Continuous Matrix Product States for Quantum Fields: An Energy Minimization Algorithm
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Bibliographic record
Abstract
The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough Letter of Verstraete and Cirac [Phys. Rev. Lett. 104, 190405 (2010).PRLTAO0031-900710.1103/PhysRevLett.104.190405], provides a powerful variational ansatz for the ground state of strongly interacting quantum field theories in one spatial dimension. A continuous MPS (cMPS) approximation to the ground state can be obtained by simulating a Euclidean time evolution. In this Letter we propose a cMPS optimization algorithm based instead on energy minimization by gradient methods and demonstrate its performance by applying it to the Lieb-Liniger model (an integrable model of an interacting bosonic field) directly in the thermodynamic limit. We observe a very significant computational speed-up, of more than 2 orders of magnitude, with respect to simulating a Euclidean time evolution. As a result, a much larger cMPS bond dimension D can be reached (e.g., D=256 with moderate computational resources), thus helping unlock the full potential of the cMPS representation for ground state studies.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it