Current Algebra of the HK Model

yzj5306@psu.edu (Yiyang Jiang) — Mon, 24 Aug 2026 16:30:00 -0400


Presenter	Yuting Bai (Prof. Philip W. Phillips’s group, UIUC)
Date	August 24, 2026 · 4:30–6:00 PM
Location	Davey 339
Topic	Application of the current-algebra method to a strongly correlated problem

Current algebra asks a deceptively simple question: instead of building a many-body theory out of particles $c_{\mathbf k}, c^\dagger_{\mathbf k}$, can we build it out of the fluid variables — the densities and currents that experiments actually measure? For free fermions in one dimension the answer is the familiar $U(1)$ Kac–Moody algebra, but the standard derivation leans hard on a filled Fermi sea, a linearized dispersion and a momentum cutoff. This talk replaces that derivation with the Bjorken–Johnson–Low prescription, which extracts the equal-time commutator from the high-frequency tail of a correlation function and therefore never has to assume what the ground state looks like. Applied to the Hatsugai–Kohmoto (HK) model — an exactly solvable non-Fermi liquid that violates Luttinger’s theorem — the method shows that the natural low-energy objects are not bare currents but parton (holon/doublon) currents, that they close into an affine $\mathfrak{su}(2)$ algebra, and that a manifestly local Sugawara-type Hamiltonian built from them reproduces the HK equations of motion and two-body correlators in the infrared. The suggested moral: the notorious non-locality of the HK model may be an artifact of writing local degrees of freedom in non-local variables.

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Current Algebra of the HK Model