Quasiparticle breakdown in quantum spin liquid

1
Quasiparticle breakdown in quantum spin liquid
Igor Zaliznyak Neutron Scattering Group,
Brookhaven National Laboratory

• Collaborators
• M. B. Stone
• D. Reich, T. Hong
• C. Broholm

2
What is quantum liquid?

• 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

3
Excitations in quantum Bose liquid superfluid 4He
maxon
roton
phonon
Woods Cowley, Rep. Prog. Phys. 36 (1973)
4
The cutoff point of the quasiparticle spectrum
in the quantum Bose-liquid
5
Spectrum termination in 4He experiment
6
What is quantum spin liquid?

• Quantum liquid state for a system of Heisenberg
  spins
• H JS SiSi? J?S SiSiD?

• Exchange couplings J, J? through orbital
  overlaps may be different
• J/J? gtgt 1 (ltlt1) parameterize quasi-1D
  (quasi-2D) case

7
Simple example coupled S1/2 dimers
Single dimer antiferromagnetically coupled S1/2
pair
H J0 (S1S2) J0/2 (S1 S2)2 const.
8
Simple example coupled S1/2 dimers
Chain of weakly coupled dimers
H J0 S(S2iS2i1) J1S (S2i S2i2)
Dispersion e(q) J0 J1cos(q)
triplet
?
9
Dimers in 1D (aka alternating chain)
Chains of weakly interacting dimers
in Cu(NO3)2x2.5D2O
Cu2 ? 3d9 S1/2
E (meV)
10
Weakly interacting dimers in Cu(NO3)2x2.5D2O
D. A. Tennant, C. Broholm, et. al. PRB 67, 054414
(2003)
Spin excitations never cross into 2-particle
continuum and live happily ever after
11
2D quantum spin liquid a lattice of frustrated
dimers
M. B. Stone, I. Zaliznyak, et. al. PRB
(2001) (C4H12N2)Cu2Cl6 (PHCC)
Cu2 ? 3d9 S1/2

• singlet disordered ground state
• gapped triplet spin excitation

12
PHCC a two-dimensional quantum spin liquid

• gap D 1 meV
• bandwidth 1.8 meV

13
Quasiparticle spectrum termination line in PHCC
maxE2-particle (q)
minE2-particle (q)
Spectrum termination line
E1-particle(q)
14
PHCC dispersion along the diagonal
Q (0.5,0,-1.5)
resolution-corrected fit
Intensity (counts in 1 min)
Q (0.25,0,-1.25)
resolution-corrected fit
Q (0.15,0,-1.15)
resolution-corrected fit
E (meV)
E (meV)
15
2D map of the spectrum along both directions
16
Compare spectrum end point in helium-4
17
Summary and conclusions

• Quasiparticle breakdown at E gt 2? is a generic
  property of quantum Bose (spin) fluids
• observed in the superfluid 4He
• observed in the Haldane spin chains in CsNiCl3
  (I. Zaliznyak, S.-H. Lee and S. V. Petrov, PRL
  017202 (2001))
• observed in the 2D frustrated quantum spin liquid
  in PHCC
• A real physical alternative to the ad-hoc
  excitation fractionalization explanation of
  scattering continua
• Implications for the high-Tc cuprates spin gap
  implies disappearance of coherent spin modes at
  high E

18
Temperature dependence in PHCC
19
Temperature dependence in copper nitrate
20
Dispersion along the side (l) in PHCC
Intensity (counts in 1 min)
E (meV)
21
What would be a spin solid?

• Heisenberg antiferromagnet with classical spins,
  S gtgt 1

22
1D quantum spin liquid Haldane spin chain

• Heisenberg antiferromagnetic chain with S 1

23
Spin-quasiparticles in Haldane chains in CsNiCl3
24
Spin-quasiparticles in Haldane chains in CsNiCl3
25
Spectrum termination point in CsNiCl3
I. A. Zaliznyak, S.-H. Lee, S. V. Petrov, PRL
017202 (2001)