Spin Waves - 2007, St Spin Waves - 2007, St Petersburg Petersburg Conservation laws and magnon Conservation laws and magnon decay in quantum spin liquids decay in quantum spin liquids Igor Zaliznyak Igor Zaliznyak Neutron Scattering Group, Brookhaven National Laboratory
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Conservation laws and magnon decay in quantum spin liquids
Conservation laws and magnon decay in quantum spin liquids. Igor Zaliznyak Neutron Scattering Group, Brookhaven National Laboratory. O AK R IDGE N ATIONAL L ABORATORY. / U. Virginia. Collaborators. M. B. Stone C. Broholm, D. Reich, T. Hong S.-H. Lee S. V. Petrov. - PowerPoint PPT Presentation
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Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
Conservation laws and magnon Conservation laws and magnon decay in quantum spin liquidsdecay in quantum spin liquids
Igor ZaliznyakIgor Zaliznyak
Neutron Scattering Group, Brookhaven National Laboratory
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
CollaboratorsCollaborators
• M. B. Stone
• C. Broholm, D. Reich, T. Hong
• S.-H. Lee
• S. V. Petrov
/ U. Virginia/ U. Virginia
OAK RIDGE NATIONAL LABORATORY
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
Particles in the UniverseParticles in the Universe
MeVMeV GeVGeV
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
Quasiparticles in condensed matterQuasiparticles in condensed matter
neutron out
neutron outkkff
meV, meV, μμeVeV
Quasiparticle:Quasiparticle:
phonon, magnonphonon, magnon
q = kq = kii - k - kff
neutron in
neutron in
kk ii
1 meV = 11.6 K1 meV = 11.6 K
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
Neutron scattering: how neutrons measure Neutron scattering: how neutrons measure quasiparticles.quasiparticles.
fi
fiffiii
zif
zf
i
f
m
k
m
kηEηEηSηS
k
k
dEdΩ
Ed
,
,b,,
22
2222 q
q
fi kkq m
k
m
kηEηEE fi
iiff 22
22
, ,2
22
20
,
dt
tMMeeq
qqr
k
k
dEdΩ
Ed
jjjj
iEti
mi
fmag jj RRqq
magnetic scattering length, rm = -5.39*10-13 cm
jj
tiiEti
jji
fnuc dteeebb
k
k
dEdΩ
Edjj
,
*,
20
2RqRqq
nuclear scattering length, b ~ 10-13 cm qqq
ESdEdΩ
Ed~
,2
Long-lived quasiparticle (magnon)
delta-function singularity in cross-section
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
What is quantum liquid?What is quantum liquid?
• What is liquid?− no shear modulus− no elastic scattering = no static correlation of density fluctuations
‹ρ(r1,0)ρ (r2,t)› → 0t → ∞
• What is quantum liquid? − all of the above at T → 0 (i.e. at temperatures much lower than inter-particle interactions in the system)
• Elemental quantum liquids:− H, He and their isotopes− made of light atoms strong quantum fluctuations
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
ε(q
) (K
elvi
n)
q (Å-1)
phonon
roton
maxonwhatsgoingon?
Excitations in quantum Bose liquid: Excitations in quantum Bose liquid: superfluid superfluid 44HeHe
Woods & Cowley, Rep. Prog. Phys. 36 (1973)
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
The “cutoff point” of the quasiparticle The “cutoff point” of the quasiparticle spectrum in the quantum Bose-liquidspectrum in the quantum Bose-liquid
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
Breakdown of the excitations in Breakdown of the excitations in 44He: He: experimentexperiment
H = qε (q) aq+
aq + q,q′ Vq,q′(aqa+q′a+
q-q′ + H.c.) + …
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
Roton decays and conservation lawsRoton decays and conservation laws
• Breakdown of roton quasiparticle spectrum at E > 2 due to pair decays satisfies:
– Particle non-conservation: cubic terms in the boson Hamiltonian
=> Vq,q′(aqa+q′a+
q-q′ + H.c.)
– Energy-momentum conservation
qq’
q”
q = q’ + q”
(q) = (q’) + (q”)
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg
Quantum spin liquid: what is it?Quantum spin liquid: what is it?
• Quantum liquid state for a system of Heisenberg spins
H = J|| SiSi+||+ JSiSi
• Exchange couplings J||, J through orbital overlaps may be different
− J||/J >> 1 (<<1) parameterize quasi-1D (quasi-2D) case
Coupled chains
J||/J>> 1Coupled planes
J||/J<<1• no static spin correlations
‹Siα (0)Sj
β (t)› → 0, i.e. ‹Si
α (0)Sjβ (t)› = 0
• hence, no elastic scattering (e.g. no magnetic Bragg peaks)
t → ∞
Spin Waves - 2007, St PetersburgSpin Waves - 2007, St Petersburg