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 strong-coupled Hubbard chain in the \textit{spin-incoherent} Luttinger liquid (LL) regime: $J(\equiv 4t^2/U)\ll k_{B}T\ll E_F$, where $t$ is the hopping amplitude, $U(\gg t)$ is the repulsive on-site Coulomb interaction, and $k_{B}T(E_F\sim t)$ is the thermal (Fermi) energy. We introduce a fractional Landau LL approach, whose $U=\infty$ fixed point is exactly mapped onto an ideal gas with two species obeying the Haldane-Wu \textit{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 $U\gg k_{B}T$. 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.

16 pages, 6 figures

References in corpus (20)

• A one-dimensional liquid of fermions with tunable spin
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Scaling Behavior of Heavy Fermion Metals
• Green's function for magnetically incoherent interacting electrons in one dimension
• Statistics of fractionalized excitations through threshold spectroscopy
• Spin-Incoherent Transport in Quantum Wires
• Theory of momentum resolved tunneling into a short quantum wire
• Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets
• Transport in a spin incoherent Luttinger liquid
• Asymmetric Zero-Bias Anomaly for Strongly Interacting Electrons in One Dimension
• Frustration-induced quantum phase transitions in a quasi-one-dimensional ferrimagnet: Hard-core boson map and the Ton ks-Girardeau limit
• Universal properties of high-temperature superconductors from real-space pairing III: The role of correlated hopping and intersite Coulomb interaction within the t-J-U model
• Numerically exploring the 1D-2D dimensional crossover on spin dynamics in the doped Hubbard model
• High temperature expansion of emptiness formation probability for isotropic Heisenberg chain
• Spin-incoherent behavior in the ground state of strongly correlated systems
• Fermi-edge singularity in a spin-incoherent Luttinger liquid
• Three-body interaction effects on the ground state of one-dimensional anyons
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime
• Luttinger liquids, Fermi liquids and fractional statistics

Cited by in corpus (1)

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