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

Journal of Physics A Mathematical and Theoretical

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

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

Published Nov 2, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1751-8121/ac9f89

Related papers

Mutual exclusion statistics and the infinite-range Hubbard model: critical behavior in the quantum regime

Gabriel F. O. Ramos, Weverton Lucas da Silva Rosendo, Ernesto P. Raposo +1 more

Abstract We investigate the critical behavior in the quantum regime of the Hubbard model in d-dimensional hypercubic lattices with infinite-range Coulomb interaction. The Haldane–Wu mutual exclusion statistics approach, which comprises three species of exclusions, allows us to derive the singular part of the free energy, entropy, and specific heat in the quantum regime g > T, where g is the scaling interaction parameter and T is the temperature. We present results from the analytic series expansions of observables near the quantum critical point: T = g = μ = 0 , where µ is the chemical potential. The signature of the mutual exclusion statistics manifests through the appearance of polylogarithms related to Lerch functions in the coefficients of the free energy series in powers of T / g . The calculated critical exponents from the analytic series are consistent with our scaling analysis in the quantum regime. In particular, the specific heat is shown to display a variety of critical behaviors, C / T ∼ g − α g , g → 0 + , depending on the lattice dimension: from a singular behavior in d = 1 ( α g = 1 / 2 ) to a constant value in d = 2 ( α g = 0 ), and regular behavior for d > 2 ( α g = 1 − d / 2 < 0 ).

Journal of Physics A Mathematical and Theoretical•Jan 10, 2025•0 citations

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

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.

arXiv:1808.09159•Physical review. B./Physical review. B•Aug 20, 2018•6 citations

Metal-insulator transition with infinite-range Coulomb coupling: Fractional statistics and quantum critical properties

Carlindo Vitoriano, Lucian Bogdan Bejan, A. M. S. Macêdo +1 more

We show that the Hubbard model with infinite-range Coulomb coupling is equivalent to an ideal gas of three species of particles obeying fractional exclusion statistics. A full appreciation of this mapping requires an extension of the pertinent formalism. This very simple, but rather peculiar model is exactly solvable in any dimension and exhibits a Mott metal-insulator transition, whose universality class is shown to be that of a free spinless Fermi gas. A modified version of the Luttinger theorem is shown to apply in any dimension. We also characterize the metallic and insulating phases by obtaining the electronic band structure as well as the interacting density of states. The fractional statistics manifests itself on the amplitudes of several thermodynamic quantities and, in particular, the Pauli spin susceptibility is subdominant in all metallic phases, and a Curie-type of response appears.

Physical review. B, Condensed matter•Mar 15, 2000•19 citations

Hubbard model with infinite-range attractive interaction

Carlindo Vitoriano, K. Rocha, Mauricio D. Coutinho-Filho

The ground state and low-temperature properties of the Hubbard model with infinite-range attractive interaction in the presence of a magnetic field are considered. This model is exactly solvable in any dimension and is mapped onto an ideal gas of three species of exclusons. The system is found to behave as a noninteracting Fermi gas whenever the correlation function $C(\mathbf{k})=⟨{n}_{\mathbf{k}\ensuremath{\uparrow}}{n}_{\mathbf{k}\ensuremath{\downarrow}}⟩\ensuremath{-}⟨{n}_{\mathbf{k}\ensuremath{\uparrow}}⟩⟨{n}_{\mathbf{k}\ensuremath{\downarrow}}⟩$ is negligible, otherwise it displays nontrivial correlated behavior which manifests as fractional statistical effects. The corresponding effective Hamiltonians and free energies governing the distinct regimes are presented. In one dimension, our results are analyzed in light of those derived using the on-site attractive Hubbard chain.

Physical Review B•Oct 19, 2005•9 citations

Three-dimensional Hubbard model in the thermodynamic limit

Ehsan Khatami

We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the N\'eel ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods.

arXiv:1603.02681•Physical review. B./Physical review. B•Sep 9, 2016•26 citations

Pseudogap Effects in the Strongly Correlated Regime of the Two-Dimensional Fermi Gas

Shasta Ramachandran, S. Jensen, Y. Alhassid

The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum Monte Carlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.

arXiv:2212.14880•Physical Review Letters•Oct 4, 2024•2 citations
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.
Abstract We investigate the critical behavior in the quantum regime of the Hubbard model in d-dimensional hypercubic lattices with infinite-range Coulomb interaction. The Haldane–Wu mutual exclusion statistics approach, which comprises three species of exclusions, allows us to derive the singular part of the free energy, entropy, and specific heat in the quantum regime g > T, where g is the scaling interaction parameter and T is the temperature. We present results from the analytic series expansions of observables near the quantum critical point: T = g = μ = 0 , where µ is the chemical potential. The signature of the mutual exclusion statistics manifests through the appearance of polylogarithms related to Lerch functions in the coefficients of the free energy series in powers of T / g . The calculated critical exponents from the analytic series are consistent with our scaling analysis in the quantum regime. In particular, the specific heat is shown to display a variety of critical behaviors, C / T ∼ g − α g , g → 0 + , depending on the lattice dimension: from a singular behavior in d = 1 ( α g = 1 / 2 ) to a constant value in d = 2 ( α g = 0 ), and regular behavior for d > 2 ( α g = 1 − d / 2 < 0 ).
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 ttt 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-TTT 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-TTT limit observed in previous DMRG studies.
We show that the Hubbard model with infinite-range Coulomb coupling is equivalent to an ideal gas of three species of particles obeying fractional exclusion statistics. A full appreciation of this mapping requires an extension of the pertinent formalism. This very simple, but rather peculiar model is exactly solvable in any dimension and exhibits a Mott metal-insulator transition, whose universality class is shown to be that of a free spinless Fermi gas. A modified version of the Luttinger theorem is shown to apply in any dimension. We also characterize the metallic and insulating phases by obtaining the electronic band structure as well as the interacting density of states. The fractional statistics manifests itself on the amplitudes of several thermodynamic quantities and, in particular, the Pauli spin susceptibility is subdominant in all metallic phases, and a Curie-type of response appears.
The ground state and low-temperature properties of the Hubbard model with infinite-range attractive interaction in the presence of a magnetic field are considered. This model is exactly solvable in any dimension and is mapped onto an ideal gas of three species of exclusons. The system is found to behave as a noninteracting Fermi gas whenever the correlation function $C(\mathbf{k})=⟨{n}_{\mathbf{k}\ensuremath{\uparrow}}{n}_{\mathbf{k}\ensuremath{\downarrow}}⟩\ensuremath{-}⟨{n}_{\mathbf{k}\ensuremath{\uparrow}}⟩⟨{n}_{\mathbf{k}\ensuremath{\downarrow}}⟩$ is negligible, otherwise it displays nontrivial correlated behavior which manifests as fractional statistical effects. The corresponding effective Hamiltonians and free energies governing the distinct regimes are presented. In one dimension, our results are analyzed in light of those derived using the on-site attractive Hubbard chain.
We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the N\'eel ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods.
The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum Monte Carlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.