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:cond-mat/9502073 · Physical review. B, Condensed matter

Susceptibility of the one-dimensional dimerized Hubbard model

Frédéric Mila, Karlo Penc

Published Jan 15, 1995• 14 citations
arXivHTMLPDF

Abstract

We show that the zero-temperature susceptibility of the one-dimensional, dimerized Hubbard model at quarter-filling can be accurately determined on the basis of exact diagonalization of small clusters. The best procedure is to perform a finite-size scaling of the spin velocity ${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$, and to calculate the susceptibility from the Luttinger-liquid relation \ensuremath{\chi}=2/\ensuremath{\pi}${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$. We show that these results are reliable by comparing them with the analytical results that can be obtained in the weak- and strong-coupling limits. We have also used quantum Monte Carlo simulations to calculate the temperature dependence of the susceptibility for parameters that should be relevant to the Bechgaard salts. This shows that, used together, these numerical techniques are able to give precise estimates of the low-temperature susceptibility of realistic one-dimensional models of correlated electrons.

DOI
10.1103/physrevb.51.1997

Related papers

Charge Susceptibility of the Two-Dimensional Hubbard Model near the Half-Filled Band -A Monte Carlo Study-

Hiromi Otsuka

Using the quantum Monte Carlo simulation technique for the lattice fermion systems, we study the charge susceptibility of the two-dimensional Hubbard near the half-filled band. Lattice sizes up to 6×6 and inverse temperatures up to 6 t ( t : hopping parameter) are studied. We find that the behavior of the charge susceptibility is strongly dependent on the electron concentration at low temperature: the charge susceptibility is suppressed at the half-filled band, while it is considerably enhanced in non-half-filled band cases by the electron correlation. The above behavior of the charge susceptibility is quite similar to the recent Bethe-Ansatz result for the one-dimensional Hubbard model.

Journal of the Physical Society of Japan•Aug 15, 1990•10 citations

Quantum Monte Carlo study of spin correlations in the one-dimensional Hubbard model

Anders W. Sandvik, Douglas J. Scalapino, C. Singh

The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding T=0 correlation function of the infinite system. For the T\ensuremath{\rightarrow}0 divergence of the q=2${\mathit{k}}_{\mathit{F}}$ spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2${\mathit{k}}_{\mathit{F}}$)\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.

Physical review. B, Condensed matter•Jul 15, 1993•15 citations

Magnetism in the Hubbard model: An effective spin Hamiltonian approach

Michael A. Tusch, Yolande H. Szczech, David E. Logan

We present an approach to the magnetic properties of the half-filled Hubbard model, based on an approximate mapping of its low-energy transverse spin excitations on to those of an effective underlying Heisenberg model, but with effective spin interactions which are self-consistently determined and not confined solely to nearest-neighbor couplings. The mapping is exact in strong-coupling and is found to be accurate over a very wide range of interaction strengths, down to weak coupling. At zero temperature, it permits ready evaluation at finite U of the one-loop effects of zero-point spin fluctuations on, e.g., the sublattice magnetization. At finite temperatures, thermodynamic properties of the system in the thermal paramagnet are studied via a physically transparent Onsager reaction field approach, which amounts to a self-consistent treatment of paramagnetic spin correlations. This is central not only in recovering the correct dimensionality dependence of antiferromagnetic long-ranged order, but also for the d=3 case of primary interest here yields a N\'eel temperature in close agreement with known strong- and weak-coupling limits. Spin correlation functions and magnetic susceptibilities also show very good agreement with quantum Monte Carlo calculations over an appreciable temperature range in which the low-lying transverse spin excitations are thermally dominant. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Mar 1, 1996•16 citations

The one-dimensional Hubbard model with open ends: universal divergent contributions to the magnetic susceptibility

Michael Bortz, Jesko Sirker

The magnetic susceptibility of the one-dimensional Hubbard model with open boundary conditions at arbitrary filling is obtained from field theory at low temperatures and small magnetic fields, including leading and next-leading orders. Logarithmic contributions to the bulk part are identified as well as algebraic-logarithmic divergences in the boundary contribution. As a manifestation of spin-charge separation, the result for the boundary part at low energies turns out to be independent of filling and interaction strength and identical to the result for the Heisenberg model. For the bulk part at zero temperature, the scale in the logarithms is determined exactly from the Bethe ansatz. At finite temperature, the susceptibility profile as well as the Friedel oscillations in the magnetisation are obtained numerically from the density-matrix renormalisation group applied to transfer matrices. Agreement is found with an exact asymptotic expansion of the relevant correlation function.

arXiv:cond-mat/0602511•Journal of Physics A Mathematical and General•May 23, 2006•2 citations

Magnetic susceptibility of the two-dimensional Hubbard model

Adriana Moreo

Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.

Physical review. B, Condensed matter•Aug 1, 1993•39 citations

Monte Carlo study of a one-dimensional degenerate Hubbard model

Wonpyong Gill, Douglas J. Scalapino

Correlations of a one-dimensional doubly degenerate Hubbard model are studied for the one-quarter-filled case. Exact calculations on a four-site lattice show that a ferromagnetic state exists in the strong-coupling regime. For a one-dimensional chain, a strong-coupling effective Hamiltonian was studied using a self-consistent calculation, a high-temperature expansion, and quantum Monte Carlo simulations. The results provide information on the parameters needed for ferromagnetic correlations, and the temperature dependence of the spin and orbital correlations.

