didier poilblanc- the physics of doped quantum dimer models
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8/3/2019 Didier Poilblanc- The physics of doped Quantum Dimer Models
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Didier Poilblanc
Laboratoire de Physique Thorique
CNRS & Universit de Toulouse
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Emergence of quantum Dimer dynamics Mott phases of strongly correlated bosons/
fermions on frustrated lattices
charge dynamics
RVB physics in HiTc cuprates
spin dynamics
Physical properties of Quantum DimerModels Brief reminder of phase diagram at x=0
Spinon & holon doping of QDMs
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Pyrochlore lattice Checkerboard lattice
Exchange/N.N. Coulomb is FRUSTRATED
A lattice for theorists !
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Itinerant system at (near) commensurate densities:- hard-core bosons[XXZ-magnet under magnetic field]- strongly correlated fermions
U= and V >> textended-Hubbard model
Ice rule constraint:Exactly 2 or1 particles/tetraedra
Quantum Loop or Quantum Dimermodel
MIT
Pollman, Fulde et al.
DP, K. Penc & N. Shannon, PRB 75, 220503 (2007)DP, PRB 76, 115104 (2007)
F. Trousselet, DP & R. Moessner, ArXiv 2008.
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RVB fluctuatingbackground
Anderson (1987)
Spin-pairing in the Mott insulator
superconductorunder doping
Holon (Q=e, S=0)
spin-charge separation
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A typical (hard-core) dimercovering of the square lattice
Effective model
Quantum Dimer Model
Rokhsar & Kivelson, PRL 88
Dimer flip
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SU(2) Valence Bond dimer covering
Length of the loops of overlap graph
- Sutherland, 1988:
Rokhsar and Kivelson,1988:
Orthogonal basis by construction
More complicated dimer Hamiltonians with higher-order terms
- Other route: large-N Sp(2N) -- Sachdev 1992
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A wide range of applications
RVB physics
Correlated fermions on frustrated lattices (Mott)
XXZ (frustrated) magnets under magnetic field
Ultra-cold atom systems Josephson junction arrays
Spin orbital models
Quantum computing
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For J=V: sum of projectors
exact GS with energy E=0
Infinite-T
Classical DM
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Moessner & Sondhi, PRL 2001
Finite correlation lengthExponential decay
of dimer-dimer correlations
{Degeneracy from topological orderGS have different winding numbers
E
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Rich phase diagrams at zero doping:valence bond crystals and RVB phases
Moesner & Sondhi PRB (2001)Syljuasen, PRB (2006)Ralko, Poilblanc & Moesner, PRL (2008)
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Inject monomers (by pairs)& add new term to H:
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Monomer doping
Spinon doping(magnetic field)
Holon doping(chemical substitution)
Spinon are polarized
( Nagaoka effect )
Ralko, Becca & DP, PRL sept. 2008
DP, PRL 100, 157206 (2007)
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Spinon vs holon doping
monomers
holons
spinons
Chemicaldoping
AppliedMagnetic field
definitionof
dimer operator
bare monomerstatistics
bosonic
bosonic
Signof J
J0Frobenius
true monomerstatistics
bosonic/fermionic
bosonic
Input in Hamiltonian emerging
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Phase diagram vs spinon doping / magnetic field
VBC insulator
J, t > 0 :
No - sign problem GF MonteCarlo
A. Ralko, F. Mila & DP, PRL (2007); A. Ralko, F. Becca, DP, PRL (2008)
square lattice
triangular lattice
square lattice
boson condensation of spinons !
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Role of topological defects:vortex or Z2 vison
Holon (boson) + vortex spinless fermion !
Variational RVB
PRB 89
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Holon doped QDM
Physical case:
J
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Phase diagram Physical case:J
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Can replace efficiently microscopic models(since easier to simulate) :
Model for magnetic field induced QCP: BEC ofspinons
Model capturing RVB physics: very rich phasediagram (d-wave pairing, supersolid(?), Bosesuperfluid, )
Emergent fermionic excitations
To do list:
- optics, transport, impurity doping,
- connection with Z2 gauge field theory
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Fabien Trousselet (PhD)
Karlo Penc (Budapest)
Nic Shannon (Bristol)
Arnaud Ralko (Post-doc Toulouse-> Inst. Nel)
Federico Becca (Trieste)
Roderich Moessner (Dresden)
Frdric Mila (Lausanne)
Quantum Dimer Models(w. & without doping)
Itinerant fermionson frustrated magnets
mapped ontoQuantum Dimer Models
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doping ratio
Green function Monte Carlo computations
Square latticeV/J=0.9 & t/J=0.1
Maxwell construction:
Phase separation
A. Ralko et al., PRL (2007)
(projector MC needs a trial wf)
J, t > 0 :No - sign problem
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Phase diagram vs doping
VBC insulator
Flux quantization: in terms of h/2e
2e-Cooper pairs
Role of gauge field
0-flux1/2-flux quantum
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ARPES (Bi2212)Campuzano et al.
NMR (YBaCuO)Alloul et al.
QP
Inelastic Neutron ScatteringRossat-Mignot at al.
SPIN PSEUDO-GAP
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