Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1808.09159 · Physical review. B./Physical review. B

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

Carlindo Vitoriano, R. R. Montenegro-Filho, Mauricio D. Coutinho-Filho

Published Aug 20, 2018• 6 citations
arXivHTMLPDF

Abstract

Bethe ansatz and bosonization procedures are used to describe the thermodynamics of the strong-coupled Hubbard chain in the spin-incoherent Luttinger liquid (LL) regime: $J(\ensuremath{\equiv}4{t}^{2}/U)\ensuremath{\ll}{k}_{B}T\ensuremath{\ll}{E}_{F}$, where $t$ is the hopping amplitude, $U(\ensuremath{\gg}t)$ is the repulsive on-site Coulomb interaction, and ${k}_{B}T({E}_{F}\ensuremath{\sim}t)$ is the thermal (Fermi) energy. We introduce a fractional Landau LL approach, whose $U=\ensuremath{\infty}$ 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 $t\text{\ensuremath{-}}J$ 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 $t\text{\ensuremath{-}}J$ model, under the condition $U\ensuremath{\gg}{k}_{B}T$. 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.

DOI
10.1103/physrevb.98.085130

Related papers

Exact results of one-dimensional repulsive Hubbard model

Jiajia Luo, Han Pu, Xi‐Wen Guan

We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation functions, Contact susceptibilities and quantum cooling. Using the exact solutions of the Bethe Ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. Based on the analysis on the fractional charge and spin excitations, the spin-incoherent Luttinger liquid with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of the conformal field theory. Near quadruple critical point, we then further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions in terms of chemical potential, magnetic field and interaction. In particular, we determine additivity rules of spin and charge susceptibilities, and derive explicit forms of thermodynamics of spin-incoherent Luttinger liquid. Finally, in order to capture deeper insight into the Mott insulator and interaction driven criticality, we further study the double occupancy and its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme upon the quantum criticality is introduced.

arXiv:2307.00890•Jul 3, 2023•0 citations

Spectral properties of a spin-incoherent Luttinger liquid

Adrian E. Feiguin, Gregory A. Fiete

We present time-dependent density-matrix renormalization-group (DMRG) results for strongly interacting one-dimensional fermionic systems at finite temperature. When interactions are strong the characteristic spin energy can be greatly suppressed relative to the characteristic charge energy, allowing for the possibility of spin-incoherent Luttinger liquid physics when the temperature is high compared to the spin energy, but small compared to the charge energy. Using DMRG we compute the spectral properties of the $t\text{\ensuremath{-}}J$ model at arbitrary temperatures with respect to both spin and charge energies. We study the full crossover from the Luttinger liquid regime to the spin-incoherent regime, focusing on small $J/t$, where the signatures of spin-incoherent behavior are more manifest. Our method allows us to access the analytically intractable regime where temperature is on the order of the spin energy, $T\ensuremath{\sim}J$. Our results should be helpful in the interpretation of experiments that may be in the crossover regime, $T\ensuremath{\sim}J$, and apply to one-dimensional cold atomic gases where finite-temperature effects are appreciable. The technique may also be used to guide the development of analytical approximations for the crossover regime.

arXiv:0910.3957•Physical Review B•Feb 10, 2010•52 citations

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

Gabriel F. O. Ramos, Mauricio D. Coutinho-Filho

Abstract The infinity-range Hubbard model on a d-dimensional hypercubic lattice is mapped onto an ideal gas with three species obeying the Haldane-Wu fractional exclusion statistics (FESs). Using this map, we study this system in the spin-incoherent regime and strong coupling limit. We have derived the polynomial series of the grand-canonical free, whose coefficients are Lerch functions, a signature of our FES description, as demonstrated for the entropy and specific heat in any dimension. For even dimensions the series are finite, and a table of coefficients versus dimensionality can be written, while for odd dimensions, the series diverges asymptotically, and can thus be circumvented by Borel summation.

Journal of Physics A Mathematical and Theoretical•Nov 2, 2022•2 citations

Spin-incoherent liquid and interaction-driven criticality in the one-dimensional Hubbard model

Jiajia Luo, Han Pu, Xi-Wen Guan

Although the one-dimensional repulsive Fermi-Hubbard model has been intensively studied over many decades, a rigorous understanding of many aspects of the model is still lacking. In this work, based on the solutions to the thermodynamic Bethe ansatz equations, we provide a rigorous study on the following. (1) We calculate the fractional excitations of the system in various phases, from which we identify the parameter regime featuring the spin-incoherent Luttinger liquid (SILL). We investigate the universal properties and the asymptotic of correlation functions of the SILL. (2) We study the interaction-driven phase transition and the associated criticality, and build up an essential connection between the contact susceptibilities and the variations of density, magnetization, and entropy with respect to the interaction strength. As an application of these concepts, which hold true for higher-dimensional systems, we propose a quantum cooling scheme based on the interaction-driven refrigeration cycle.

arXiv:2209.08336•Physical review. B./Physical review. B•May 4, 2023•5 citations

Fractional Exclusion Statistics for thet-JModel with Long Range Exchange and Hopping

Yusuke S. Kato, Yoshio Kuramoto

We construct thermodynamics of the one-dimensional supersymmetric t-J model with the 1/sin 2 interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component t-J model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.

