The influence of the staggered magnetic field h on properties of the one-dimensional t-J and Hubbard models with nearly half-filled bands are studied. Using the exact diagonalization method for small systems as well as analytical approaches possible in the anisotropic model and for h\ensuremath{\gg}t, we determine the phase diagram of the t-J-h model at low doping, which displays three different regimes: the phase with repelling holes for J ${\mathit{J}}_{\mathit{c}}$ , the phase with paired holes for ${\mathit{J}}_{\mathit{c}}$ J ${\mathit{J}}_{\mathit{s}}$ , and the phase separation for J> ${\mathit{J}}_{\mathit{s}}$ . Employing for h\ensuremath{\ne}0 the analogy with the universal behavior of one-dimensional interacting fermions within the Luther-Emery regime, we calculate the charge exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$, which can be ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1 in the pairing regime, indicating dominant superconducting fluctuations. An analogous analysis, in particular the perturbation expansion in t/h, performed for the Hubbard t-U-h model shows a phase of stable hole pairs for U ${\mathit{U}}_{\mathit{c}}$ . Again ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ seems to approach a nonuniversal value at half-filling.The influence of the staggered magnetic field h on properties of the one-dimensional t-J and Hubbard models with nearly half-filled bands are studied. Using the exact diagonalization method for small systems as well as analytical approaches possible in the anisotropic model and for h\ensuremath{\gg}t, we determine the phase diagram of the t-J-h model at low doping, which displays three different regimes: the phase with repelling holes for J${\mathit{J}}_{\mathit{c}}$, the phase with paired holes for ${\mathit{J}}_{\mathit{c}}$J${\mathit{J}}_{\mathit{s}}$, and the phase separation for J>${\mathit{J}}_{\mathit{s}}$. Employing for h\ensuremath{\ne}0 the analogy with the universal behavior of one-dimensional interacting fermions within the Luther-Emery regime, we calculate the charge exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$, which can be ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1 in the pairing regime, indicating dominant superconducting fluctuations. An analogous analysis, in particular the perturbation expansion in t/h, performed for the Hubbard t-U-h model shows a phase of stable hole pairs for U${\mathit{U}}_{\mathit{c}}$. Again ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ seems to approach a nonuniversal value at half-filling.

Physical review. B, Condensed matterMay 1, 19934 citations

Ferromagnetic domains in the large- $U$ Hubbard model with a few holes: an FCIQMC studyFerromagnetic domains in the large-$U$ Hubbard model with a few holes: an FCIQMC study

Yun, Sujun, Werner Dobrautz, Luo Hongjun +3 more

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large- $U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$ ), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$ . The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or $\frac{1}{2}$ , depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.Two-dimensional Hubbard lattices with two or three holes are investigated as a function of $U$ in the large-$U$ limit. In the so-called Nagaoka limit (one-hole system at infinite $U$), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing $U$. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or $\frac{1}{2}$, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.

arXiv:2210.12049Oct 21, 20221 citation

Hole pairing in the Hubbard model

Luis Antonio Pérez, C. Wang

Journal of Magnetism and Magnetic MaterialsJan 1, 19981 citation

Hole pairing in an extended Hubbard model

J. H. Jefferson

Physica B Condensed MatterApr 1, 19902 citations

{\mathit{J}}_{\mathit{c}}

, the phase with paired holes for

{\mathit{J}}_{\mathit{c}}

{\mathit{J}}_{\mathit{s}}

, and the phase separation for J>

{\mathit{J}}_{\mathit{s}}

. Employing for h\ensuremath{\ne}0 the analogy with the universal behavior of one-dimensional interacting fermions within the Luther-Emery regime, we calculate the charge exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$, which can be ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$>1 in the pairing regime, indicating dominant superconducting fluctuations. An analogous analysis, in particular the perturbation expansion in t/h, performed for the Hubbard t-U-h model shows a phase of stable hole pairs for U

{\mathit{U}}_{\mathit{c}}

. Again ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ seems to approach a nonuniversal value at half-filling.

Ferromagnetic domains in the large-

U

Hubbard model with a few holes: an FCIQMC study

Two-dimensional Hubbard lattices with two or three holes are investigated as a function of

U

in the large-

U

limit. In the so-called Nagaoka limit (one-hole system at infinite

U

), it is known that the Hubbard model exhibits a ferromagnetic ground-state. Here, by means of exact FCIQMC simulations applied to periodic lattices up to 24 sites, we compute spin-spin correlation functions as a function of increasing

U

. The correlation functions clearly demonstrate the onset of ferromagnetic domains, centred on individual holes. The overall total spin of the wavefunctions remain the lowest possible (0, or

\frac{1}{2}

, depending on the number of holes). The ferromagnetic domains appear at interaction strengths comparable to the critical interaction strengths of the Nagaoka transition in finite systems with strictly one hole. The existence of such ferromagnetic domains is the signature of Nagaoka physics in Hubbard systems with a small (but greater than one) number of holes.