Infinitely dimensional Lax structure for one-dimensional Hubbard model

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.

5 pages in RevTex, 1 figure, version as accepted by Phys. Rev. Lett

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• Efficient quantum information probes of non-equilibrium quantum criticality
• Integrability versus chaos in the steady state of many-body open quantum systems
• Exact steady states of the impurity-doped XXZ spin chain coupled to dissipators
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems