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August 11
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Aug. 11 - 8p
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14:00 - 14:30
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14:30 - 15:00
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15:00 - 15:30
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| The correlation density matrix: new tool for analyzing exact diagonalizations? |
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C. L. Henley |
| Is there an unbiased way to determine numerically any important correlations, even unforeseen ones, in a lattice model of strongly interacting spins or fermions? Let ρ A, ρ B, and ρ A∪B be the reduced, many-body density matrices for (respectively) the small clusters A and B, offset by a vector r, and their (disconnected) union. Then all possible correlations are contained in the ``correlation density matrix'', ρC(r) = ρAB -ρA &otimes ρB. Via singular-value decomposition we write ρcorr = &sum i λi Φi(A) Φ'i(B), where Φi and Φ'i are normalized operators on the respective clusters; the terms represent different correlation functions, their strength given by the magnitudes |λi|.
The procedure, tested on a ladder model of spinless fermions, correctly identified the growth of superconducting correlations, but only a DMRG-based version of the method would have a chance to probe the (Luttinger liquid) criticality. We propose that the correlation density matrix is more promising for non-critical states: to detect any strong order in an ordered state, or to confirm the nonexistence of any order in a spin liquid state. |