didier poilblanc- the physics of doped quantum dimer models

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

didier poilblanc- the physics of doped quantum dimer models

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