ucsd

Slide1: 

Antoine Georges Olivier Parcollet Nick Read Subir Sachdev Jinwu Ye Mean field theories of quantum spin glasses Talk online: Sachdev

Slide2: 

Classical Sherrington-Kirkpatrick model Jij : a Gaussian random variable with zero mean

Slide3: 

Two routes to quantization A. Quantum rotor model n=1: Ising model is a transverse field g Spectrum at Jij=0 g n=3: randomly coupled spin dimers Spectrum at Jij=0 g

Slide4: 

Two routes to quantization B. Heisenberg spins Spectrum at Jij=0 (2S+1)-fold degeneracy Generalize model to SU(N) spins and explore phase diagram in N, S plane

Slide5: 

Outline Insulating quantum rotors. Insulating Heisenberg spins DMFT of a random t-J model Metallic spin glasses: DMFT of a random Kondo lattice

Slide6: 

A. Insulating quantum rotors

Slide7: 

A. Quantum rotor model Jij : a Gaussian random variable with zero mean

Slide8: 

g Spin glass Paramagnet T=0 phases Local dynamic spin susceptibility Specific heat C ~ T (?) D.A. Huse and J. Miller, Phys. Rev. Lett. 70, 3147 (1993). J. Ye, S. Sachdev, and N. Read, Phys. Rev. Lett. 70, 4011 (1993). N. Read, S. Sachdev, and J. Ye, Phys. Rev. B 52, 384 (1995). A. Georges, O. Parcollet, and S. Sachdev, Phys. Rev. B 63, 134406 (2001).

Slide9: 

T > 0 phase diagram g J. Ye, S. Sachdev, and N. Read, Phys. Rev. Lett. 70, 4011 (1993). N. Read, S. Sachdev, and J. Ye, Phys. Rev. B 52, 384 (1995). gc

Slide10: 

B. Insulating Heisenberg spins

Slide11: 

B. Heisenberg spin glass Jij : a Gaussian random variable with zero mean S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993).

Slide12: 

T=0 phase diagram S N Spin glass order Specific heat C ~ T (C ~ T2 ?) S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993). A. Georges, O. Parcollet, and S. Sachdev, Phys. Rev. Lett. 85, 840 (2000). A. Camjayi and M. J. Rozenberg, Phys. Rev. Lett. 90, 217202 (2003).

Slide13: 

Quantum critical phase is described by fractionalized S=1/2 neutral spinon excitations w Spinon spectral density S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993).

Slide14: 

S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339 (1993). A. Georges, O. Parcollet, and S. Sachdev, Phys. Rev. Lett. 85, 840 (2000). A. Camjayi and M. J. Rozenberg, Phys. Rev. Lett. 90, 217202 (2003). T > 0 phase diagram

Slide15: 

C. Doping the quantum critical spin liquid

Slide16: 

C. DMFT of a random t-J model Jij : a Gaussian random variable with zero mean O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999).

Slide17: 

O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999). = carrier density

Slide18: 

O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999). Physical consequences of quantum criticality 1. Electron spectral function (photoemission) Momentum resolved spectral density

Slide19: 

O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999). Physical consequences of quantum criticality 2. d.c Resistivity

Slide20: 

O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999). Physical consequences of quantum criticality 3. NMR 1/T1 relaxation rate

Slide21: 

O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999). Physical consequences of quantum criticality 4. Optical conductivity

Slide22: 

O. Parcollet and A. Georges, Phys. Rev. B 59, 5341 (1999). Phenomenological phase diagram for cuprates

Slide23: 

D. Metallic spin glasses

Slide24: 

C. DMFT of a random Kondo lattice model Jij : a Gaussian random variable with zero mean S. Sachdev, N. Read, and R. Oppermann, Phys. Rev. B 52, 10286 (1995). A. M. Sengupta and A. Georges, Phys. Rev. B 52, 10295 (1995).  

Slide25: 

S. Sachdev, N. Read, and R. Oppermann, Phys. Rev. B 52, 10286 (1995). A. M. Sengupta and A. Georges, Phys. Rev. B 52, 10295 (1995).   JK

Slide26: 

Outlook Spin glass order is an attractive candidate for a quantum critical point in the cuprates, on both theoretical and experimental grounds. (Impurities break the translational symmetry associated with charge-ordered states, and the Imry-Ma argument then prohibits a quantum critical point associated with charge order in the presence of randomness in two dimensions) A simple mean-field theory of a doped Heisenberg spin glass naturally reproduces all the “marginal” phenomenology. Needed: better theory of fluctuations in low dimensions