Physical review. B, Condensed matter•Jan 1, 1987•34 citations
We show that the zero-temperature susceptibility of the one-dimensional, dimerized Hubbard model at quarter-filling can be accurately determined on the basis of exact diagonalization of small clusters. The best procedure is to perform a finite-size scaling of the spin velocity u\ensuremathσ{\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}u\ensuremathσ​, and to calculate the susceptibility from the Luttinger-liquid relation \ensuremath{\chi}=2/\ensuremath{\pi}u\ensuremathσ{\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}u\ensuremathσ​. We show that these results are reliable by comparing them with the analytical results that can be obtained in the weak- and strong-coupling limits. We have also used quantum Monte Carlo simulations to calculate the temperature dependence of the susceptibility for parameters that should be relevant to the Bechgaard salts. This shows that, used together, these numerical techniques are able to give precise estimates of the low-temperature susceptibility of realistic one-dimensional models of correlated electrons.
Using the quantum Monte Carlo simulation technique for the lattice fermion systems, we study the charge susceptibility of the two-dimensional Hubbard near the half-filled band. Lattice sizes up to 6×6 and inverse temperatures up to 6 t ( t : hopping parameter) are studied. We find that the behavior of the charge susceptibility is strongly dependent on the electron concentration at low temperature: the charge susceptibility is suppressed at the half-filled band, while it is considerably enhanced in non-half-filled band cases by the electron correlation. The above behavior of the charge susceptibility is quite similar to the recent Bethe-Ansatz result for the one-dimensional Hubbard model.
The one-dimensional Hubbard model is studied at and close to half-filling using a generalization of Handscomb's quantum Monte Carlo method. Results for spin-correlation functions and susceptibilities are presented for systems of up to 128 sites. The spin-correlation function at low temperature is well described by a recently introduced formula relating the correlation function of a finite periodic system to the corresponding T=0 correlation function of the infinite system. For the T\ensuremath{\rightarrow}0 divergence of the q=2kF{\mathit{k}}_{\mathit{F}}kF​ spin susceptibility, our results are consistent with the form \ensuremath{\chi}(2kF{\mathit{k}}_{\mathit{F}}kF​)\ensuremath{\sim}\ensuremath{\Vert}ln(T)${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\sigma}}}$${\mathit{T}}_{\mathrm{\ensuremath{\rho}}}^{\mathit{K}}$-1, with \ensuremath{\sigma}=1/2.
We present an approach to the magnetic properties of the half-filled Hubbard model, based on an approximate mapping of its low-energy transverse spin excitations on to those of an effective underlying Heisenberg model, but with effective spin interactions which are self-consistently determined and not confined solely to nearest-neighbor couplings. The mapping is exact in strong-coupling and is found to be accurate over a very wide range of interaction strengths, down to weak coupling. At zero temperature, it permits ready evaluation at finite U of the one-loop effects of zero-point spin fluctuations on, e.g., the sublattice magnetization. At finite temperatures, thermodynamic properties of the system in the thermal paramagnet are studied via a physically transparent Onsager reaction field approach, which amounts to a self-consistent treatment of paramagnetic spin correlations. This is central not only in recovering the correct dimensionality dependence of antiferromagnetic long-ranged order, but also for the d=3 case of primary interest here yields a N\'eel temperature in close agreement with known strong- and weak-coupling limits. Spin correlation functions and magnetic susceptibilities also show very good agreement with quantum Monte Carlo calculations over an appreciable temperature range in which the low-lying transverse spin excitations are thermally dominant. \textcopyright{} 1996 The American Physical Society.
The magnetic susceptibility of the one-dimensional Hubbard model with open boundary conditions at arbitrary filling is obtained from field theory at low temperatures and small magnetic fields, including leading and next-leading orders. Logarithmic contributions to the bulk part are identified as well as algebraic-logarithmic divergences in the boundary contribution. As a manifestation of spin-charge separation, the result for the boundary part at low energies turns out to be independent of filling and interaction strength and identical to the result for the Heisenberg model. For the bulk part at zero temperature, the scale in the logarithms is determined exactly from the Bethe ansatz. At finite temperature, the susceptibility profile as well as the Friedel oscillations in the magnetisation are obtained numerically from the density-matrix renormalisation group applied to transfer matrices. Agreement is found with an exact asymptotic expansion of the relevant correlation function.
Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.
Correlations of a one-dimensional doubly degenerate Hubbard model are studied for the one-quarter-filled case. Exact calculations on a four-site lattice show that a ferromagnetic state exists in the strong-coupling regime. For a one-dimensional chain, a strong-coupling effective Hamiltonian was studied using a self-consistent calculation, a high-temperature expansion, and quantum Monte Carlo simulations. The results provide information on the parameters needed for ferromagnetic correlations, and the temperature dependence of the spin and orbital correlations.