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Bethe ansatz and bosonization procedures are used to describe thethermodynamics of the strong-coupled Hubbard chain in the\textit{spin-incoherent} Luttinger liquid (LL) regime: $J(\equiv 4t^2/U)\ll k_BT\ll E_F$, where $t$ is the hopping amplitude, $U(\gg t)$ is the repulsiveon-site Coulomb interaction, and $k_B T (E_F\sim t)$ is the thermal (Fermi)energy. We introduce a fractional Landau LL approach, whose $U=\infty$ fixedpoint is exactly mapped onto an ideal gas with two species obeying theHaldane-Wu \textit{exclusion} fractional statistics. This phenomenologicalapproach sheds light on the behavior of several thermodynamic properties in thespin-incoherent LL regime: specific heat, charge compressibility, magneticsusceptibility, and Drude weight. In fact, besides the hopping (mass)renormalization, the fractional Landau LL parameters, due to quasiparticleinteraction, are determined and relationships with velocities of holons andspinons are unveiled. The specific heat thus obtained is in very good agreementwith previous density matrix renormalization group (DMRG) simulations of the$t$-$J$ model in the spin-incoherent regime. A phase diagram is provided andtwo thermodynamic paths to access this regime clarifies both the numerical andanalytical procedures. Further, we show that the high-$T$ limit of thefractional Landau LL entropy and chemical potential exhibit the expectedresults of the $t$-$J$ model, under the condition $U\gg k_B T$. Lastly,finite-temperature Lanczos simulations of the single-particle distributionfunction confirm the characteristics of the spin-incoherent regime and thehigh-$T$ limit observed in previous DMRG studies.

Fractional exclusion statistics and thermodynamics of the Hubbard chain in the spin-incoherent Luttinger liquid regime