1. Are there gels in quantum systems? Jörg Schmalian, Iowa State University and DOE Ames Laboratory Peter G. Wolynes University of California at San Diego Harry Westfahl Jr. LNLS Campinas, Brazil Misha Turlakov Cavendish Laboratory, Cambridge Univ. UK

2. reversible association of aggregates in copolymers Classical gels chemical gelsphysical gels irreversible covalent cross-linking (vulcanization) random solid weak crystals and glassy states

3. Complex aggregates form glassy states Frustrated phase separation in microemusions and copolymers Wu, Westfahl, Schmalian, Wolynes, Chem. Phys. Lett. (2002)) Most systems crystallize easily (under shear), there are glass forming systems S.-H. Chen et al. Science (2003)

4. phase A phase B: Phase separation A simple model new length scale coulomb interaction surfactant mediated interaction Real space

5. glassiness and entropy crisis trapped in a metastable state complex energy landscape In equilibrium: scan the entire landscape stripe liquid Loss of entropy exponentially many metastable states: breakdown of thermodynamics ( becomes extensive)

6. deep in the glass state Memory effects typical liquid configuration

7. Our initial motivation: charge order in transition metal oxides Quantum gels (1): cuprates  NMR: extremely slow relaxation  glassiness  Glassiness: intrinsic, tied to unconventional properties of cuprates Panagopoulos et al. (2001)) Is there a universal origin for glassiness?

8. Inhomogeneous spectral features ( J. C. Davis et al. Science (2001)) 01025d02 avg delta 01025d02 neg val 30 mV 65 mV 1.5 nS 0.7 nS  A(  ) 0 Å 140 Å 91126153 from typical linecut on Ni BSCCO 22 A(-  A(+  High-temperature superconductors

9. Self generated stripe glass Using: Yamada et al. PRB (1998) SC AF Stripe glass Stripe liquid J.S. and P. Wolynes Phys. Rev. Lett. 85, 836 (2000); H. Westfahl Jr., J. S., and P. G. Wolynes, Phys. Rev. B 64, 174203 (2001); ibid. Intl. J. Mod. Phys. B 15, 3292 (2001), ibid Phys, Rev. B 68, 134203 (2003) region 10 (20) times l m contains 6 (10 6 ) states

10. (J. S. and M. Turlakov, Phys. Rev. Lett. (2004)) MnSi: no-inversion symmetry (Ch. Pfleiderer et al. Nature 2001) 1 st -order transition 2 nd -order transition helical magnet true non Fermi liquid behavior Quantum gels (2): MnSi, magnetic rotons

11. neutron scattering (C. Pfleiderer et al. Nature (2004) ) magnetic rotons: (J.S. and M. Turlakov) dramatic increase in the phase space of magnetic excitations due to helix fluctuations fluctuation induced 1 st order transition non-Fermi liquid transport Amorphous ordering of helices at high pressure (“roton glass”)

12. relation to MnSi anomalous transport due to amorphous helical order ordinary second order transition speculate: anomalous Hall effect

13. Quantum melting of a stripe glass Liquid droplet formation and coexistence of liquid and glass at the quantum melting point ! quantum glass quantum liquid mixed state (at T=0) unique (pure) ground state discontinuous transition

14. Conclusions  Competing interactions in correlated electron systems can lead to non-equilibrium dynamics in quantum systems and glassy behavior not necessarily related to quenched disorder