Exact diagonalization on spin-1/2 pyrochlore cluster with spin configuration and entanglement discussion
Bibliographic record
Abstract
In quantum physics, if we can find the eigenstates |Φᵢ⟩ of a Hamiltonian 𝐻, and the respective eigenergies 𝐸ᵢ, we can calculate many aspects such as time evolution, or its thermal properties. Exact diagonalization is a method which can solve the Hamiltonian numerically. For a small Hamiltonian system, we can find the eigenvalues by solving the characteristic polynomial equation of the matrix. However, as the system grows larger, the calculation will grow exponentially. Instead of calculating the eigenstates directly, we will use the unitary transformation matrix to block diagonalize the Hamiltonian first. As a consequence, instead of solving the Hamiltonian directly, we will solve each block. In order to find the unitary transformation matrix U, we will use the symmetry of the Hamiltonian, and with the help of group theory, we can construct 𝑈 matrix and do the block diagonalization. In Chapter 3 we do the block diagonaliztion on a 16-site cluster of pyrochlore magnet. We use the full space group No. 227 to block diagonalize the Hamiltonian matrix into 14 blocks with different degeneracy. In Chapter 4, we analyze the spin states by varying the exchange constants. In Chapter 5, we use the ground state to discuss the quantum entanglement between different sites in the ground state. We also evaluate the ~I~ concurrence of the ground states.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.007 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".