glass (2) Erasing Memories  HOLE-BURNING in a SPIN LIQUID Dilute “AntiGlass”: Intrinsic Quantum Mechanics (1) Non-Linear Dynamics

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Quantum Spin Glasses & Spin Liquids

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  1. Quantum Spin Glasses & Spin Liquids

  2. QUANTUM RELAXATION Ising Magnet in a Transverse Magnetic Field (1) Aging in the Spin Glass (2) Erasing Memories  HOLE-BURNING in aSPIN LIQUID Dilute “AntiGlass”: Intrinsic Quantum Mechanics (1) Non-Linear Dynamics (2) Coherent Spin Oscillations (3) Quantum Magnet in a Spin Bath -------------------------------------------------------- S. Ghosh et al., Science 296, 2195 (2002) and Nature 425, 48 (2003). H. Ronnow et al., Science 308, 389 (2005). C. Ancona-Torres et al., unpublished.

  3. 10.75 Å 5.175 Å LiHoxY1-xF4 • Ho3+ magnetic, Y3+ inert • Ising (g// = 14) • Dipolar coupled (long ranged) • x = 1Ferromagnet TC = 1.53 K • x ~ 0.5Glassy FM TC = xTC(x=1) • x ~ 0.2 Spin Glass Frozen short-range order • x ~ 0.05 Spin Liquid Short-range correlations

  4. Effect of a Transverse Field with [ H,sz] ≠ 0

  5. Experimental Setup G ~ Ht2 hac, Ising axis

  6. Paramagnet  (K) Glass Net Moment T (mK) LiHo0.20Y0.80F4Aging & Memory in the Quantum Spin Glass

  7. Temperature Time  Temperature Aging in ac • Cool at constant rate • decreases at fixed temperature • Aging reinitialized when cooling resumes

  8. ’ (emu/cm3) Aging Cooling Reference Warming Reference Temperature (K) ’ (emu/cm3) Aging Decreasing Reference Increasing Reference Ht (kOe) Thermal vs. Quantum Aging • Quantum aging • More pronounced • & crosses hysteresis • Quantum rejuvenation • Increases to meet • the reference curve

  9. t3 t2 t1 ’ (emu/cm3) 2.5kG 2kG 2.5kG Time (s) ’ (emu/cm3.) ’ (emu/cm3) Time (s) Erasing the Memory Quench system into the spin glass and age (2) Small step to a lower Ht rejuvenates (3) On warming, system should remember the original state Negative effective aging time Time (s)

  10. ’ (emu/cm3.) Time (s) Time (s) Greater Erasure with Greater Excursions Grandfather states

  11. The Spin Liquid • No long range order as T  0 • Not a spin glass – spins not frozen, fluctuations persist • Not a paramagnet– develops short-range correlations • Collectivebehavior Examples: CuHpCl, Gd3Ga5O12 (3D geometric frustration) Tb2Ti2O7, LiHo0.045Y0.955F4(quantum fluctuations) SrCu2(BO3)2, Cs2CuCl4(2D triangular lattice) • Geometric frustration • Quantum fluctuations • Reduced dimensionality What prevents freezing ?

  12. LiHo0.045Y0.955F4Addressing Bits in the Spin Liquid Use non-linear dynamics to… • Encode Information • Excite collective excitations with long coherence times (seconds): Rabi Oscillations • Separate competing ground states

  13. Signatures of spin liquid dc susceptibility T-1 • no peak in  •  no LRO • sub-Curie T dependence •  correlations T-0.76

  14. H H Ising axis E ++ a+ E  E – H= 0 H≠ 0 – -E  -E + + b+ -E Quantum fluctuations

  15. Quantum spin liquid Ht = 0 Ht≠ 0

  16. Dynamic magnetic susceptibility ac narrows with decreasing T  “Antiglass”

  17. Scaled susceptibility Relaxation spectral widths : • Debye width (1.14 decades in f) single relaxation time • if broader… multiple relaxation times e.g. glasses • if narrower… not relaxation spectrum FWHM ≤ 0.8 decades in f

  18. pump probe Hole Burning * 1017 cm-3 spins missing ~ 1% available * Excitations labeled by f

  19. Simultaneous Encoding 9 Hz hole 3 Hz hole Square pump at 3 Hz

  20. Coherent Oscillations 5Hz Q ~ 50

  21. Brillouin Fit Magnetization Spins per Cluster Phase ac Excitation

  22. Gd3Ga5O12 Phase diagram GGG : Geometrically frustrated, Heisenberg AFM exchange coupling P.Schiffer, A. Ramirez, D. A. Huse and A. J. Valentino PRL 73 1994 2500-2503

  23. …in the liquid but not in the glass Encryption in GGG…

  24. Decoherence from the (nuclear) Spin Bath

  25. Conclusions • Li(Ho,Y)F4 a model solid state system to test quantum annealing – quantum fluctuations and ground state complexity can be regulated independently • Quantum annealing allows search of different minima, speedier optimization and memory erasure in glasses • Coherent excitations in spin liquids of hundreds of spins labeled by frequency can encode information: cf. NMR computing Self-assembly common to “hard” quantum systems

  26. S. Ghosh, J. Brooke, R. Parthasarathy, C. Ancona-Torres, T. F. Rosenbaum University of Chicago G. Aeppli University College, London S. N. Coppersmith University of Wisconsin, Madison

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