SiewAnn CHEONG Division of Physics and Applied Physics
- Slides: 16
Siew-Ann CHEONG Division of Physics and Applied Physics, School of Physical and Mathematical Sciences Numerical Methods as Exploration Tools for Theoretical Condensed Matter Physics
Life in Cornell University | Sep 12, 2014 2
Nanyang Technological University Nanyang Technological Institute （1981– 1990） Nanyang University （1956– 1980） Nanyang Technological University （1991–） School of Physical and Mathematical Sciences Nanyang Technological University Singapore University of Technology and Design National University of Singapore Management University Former Central Library Cornell University | Sep 12, 2014 SINGAPORE Presently Chinese Heritage Centre 3
teacher for a day 一日为 师 终生为 父 teacher/ mentor/ master father for life Cornell University | Sep 12, 2014 4
My Current Research Cornell University | Sep 12, 2014 5
Density Matrix of a Chain of Fermions Cornell University | Sep 12, 2014 6
Projection Operators & Conjecture Define Example: = Green function matrix of chain = Green function matrix of block For written in terms of Cornell University | Sep 12, 2014 7
Grand Canonical Density Matrix grand canonical ensemble matrix elements Cornell University | Sep 12, 2014 Fermi-Dirac distribution 8
Grassmannian Trace Formulas fermionic coherent state overcomplete basis 1 2 3 Cornell University | Sep 12, 2014 9
Exact Formula for ρ block environment Cornell University | Sep 12, 2014 Cheong & Henley, PRB 69, 075111 (2004) 10
ρ as a Diagnostic Tool model Hamiltonian long-range order? non-trivial local structure? Hamiltonian matrix exact diagonalization (ED) ρ of two blocks r apart Cornell University | Sep 12, 2014 ED ground state Cheong & Henley, PRB 79, 212402 (2009) 11
Physical Intuition & Mapping Cornell University | Sep 12, 2014 12
Exact Ground State different number of configurations Bloch state exact in the limit Cornell University | Sep 12, 2014 13
Exact Correlations corresponding local observables corresponding nonlocal observables intervening particle expansion p = specific occupation of sites between j and j + r Cornell University | Sep 12, 2014 14
Asymptotic Behavior of Correlations Cornell University | Sep 12, 2014 Cheong & Henley, PRB 80, 165124 (2009) 15
Conclusions • Numerical explorations – Matrix computation and diagonalization of ρ – Exact diagonalization of Ht, V=∞ • Analytical insights – Connection between ρ and G – Connection between Ht, V=∞ and Ht, V=0 • Exact formulas – – Cornell University | Sep 12, 2014 16
