Quantum Spin Glasses & Spin Liquids
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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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Quantum spin glasses spin liquids

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 aSPIN LIQUID

Dilute “AntiGlass”: Intrinsic Quantum Mechanics

(1) Non-Linear Dynamics

(2) Coherent Spin Oscillations

(3) Quantum Magnet in a Spin Bath

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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C. Ancona-Torres et al., unpublished.


Liho x y 1 x f 4

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


Effect of a transverse field

Effect of a Transverse Field

with [ H,sz] ≠ 0


Experimental setup

Experimental Setup

G ~ Ht2

hac, Ising axis


Liho 0 20 y 0 80 f 4 aging memory in the quantum spin glass

Paramagnet

 (K)

Glass

Net Moment

T (mK)

LiHo0.20Y0.80F4Aging & Memory in the Quantum Spin Glass


Aging in ac

Temperature

Time

Temperature

Aging in ac

  • Cool at constant rate

  • decreases at fixed temperature

  • Aging reinitialized when cooling resumes


Thermal vs quantum aging

’ (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


Quantum spin glasses spin liquids

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)


Greater erasure with greater excursions

’ (emu/cm3.)

Time (s)

Time (s)

Greater Erasure with Greater Excursions

Grandfather states


The spin liquid

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 ?


Liho 0 045 y 0 955 f 4 addressing bits in the spin liquid

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


Signatures of spin liquid

Signatures of spin liquid

dc susceptibility

T-1

  • no peak in 

  •  no LRO

  • sub-Curie T dependence

  •  correlations

T-0.76


Quantum fluctuations

H

H

Ising axis

E

++ a+

E



E

–

H= 0

H≠ 0

–

-E



-E

+ + b+

-E

Quantum fluctuations


Quantum spin liquid

Quantum spin liquid

Ht = 0

Ht≠ 0


Quantum spin glasses spin liquids

Dynamic magnetic susceptibility

ac narrows with decreasing T

 “Antiglass”


Scaled susceptibility

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


Hole burning

pump

probe

Hole Burning

* 1017 cm-3 spins missing

~ 1% available

* Excitations

labeled by f


Simultaneous encoding

Simultaneous Encoding

9 Hz hole

3 Hz hole

Square pump at 3 Hz


Quantum spin glasses spin liquids

Coherent Oscillations

5Hz

Q ~ 50


Brillouin fit

Brillouin Fit

Magnetization

Spins per

Cluster

Phase

ac Excitation


Quantum spin glasses spin liquids

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


Encryption in ggg

…in the liquid

but not in the glass

Encryption in GGG…


Quantum spin glasses spin liquids

Decoherence from the (nuclear) Spin Bath


Conclusions

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


Quantum spin glasses spin liquids

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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