Scaling hypotheses for non-fermi liquid quantum criticality

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Scaling hypotheses for non-fermi liquid quantum
criticality

• T. Senthil (MIT)
• TS, forthcoming
• Precursor TS, Annals of Physics, 06

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Killing a Fermi surface
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Non-fermi liquid metals
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Quantum criticality a route to non-Fermi liquid
metals
T
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Best studied examples heavy electron metals

• CePd2Si2, CeCu6-xAux, YbRh2Si2,

(Quantum) critical point with striking non-fermi
liquid physics
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Best studied examples heavy electron metals

• CePd2Si2, CeCu6-xAux, YbRh2Si2,

(Quantum) critical point with striking non-fermi
liquid physics
Partially filled f-orbitals form localized
magnetic moments.
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Best studied examples heavy electron metals

• CePd2Si2, CeCu6-xAux, YbRh2Si2,

(Quantum) critical point with striking non-fermi
liquid physics
Partially filled f-orbitals form localized
magnetic moments. Model as lattice of localized
magnetic moments coupled to conduction electrons
by spin exchange (the Kondo lattice)
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Magnetic quantum critical points in heavy fermion
liquids
CeCu6-xAux
CePd2Si2
AF metal
AF metal
Fermi liquid
N. Mathur et al, Nature 1998
Fermi liquid
H. v. Löhneysen et al, PRL 1994
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Representative data in YbRh2Si2
Trovarelli et al, PRL 2000
T-dependence of resistivity at critical point
?(T) T for three decades in temperature!
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Scaling of dynamic spin correlationsInelastic
neutron scattering near ordering wavevector
A. Schröder et al., Nature 00 PRL 98
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Quantum criticality a route to non-Fermi liquid
metals
T
Non Fermi Liquid Universal physics associated
with quantum critical point between phases A and
B.
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• However Landauesque theory of fluctuations of
  magnetic order parameter in metallic environment
  spectacularly inconsistent with non-fermi liquid
  physics near magnetic quantum critical points.
• Moriya, Hertz, Millis,.. 1973-present

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Non fermi liquid due to fluctuations different
from natural order parameter?
MetalLocal moments part of Fermi sea
Local moments not Involved in Fermi sea?
Does quantum phase transition involve loss of
local moments from Fermi sea? (Coleman et al, Si
et al 02) Non-fermi liquid physics due to
associated fluctuations? Concrete model
Senthil, Vojta, Sachdev, 04
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Fermi surface and quantum phase transitions
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Evidence from experiments I Hall effect in
YbRh2Si2
S. Paschen et al., Nature 432, 881 (2004)
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Evidence from experiments II dHvA in
CeRhIn5CeRhIn5
H. Shishido, R. Settai, H. Harima, Y. Onuki,
JPSJ 74, 1103 (2005)
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Simpler example Mott transition of one band
systems
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Possible experimental realization of a second
order Mott transition
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Killing a Fermi surface
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How might a Fermi surface disappear?
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Electronic structure at criticality Critical
Fermi surface
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Critical fermi surface another rationale
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Evolution of minimu gap surface
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Some obvious consequences/questions
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Review scaling at bosonic quantum critical points
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Review scaling at bosonic quantum critical points
T
g
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Review scaling at bosonic quantum critical points
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Review scaling at bosonic quantum critical points
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Review scaling at bosonic quantum critical points
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Generalization to critical fermions
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Critical Fermi surface scaling for single
particle physics
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New possibility angle dependent exponents
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Critical Fermi surface scaling for single
particle physics
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Critical Fermi surface scaling for single
particle physics
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Leaving the critical point
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Example Mott transition
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Implications of angle dependent exponents
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Finite T crossovers
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Thermodynamics
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Thermodynamics
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Transport ?
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Model calculation with a critical Fermi surface
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Model calculation with a critical Fermi surface
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Model calculation with a critical Fermi surface
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Summary

• At some metallic quantum critical points there
• will be an entire surface of critical fermionic
  modes
• a critical Fermi surface.
• Presence of critical fermi surface will change
  the scaling phenomena associated with universal
  critical singularities.
• Specific scaling ansatz for single particle and
  thermodynamic quantities.
• Possibility of angle dependent exponents with
  interesting consequences (eg metals with
  T-dependent Fermi arcs at intermediate
  temperature)

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Future

• Scaling for transport?
• Verify in concrete theoretical models/experiments
• Theoretical framework to describe critical Fermi
  surfaces?