Electron addition spectral functions of low-density polaron liquids
Bibliographic record
Abstract
Spectral functions are important quantities that contain a wealth of information about the quasiparticles of a system, and that can also be measured experimentally. For systems with electron-phonon coupling, good approximations for the spectral function are available only in the Migdal limit (at Fermi energies much larger than the typical phonon frequency, E_F\gg \Omega <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>F</mml:mi> </mml:msub> <mml:mo>≫</mml:mo> <mml:mi>Ω</mml:mi> </mml:mrow> </mml:math> , requiring a large carrier concentration x <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>x</mml:mi> </mml:math> ) and in the single polaron limit (at x=0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). Here we show that the region with x\ll 1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>≪</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ( E_F&lt;\Omega <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>F</mml:mi> </mml:msub> <mml:mo><</mml:mo> <mml:mi>Ω</mml:mi> </mml:mrow> </mml:math> ) can also be reliably investigated with the Momentum Average (MA) variational approximation, which essentially describes the formation of a polaron above an inert Fermi sea. Specifically, we show that for the one-dimensional spinless Holstein model, the MA spectral functions compare favorably with those calculated using variationally exact density matrix renormalization group simulations (DMRG) evaluated directly in frequency-space, so long as x&lt;0.1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo><</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> and the adiabaticity ratio \Omega/t&gt;0.5 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Ω</mml:mi> <mml:mi>/</mml:mi> <mml:mi>t</mml:mi> <mml:mo>></mml:mo> <mml:mn>0.5</mml:mn> </mml:mrow> </mml:math> . Unlike in the Migdal limit, here 'polaronic physics’ emerges already at moderate couplings. The relevance of these results for a spinful low- x <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>x</mml:mi> </mml:math> metal is also discussed.
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How this classification was reachedexpand
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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".