Quantum%20Criticality%20and%20Fractionalized%20Phases.

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Quantum Criticality and Fractionalized Phases.

• Discussion Leader G. Kotliar
• Grodon Research Conference on Correlated
  Electrons 2004

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• Steve Julian overview of phase transitions in
  heavy fermion systems.
• Z.X. Shen ARPES Investigations of Cuprate
  Superconductors.
• Senthil Deconfined Criticality.

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Heavy Fermions.

• Fermi Liquid . . Correspondence between a system
  of non interacting particles and the full
  Hamiltonian.
• High temperatures, system of moments and light
  electrons.
• Low temperature, heavy fermion liquid or
  ordered magnet .Doniach Criteria .
• In the early 80s , poster boy for Fermi Liquid
  Theory.

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Late 80s early 90s Cuprate Superconductivity
Broad region of parameters where Fermi liquid
theory does not apply .
Search for new paradigms, need a starting point
to describe this phenomena.
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Heavy Fermions. 90s.
No longer a poster boy for Fermi liquid theory.
Several examples exhibiting, magnetism,
superconductivity, and their disapearence, and
regimes where Fermi liquid theory failed to give
a proper description.Megan Aronson this
morning Steve Julians talk
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Quantum Phase Transitions Standard approach
Hertz, Moriya, Millis

• Identify order parameter (s), e.g. m, D
• Write effective Lagrangian for the order
  parameter.
• Imaginary time is like an additional dimension.
• Carry out standard R.G, make predictions which
  can be compared with experiments.
• Caveat, fermions have been integrate out,
• and these are low energy degrees of freedom.
  Ignore Berry phases.

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• In several materials,e.g. YbRh2Si2
  experimental evidence has accumulated showing
  that some AF to FL transitions ARE NOT described
  by the standard approach.
• Senthils talk, a new class of quantum critical
  point, where degrees of freedom which are not
  manifestly present in a description based on an
  order parameter play a fundamental role.

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Quantum Criticality in Cupratesfrom Tallon and
Loram
Use the existence of an hypothetical or physical
quantum critical point, as a tool to approach
the physics of the cuprates . Theoretical ideas,
S. Sachdev.
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The QCP paradigm the area of influence of a
quantum critical point
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A different Approach

• The evolution of the electronic structure away
  from the Mott insulating state, is key.
• Need to understand this problem and the
  correponding phases, before the phase
  transitions.
• Talk by Z.X. Shen . Photoemission studies of high
  Tc.
• Recent progress in understanding this problem
  using cellular DMFT. )

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RVB phase diagram of the Cuprate Superconductors

• P.W. Anderson. Baskaran Zou and Anderson.
  Connection between high Tc and Mott physics.
• ltbgt coherence order parameter.
• K, D singlet formation order paramters.

G. Kotliar and J. Liu Phys.Rev. B 38,5412 (1988)
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• High temperature superconductivity is an
  unavoidable consequence of the need to connect
  with Mott insulator that does not break any
  symmetries to a metallic state.
• Tc decreases as the quasiparticle residue goes to
  zero at half filling and as the Fermi liquid
  theory is approached.
• Early on, accounted for the most salient features
  of the phase diagram. d-wave superconductivity,
  anomalous metallic state, pseudo-gap state

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Problems with the approach.

• Numerous other competing states. Dimer phase, box
  phase , staggered flux phase , Neel order,
• Stability of the pseudogap state at finite
  temperature.
• Missing finite temperature . fluctuations of
  slave bosons ,
• Temperature dependence of the penetration depth
  Wen and Lee , Ioffe and Millis Theory
• rTx-Ta x2 , Exp rT x-T a.
• Theory has uniform Z on the Fermi surface, in
  contradiction with ARPES. see however Varma and
  Abrahams

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Evolution of the spectral function at low
frequency.
If the k dependence of the self energy is weak,
we expect to see contour lines corresponding to
Ek const and a height increasing as we approach
the Fermi surface. Study a model of kappa
organics. Frustration.
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Evolution of the k resolved Spectral Function at
zero frequency. ( O. Parcollet G. Biroli and
GKotliar PRL, 92, 226402. (2004))
U/D2
U/D2.25
Uc2.35-.05, Tc/D1/44
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Keeps all the goodies of the slave boson mean
field and make many of the results more solid
but also removes the main difficulties.

• Can treat coherent and incoherent spectra.
• Not only superconductivity, but also the
  phenomena of momentum space differentiation
  (formation of hot and cold regions on the Fermi
  surface) are unavoidable consequence of the
  approach to the Mott insulator.
• Can treat dynamical fluctuations between
  different singlet order parameters.
• Surprising role of the off diagonal self energy
  which renormalizes t.

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Lattice and cluster self energies
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Mechanism for hot spot formation nn self energy
! General phenomena.
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Mott transition in cluster (QMC)
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• General result ? YES. Application to model with
  isotropic t and t with possible relevance
  cuprates M. Capone, M. Civelli, V. Kancharla, O.
  Parcollet, and G.K. Switch to ED solver. See
  poster by M. Civelli .
• Switch of hot-cold regions in electron and hole
  doped system.

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Energy Landscape of a Correlated Material and a
finite temperature approach to correlated
materials.
Energy
T
Configurational Coordinate in the space of
Hamiltonians
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(No Transcript)
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Am under pressure. Lindbaum et.al. PRB
63,2141010(2001)
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ITU J.C. Griveaux J. Rebizant G. Lander
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Overview of rho (p, T) of Am

• Note strongly increasing resistivity as f(p) at
  all T. Shows that more electrons are entering the
  conduction band
• Superconducting at all pressure
• IVariation of rho vs. T for increasing p.

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DMFT study in the fcc structure. S. Murthy and G.
Kotliar
fcc
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LDADMFT spectra. Notice the rapid occupation of
the f7/2 band.
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One electron spectra. Experiments (Negele) and
LDADFT theory (S. Murthy and GK )
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Mott transition in open (right) and closed (left)
shell systems.
S
S
g T
Log2J1
???
Uc
S0
U
U
g 1/(Uc-U)
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• Approach the Mott transition, if the localized
  configuration has an OPEN shell the mass
  increases as the transition is approached.
• Consistent theory, entropy increases
  monotonically as U ? Uc .
• Approach the Mott transition, if the localized
  configuration has a CLOSED shell. We have an
  apparent paradox. To approach the Mott
  transitions the bands have to narrow, but the
  insulator has not entropy.. SOLUTION
  superconductivity intervenes.

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Mott transition in systems evolving towards a
closed shell.

• Resolution as the Mott transition is approached
  from the metallic side, eventually
  superconductivity intervenes to for a continuous
  transition to the localized side.
• DMFT study of a 2 band model for Buckminster
  fullerines Capone et. al. Science ( 2002).
• Mechanism is relevant to Americium.

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One dimensional Hubbard model .Compare 2 site
cluster (in exact diag with Nb8) vs exact Bethe
Anzats,V. Kancharla C. Bolech and GK PRB 67,
075110 (2003) M. CaponeM.Civelli V Kancharla
C.Castellani and GK Phys. Rev. B 69, 195105
(2004)
U/t4.
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What to do as a chair?

• Humour
• Make a connection ?
• Give a bit of orientation, for students
  postdocs, historical backround.
• Point of view of the relevance of quantum
  critical phenomena.
• Advertise a different philosophy, and approach.