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arXiv · 2608.01817

Emergent modular Luttinger liquid from spin-partitioned entanglement in the one-dimensional Hubbard model

Ádám Bácsi·Catalin Pascu Moca·Balázs Dóra
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Abstract

We study the spin-partitioned entanglement Hamiltonian of the one-dimensional repulsive Hubbard model. By combining bosonization with exact diagonalization, we show that tracing out one spin species produces a modular Luttinger liquid, whose properties fundamentally differ from those of the physical system. While the modular spectrum is fully dispersionless and possesses a momentum-independent entanglement gap, its eigenstates exhibit algebraic correlations governed by a single effective Luttinger parameter equal to the geometric mean of the charge and spin Luttinger parameters. The resulting entanglement spectrum displays a universal branching hierarchy in excellent agreement with exact diagonalization. We further demonstrate that the modular ground state is nearly identical to that of the spinless Luttinger liquid. These results uncover a universal modular structure in interacting one-dimensional fermionic systems.

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Ádám Bácsi, Catalin Pascu Moca, Balázs Dóra. 2026-08-03. Emergent modular Luttinger liquid from spin-partitioned entanglement in the one-dimensional Hubbard model. https://arxiv.org/abs/2608.01817

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