Journal of the Physical Society of Japan•Jun 15, 1996•25 citations

Fractional Exclusion Statistics for the t-J Model

Yusuke S. Kato, Yoshio Kuramoto

We construct thermodynamics of the one-dimensional supersymmetric {\it t-J} model with the $ 1/\sin^2$ interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component {\it t-J} model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.

arXiv:cond-mat/9601132•Jan 27, 1996•0 citations
Bethe ansatz and bosonization procedures are used to describe the thermodynamics of the strong-coupled Hubbard chain in the spin-incoherent Luttinger liquid (LL) regime: J(\ensuremath≡4t2/U)\ensuremath≪kBT\ensuremath≪EFJ(\ensuremath{\equiv}4{t}^{2}/U)\ensuremath{\ll}{k}_{B}T\ensuremath{\ll}{E}_{F}J(\ensuremath≡4t2/U)\ensuremath≪kB​T\ensuremath≪EF​, where ttt is the hopping amplitude, U(\ensuremath≫t)U(\ensuremath{\gg}t)U(\ensuremath≫t) is the repulsive on-site Coulomb interaction, and kBT(EF\ensuremath∼t){k}_{B}T({E}_{F}\ensuremath{\sim}t)kB​T(EF​\ensuremath∼t) is the thermal (Fermi) energy. We introduce a fractional Landau LL approach, whose U=\ensuremath∞U=\ensuremath{\infty}U=\ensuremath∞ 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\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-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-TTT limit of the fractional Landau LL entropy and chemical potential exhibit the expected results of the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model, under the condition U\ensuremath≫kBTU\ensuremath{\gg}{k}_{B}TU\ensuremath≫kB​T. Lastly, finite-temperature Lanczos simulations of the single-particle distribution function confirm the characteristics of the spin-incoherent regime and the high-TTT limit observed in previous DMRG studies.
We present analytical results of fundamental properties of one-dimensional (1D) Hubbard model with a repulsive interaction, ranging from fractional excitations to universal thermodynamics, interaction-driven criticality, correlation functions, Contact susceptibilities and quantum cooling. Using the exact solutions of the Bethe Ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. Based on the analysis on the fractional charge and spin excitations, the spin-incoherent Luttinger liquid with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of the conformal field theory. Near quadruple critical point, we then further analytically obtain the thermodynamical properties, dimensionless ratios and scaling functions near quantum phase transitions in terms of chemical potential, magnetic field and interaction. In particular, we determine additivity rules of spin and charge susceptibilities, and derive explicit forms of thermodynamics of spin-incoherent Luttinger liquid. Finally, in order to capture deeper insight into the Mott insulator and interaction driven criticality, we further study the double occupancy and its associated Contact and Contact susceptibilities through which an adiabatic cooling scheme upon the quantum criticality is introduced.
We present time-dependent density-matrix renormalization-group (DMRG) results for strongly interacting one-dimensional fermionic systems at finite temperature. When interactions are strong the characteristic spin energy can be greatly suppressed relative to the characteristic charge energy, allowing for the possibility of spin-incoherent Luttinger liquid physics when the temperature is high compared to the spin energy, but small compared to the charge energy. Using DMRG we compute the spectral properties of the $t\text{\ensuremath{-}}J$ model at arbitrary temperatures with respect to both spin and charge energies. We study the full crossover from the Luttinger liquid regime to the spin-incoherent regime, focusing on small J/tJ/tJ/t, where the signatures of spin-incoherent behavior are more manifest. Our method allows us to access the analytically intractable regime where temperature is on the order of the spin energy, $T\ensuremath{\sim}J$. Our results should be helpful in the interpretation of experiments that may be in the crossover regime, $T\ensuremath{\sim}J$, and apply to one-dimensional cold atomic gases where finite-temperature effects are appreciable. The technique may also be used to guide the development of analytical approximations for the crossover regime.
Abstract The infinity-range Hubbard model on a d-dimensional hypercubic lattice is mapped onto an ideal gas with three species obeying the Haldane-Wu fractional exclusion statistics (FESs). Using this map, we study this system in the spin-incoherent regime and strong coupling limit. We have derived the polynomial series of the grand-canonical free, whose coefficients are Lerch functions, a signature of our FES description, as demonstrated for the entropy and specific heat in any dimension. For even dimensions the series are finite, and a table of coefficients versus dimensionality can be written, while for odd dimensions, the series diverges asymptotically, and can thus be circumvented by Borel summation.
Although the one-dimensional repulsive Fermi-Hubbard model has been intensively studied over many decades, a rigorous understanding of many aspects of the model is still lacking. In this work, based on the solutions to the thermodynamic Bethe ansatz equations, we provide a rigorous study on the following. (1) We calculate the fractional excitations of the system in various phases, from which we identify the parameter regime featuring the spin-incoherent Luttinger liquid (SILL). We investigate the universal properties and the asymptotic of correlation functions of the SILL. (2) We study the interaction-driven phase transition and the associated criticality, and build up an essential connection between the contact susceptibilities and the variations of density, magnetization, and entropy with respect to the interaction strength. As an application of these concepts, which hold true for higher-dimensional systems, we propose a quantum cooling scheme based on the interaction-driven refrigeration cycle.
We construct thermodynamics of the one-dimensional supersymmetric t-J model with the 1/sin 2 interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component t-J model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.
We construct thermodynamics of the one-dimensional supersymmetric {\it t-J} model with the $ 1/\sin^2$ interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component {\it t-J} model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.