T. Senthil (MIT)

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Quantum phases and critical points
of correlated metals
T. Senthil (MIT) Subir Sachdev Matthias Vojta
(Karlsruhe)
cond-mat/0209144 cond-mat/0305193
Transparencies online at http//pantheon.yale.edu/
subir
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• Outline
• Kondo lattice models Doniachs phase diagram
  and its quantum critical point
• Paramagnetic states of quantum antiferromagnets
  (A) Confinement of spinons and bond order (B)
  Spin liquids with deconfined spinons Z2 and U(1)
  gauge theories
• A new phase a fractionalized Fermi liquid (FL )
  
• Extended phase diagram and its critical points
• Conclusions

I. Kondo lattice models
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I. Doniachs T0 phase diagram for the Kondo
lattice
Heavy Fermi liquid with moments Kondo screened
by conduction electrons. Fermi
surface obeys Luttingers theorem.
Local moments choose some static spin arrangement
SDW
FL
JK / t
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Luttingers theorem on a d-dimensional lattice
for the FL phase
Let v0 be the volume of the unit cell of the
ground state, nT be the total number
density of electrons per volume v0.
(need
not be an integer)
A large Fermi surface
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Arguments for the Fermi surface volume of the FL
phase
Fermi liquid of S1/2 holes with hard-core
repulsion
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Arguments for the Fermi surface volume of the FL
phase
Alternatively
Formulate Kondo lattice as the large U limit of
the Anderson model
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• Outline
• Kondo lattice models Doniachs phase diagram
  and its quantum critical point
• Paramagnetic states of quantum antiferromagnets
  (A) Confinement of spinons and bond order (B)
  Spin liquids with deconfined spinons Z2 and U(1)
  gauge theories
• A new phase a fractionalized Fermi liquid (FL )
  
• Extended phase diagram and its critical points
• Conclusions

II. Paramagnetic states of quantum
antiferromagnets
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Ground states of quantum antiferromagnets
Begin with magnetically ordered states, and
consider quantum transitions which restore spin
rotation invariance
Two classes of ordered states
(b) Non-collinear spins
(a) Collinear spins
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(a) Collinear spins, Berry phases, and bond-order
S1/2 antiferromagnet on a bipartitie lattice
Include Berry phases after discretizing coherent
state path integral on a cubic lattice in
spacetime
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These principles strongly constrain the effective
action for Aam
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Simplest large g effective action for the Aam
This theory can be reliably analyzed by a duality
mapping.
(I) d2 The gauge theory is always in a
confining phase. There is an energy gap and the
ground state has bond order (induced by the Berry
phases). (II) d3 An additional topologically
ordered Coulomb phase is also possible. There
are deconfined spinons which are minimally
coupled to a gapless U(1) photon.
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989). S. Sachdev and R. Jalabert, Mod. Phys.
Lett. B 4, 1043 (1990). K. Park and S. Sachdev,
Phys. Rev. B 65, 220405 (2002).
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Paramagnetic states with
Bond order and confined spinons
S1/2 spinons are confined by a linear potential
into a S1 spin exciton
Confinement is required U(1) paramagnets in d2
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b. Noncollinear spins
Magnetic order
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• Outline
• Kondo lattice models Doniachs phase diagram
  and its quantum critical point
• Paramagnetic states of quantum antiferromagnets
  (A) Confinement of spinons and bond order (B)
  Spin liquids with deconfined spinons Z2 and U(1)
  gauge theories
• A new phase a fractionalized Fermi liquid (FL )
  
• Extended phase diagram and its critical points
• Conclusions

III. A new phase a fractionalized Fermi
liquid (FL)
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III. Doping spin liquids
Reconsider Doniach phase diagram
It is more convenient to analyze the
Kondo-Heiseberg model
Work in the regime JH gt JK
Determine the ground state of the quantum
antiferromagnet defined by JH, and then couple to
conduction electrons by JK Choose JH so that
ground state of antiferromagnet is a Z2
or U(1) spin liquid
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State of conduction electrons
At JK 0 the conduction electrons form a Fermi
surface on their own with volume determined by nc
Perturbation theory in JK is regular, and
topological order is robust, and so this state
will be stable for finite JK
So volume of Fermi surface is determined by (nT
-1) nc(mod 2), and Luttingers theorem is
violated.
The (U(1) or Z2) FL state
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III. A new phase FL
This phase preserves spin rotation invariance,
and has a Fermi surface of sharp electron-like
quasiparticles. The state has
topological order and associated neutral
excitations. The topological order can be easily
detected by the violation of Luttingers theorem.
It can only appear in dimensions d gt 1
Precursors N. Andrei and P. Coleman, Phys. Rev.
Lett. 62, 595 (1989). Yu.
Kagan, K. A. Kikoin, and N. V. Prokof'ev, Physica
B 182, 201 (1992). Q. Si, S.
Rabello, K. Ingersent, and L. Smith, Nature 413,
804 (2001). S. Burdin, D. R. Grempel, and A.
Georges, Phys. Rev. B 66, 045111 (2002).
L. Balents and M. P. A. Fisher and C.
Nayak, Phys. Rev. B 60, 1654, (1999) T.
Senthil and M.P.A. Fisher, Phys. Rev. B 62, 7850
(2000). F. H. L. Essler and
A. M. Tsvelik, Phys. Rev. B 65, 115117 (2002).
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• Outline
• Kondo lattice models Doniachs phase diagram
  and its quantum critical point
• Paramagnetic states of quantum antiferromagnets
  (A) Confinement of spinons and bond order (B)
  Spin liquids with deconfined spinons Z2 and U(1)
  gauge theories
• A new phase a fractionalized Fermi liquid (FL )
  
• Extended phase diagram and its critical points
• Conclusions

IV. Extended phase diagram and its critical
points
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Phase diagram (U(1), d3)
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Phase diagram (U(1), d3)
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Z2 fractionalization
Mean-field phase diagram
FL
FL
Pairing of spinons in small Fermi surface state
induces superconductivity at the confinement
transition
Small Fermi surface state can also exhibit a
second-order metamagnetic transition in an
applied magnetic field, associated with vanishing
of a spinon gap.
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Conclusions

• New phase diagram as a paradigm for clean metals
  with local moments.
• Topologically ordered () phases lead to novel
  quantum criticality.
• New FL allows easy detection of topological
  order by Fermi surface volume