Transcript altair.physics.ncsu.edu

New materials/electronic structure in 21st
century
Typical features:
- multi-component, hierarchies
- 0-3D (dots, chains, layers ... )
- d- and f- elements
- H: proton as a quantum part.
- organic/inorganic/solid
- bioinspired
Challenges:
- lack of a "unifying" strategy
- complexity
- competition of mechanisms:
quantum, temperature, etc
- single electron/quantum
effects important
Solving these one-by-one, ie, by a postdoc focused
on a class of materials for X years is ultimately inefficient
Unifying concept on which we all agree: Schrodinger equation
H  r 1 , r 2 ,... E  r 1 , r 2 ,...
Solve it in the many-body framework (!)
with the original Hamiltonian
H 
ZI
1
1
2


   E ionion


i
2 i
i,I r iI
ij r ij
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Computational Materials Research
Key goals:
- predict, design and optimize new materials for 21st century
- complement, guide and/or replace experiment
- new science frontier: from one-particle to many-body
Broad application areas:
- new energy sources: production/storage/processing of H
- nanosystems based materials
- bioinspired materials and processes: waste is nonexistent
Clear-cut example of previous impact:
- 3rd most cited PRL in all physics and history is Ceperley/Alder
Quantum Monte Carlo of homogeneous electron gas
Possibilities/breakthroughs with 500-fold increase in compute power:
- a few meV accuracy for energy differences
- quantum effects, temperature, dynamics on the same footing
- nanosystems in action, magnetism, supreconductivity in a wave
function framework
- H (bonded, solvated, ...): proton as a quantum particle
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Quantum Monte Carlo: a unique
strategy/opportunity for quantum manybody problems
Schrodinger equation in a propagator form
 R,t   R exp H R'  R',t d R'
-sample the wave function by walkers in R r 1 , r 2 ,..., r Nspace
-boost the efficiency with explicitly correlated trial functions
-propagate the walkers while enforcing all required symmetries
-evaluate the expectation values of interest
QMC:
- new physics/paradigm: work directly on many-body effects
- scalable, robust, highly efficient on parallel architectures
- favorable scaling in # of particles: nominally ~ O( N3)
and implentation with almost ~ O( N ) feasible
- accurate: typically ~ 95% of correlation energy across systems
0.1 eV/1% accuracy/agreement with experiment
- benchmarks for other methods, consistent results
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QMC bottlenecks and advanatges: next 5-10
years
Scientific: - beyond the fixed-node approximation, very active
research: obtain ~ 99% of correlation with polynomial scaling
- spin and spatial degrees of freedom on the same footing
- responses to external fields and spectral functions
- from wave functions to density matrices (temperature)
Mix of Science and Algorithmic/Computational:
- more efficient and accurate building of trial functions:
eg, robust stochastic optimizations
- efficient coupling and data exchange with one-particle
approaches
Hardware/
Software:
1. processor speed
2. parallelism
3. stability (QMC can test it real well)
4. memory, communication, etc, relevant but secondary
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Qauntum Monte Carlo: typical run
System: 50 atoms, 200 electrons, desired accuracy ~ 0.1 - 0.2 eV
Typical input: tens/hunderds of MB (initial/trial wave function)
Typical run: - tens of processors for days and weeks
- MPI
- 10-100s walkers in 3N-dim. space per processor
- evolved for hundreds of steps (independently, or
occasionally rebalanced)
- accumulate statistics from processors
Typical output:
- most of the data reduced to simple physical quantities
- current walker configurations stored (tens of MB per proc)
- restartable
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Materials with competing many-body
effects: hexaborides CaB6, LaxCa1-xB6 , ...
5% La-doped CaB6 is a weak magnet up to 900K (!)
No d or f electrons: - genuine itinerant magnetism ?
- promising spintronics material ?
Undoped CaB6 : insulator ? exitonic insulator ? metal ?
Experiments contardictory:
ARPES: insulator
de Haas-van Alphen: metal
Optical, etc: metal, insulator
Calculations inconclusive:
DFT: band overlap 1 eV (Swiss,...)
DFT: small gap (Japan)
GW (DFT+ pert. corr.): 1 eV gap (NL)
GW: small overlap (Japan)
Can we predict the correct gap before the experiment ?
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CaB6 band structure in Hartree-Fock
Large gap
of the order of 7 eV
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CaB6 band structure in DFT - B3LYP
Gap is now only
about 0.5 eV !
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CaB6 band structure in DFT - PW91
1 eV overlap at the
X point:
d-states on Ca !
Fixed-node
DMC gap:
1.3(3) eV
X
G
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Predict a "nanomagnet": caged transition
elements TM@Si12 TM=Sc, Ti, ... 3d, 4d, 5d
Find the smallest stable "nanomagnet" made from silicon
and a transition metal atom ...
- attempt to predict caged d-spin
- no success, hybridized, unstable
Experiment in Japan in '01!
W@Si12
APS March Meeting in '94:
L. M.: Electronic structure of Mn@Si12
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