Infinitely dimensional Lax structure for one-dimensional Hubbard model

TL;DR

This paper presents an infinite-dimensional Lax structure for the 1D Hubbard model, enabling explicit construction of steady states in non-equilibrium conditions, revealing potential new quantum symmetries.

Contribution

It introduces a novel infinite-dimensional Lax representation for the Hubbard chain, facilitating exact steady state solutions under non-equilibrium boundary conditions.

Findings

Explicit steady state density operator for non-equilibrium Hubbard chain

Potential indication of new quantum symmetries in the model

Infinite-dimensional Lax structure applicable to boundary-driven systems

Abstract

We report a two-parametric irreducible infinitely dimensional representation of the Lax integrability condition for the fermi Hubbard chain. Besides being of fundamental interest, hinting on possible novel quantum symmetry of the model, our construction allows for an explicit representation of an exact steady state many-body density operator for non-equilibrium boundary-driven Hubbard chain with arbitrary (asymmetric) particle source/sink rates at the letf/right end of the chain and with arbitrary boundary values of chemical potentials.