1. Possible realization of SU(2)_2 WZNW Quantum Critical Point in CaCu2O3
M. Tsvelik
Brookhaven National Laboratory
Experiment: Bella Lake, HMI Berlin.

2. Spin S=1/2 Heisenberg Ladders
Two S=1/2 antiferromagnetic Heisenberg chains coupled by exchange and
4-spin cyclic interactions.
Each individual chain is Quantum Critical: SU_1(2) WZNW theory. Excitations
(spinons) carry fractional quantum numbers (S=1/2).
The interactions are relevant, generate spectral gaps and lead to confinement
of spinons.

3. The Hamiltonian
We are interested in the continuum limit

5. Refermionization Shelton, Nersesyan, Tsvelik (1996).
The spectrum: triplet and singlet Majorana modes. In general they are massive,
but by fine tuning one can drive one of the masses to zero.

6. Four Ising models.
Staggered magnetizations are expressed in terms of order and disorder
parameters of four Quantum Ising models:

7. The ladders
are weekly
coupled.
3D Neel order
occurs at 25K.
J_leg = 162meV.

8. CaCu2O3. High energies: individual chains
The simulation uses the excitation spectrum generated by J.S.Caux,
and shows what would be observed in a MAPS experiment
using this model to be compared directly with the data.
The simulation includes the energy resolution from chop,
the anisotropic form factor of Cu2+.
The lattice effects become visible above 200 meV.

9. CaCu2O3: Evidence for inter-chain coupling

10. Gap in the bonding, no gap in the antibonding mode.
The singlet
gap is estimated
to be 16 +_ 2 meV.
The triplet gap
Is smaller than
2 meV.

11. Theoretical form of dynamical susceptibilities

12. Magnetic part of the specific heat will fix the central charge:
Things to measure
Magnetic part of the specific heat will fix the central charge:
Knight shift:

13. Conclusions Neutron scattering measurements on CaCu2O3
suggest that this material is close to SU_2(2) QCP.
Future measurements of NMR and magnetic specific heat will allow to bring more certainty to this matter.
By applying pressure one may drive the system out of QCP into spontaneously dimerized phase.