Manuscript Em03-H@8 · Em03-H-v8.tex · section · 91e9e3bd

Occupation representation

Frozen microscopic model and complete preparation › Occupation representation · lines 405–425

Fix real coefficients and set

H_{4} = a < b < c < d \sum J_{ab c d} χ_{a} χ_{b} χ_{c} χ_{d}, H_{B} = H_{4} - E_{m i n} I,

where $E_{m i n}$ is the minimum over both parity sectors. Quartic terms are Hermitian because reversal requires six exchanges. With $P_{B} = (- 1)^{N_{B}}$ ,

[H_{B}, P_{B}] = 0, ∥ H_{4} ∥ \leq h_{4} = \frac{1}{4} a < b < c < d \sum ∣ J_{ab c d} ∣, 0 ⪯ H_{B} ⪯ 2 h_{4} I .

Number need not commute with the quartic Hamiltonian.

SYK motivates the quartic setting but does not identify this fixed code with a black-hole microstate code MaldacenaStanford. No disorder average replaces the fixed coefficient array.

Displayed formulas in this passage

unlabeled · line 408
$H_{4} = a < b < c < d \sum J_{ab c d} χ_{a} χ_{b} χ_{c} χ_{d}, H_{B} = H_{4} - E_{m i n} I,$
unlabeled · line 415
$[H_{B}, P_{B}] = 0, ∥ H_{4} ∥ \leq h_{4} = \frac{1}{4} a < b < c < d \sum ∣ J_{ab c d} ∣, 0 ⪯ H_{B} ⪯ 2 h_{4} I .$

Occupation representation

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