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

Abstract

Bethe ansatz and bosonization procedures are used to describe the thermodynamics of the strongcoupled Hubbard chain in the spin-incoherent Luttinger liquid (LL) regime: J(≡ 4t 2 /U ) ≪ kBT ≪ EF , where t is the hopping amplitude, U (≫ t) is the repulsive on-site Coulomb interaction, and kBT (EF ∼ t) is the thermal (Fermi) energy. We introduce a fractional Landau LL approach, whose U = ∞ fixed point is exactly mapped onto an ideal gas with two species obeying the Haldane-Wu exclusion fractional statistics. This phenomenological approach sheds light on the behavior of several thermodynamic properties in the spin-incoherent LL regime: specific heat, charge compressibility, magnetic susceptibility, and Drude weight. In fact, besides the hopping (mass) renormalization, the fractional Landau LL parameters, due to quasiparticle interaction, are determined and relationships with velocities of holons and spinons are unveiled. The specific heat thus obtained is in very good agreement with previous density matrix renormalization group (DMRG) simulations of the t-J model in the spin-incoherent regime. A phase diagram is provided and two thermodynamic paths to access this regime clarifies both the numerical and analytical procedures. Further, we show that the high-T limit of the fractional Landau LL entropy and chemical potential exhibit the expected results of the t-J model, under the condition U ≫ kBT . Lastly, finite-temperature Lanczos simulations of the single-particle distribution function confirm the characteristics of the spin-incoherent regime and the high-T limit observed in previous DMRG studies.

Thermodynamics of the infinity-range hubbard model in the spin-incoherent regime

“…The formalism developed so far is quite general. In the following we will deal with the spin-incoherent regime [13], in which case the inequalities below hold:…”

“…In [12], this regime was explored in studying the ground state of strong correlated systems. Further, in [13] the Landau fractional theory was introduced and used in the context of the spin-incoherent LL regime in Hubbard chains, in which case results for the fractional Landau LL chemical potential and fractional Landau LL entropy, where put forward.…”

Quantum critical behavior and thermodynamics of the repulsive one-dimensional Hubbard model in a magnetic field

“…It took almost twenty years until a numerical implementation, with reasonable accuracy, of this system of equations was reported in the literature [62][63][64][65]. Certain simplifications appear in the strong coupling limit and in the spin-disordered regime [66][67][68][69]. A different system of equations describing the thermodynamics of the Hubbard model for all filling fractions was derived in [70] making use of the quantum transfer matrix (QTM) [71][72][73][74][75][76] (at half filling similar equations were derived in [77,78]).…”

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB 2 Hubbard chains

“…On the other hand, it has been verified that the ferrimagnetic GS of spin-1/2 Heisenberg and Hubbard/ t-J AB 2 chains, under the effect of frustration [19][20][21][22][23] or doping [7,11,24,25], are strongly affected by quantum fluctuations that might cause its destruction and the occurrence of new exotic phases: spiral incommensurate (IC) spin structures, Nagaoka (U → ∞) and resonating-valence-bond (RVB) states, phase separation (PS), and Luttinger-liquid behavior. These features can enhance the phenomenology in comparison with a linear chain, which is dominated by the nontrivial Luttinger-liquid behavior that exhibits fractional excitations [26,27], emergent fractionalized particles [28], and fractional-exclusion statistic properties [29] in the spinincoherent regime [30], in which case the Bethe ansatz and the bosonization procedures play a significant role. In addition, investigations of transport properties in AB 2 chains and related structures [31], as well as exactly solved hybrid diamond chain with localized Ising spins and mobile electrons [32], have also unveiled very interesting features.…”