The renormalization of the extended Hubbard model proposed by Zhang and Rice [Phys. Rev. B 37, 3759 (1988)] that leads to the (nearest-neighbor-only) t-J model is scrutinized in the infinite correlation limit. We demonstrate that the ${U}_{d}$ , ${U}_{p}$ \ensuremath{\rightarrow}\ensuremath{\infty} limit obtained from the extended Hubbard model does not have the same ground state as the U\ensuremath{\rightarrow}\ensuremath{\infty} extrapolation of the t-J model.The renormalization of the extended Hubbard model proposed by Zhang and Rice [Phys. Rev. B 37, 3759 (1988)] that leads to the (nearest-neighbor-only) t-J model is scrutinized in the infinite correlation limit. We demonstrate that the ${U}_{d}$,${U}_{p}$\ensuremath{\rightarrow}\ensuremath{\infty} limit obtained from the extended Hubbard model does not have the same ground state as the U\ensuremath{\rightarrow}\ensuremath{\infty} extrapolation of the t-J model.

Physical review. B, Condensed matterFeb 1, 199021 citations

Ground States of the Hubbard Model

Assa Auerbach

Graduate texts in contemporary physicsJan 1, 19940 citations

The ground state of the Hubbard model

E. O. Aiyohuyin, A. A. Oni-Ojo

Journal of the Nigerian Association of Mathematical PhysicsJun 13, 20080 citations

Mapping the Hubbard model to the t-J model using ground state unitary transformations

Yifan Tian

The effective low-energy models of the Hubbard model are usually derived from perturbation theory. Here we derive the effective model of the Hubbard model in spin space and t-J space using a unitary transformation from numerical optimization. We represent the Hamiltonian as Matrix product state(MPO) and represent the unitary transformation using gates according to tensor network methods. We obtain this unitary transformation by optimizing the unitary transformation between the ground state of the Hubbard model and the projection of the Hubbard model ground state into spin space and t-J space. The unitary transformation we get from numerical optimization yields effective models that are in line with perturbation theories. This numerical optimization method starting from ground state provides another approach to analyze effective low-energy models of strongly correlated electron systems.The effective low-energy models of the Hubbard model are usually derived from perturbation theory. Here we derive the effective model of the Hubbard model in spin space and t-J space using a unitary transformation from numerical optimization. We represent the Hamiltonian as Matrix product state(MPO) and represent the unitary transformation using gates according to tensor network methods. We obtain this unitary transformation by optimizing the unitary transformation between the ground state of the Hubbard model and the projection of the Hubbard model ground state into spin space and t-J space. The unitary transformation we get from numerical optimization yields effective models that are in line with perturbation theories. This numerical optimization method starting from ground state provides another approach to analyze effective low-energy models of strongly correlated electron systems.

arXiv:1908.03979Aug 12, 20190 citations

Ground state wave functions for single-band Hubbard models from the Gutzwiller conjugate gradient minimisation theory

Zhuo Ye, Feng Zhang, Yongxin Yao +2 more

The Gutzwiller conjugate gradient minimisation (GCGM) theory is an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. Previous applications of GCGM provides satisfying accuracy of ground-state energy of Hubbard models. In the current work, we address the problem of whether the obtained wave function is a good approximation for the true ground state by comparing the correlation functions with the benchmark data. Our results confirms the accuracy of the reproduced ground state of the regular Hubbard model, but with some exception for the frustrated Hubbard model.The Gutzwiller conjugate gradient minimisation (GCGM) theory is an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. Previous applications of GCGM provides satisfying accuracy of ground-state energy of Hubbard models. In the current work, we address the problem of whether the obtained wave function is a good approximation for the true ground state by comparing the correlation functions with the benchmark data. Our results confirms the accuracy of the reproduced ground state of the regular Hubbard model, but with some exception for the frustrated Hubbard model.

Molecular PhysicsJul 22, 20206 citations

{U}_{d}

{U}_{p}

\ensuremath{\rightarrow}\ensuremath{\infty} limit obtained from the extended Hubbard model does not have the same ground state as the U\ensuremath{\rightarrow}\ensuremath{\infty} extrapolation of the t-J model.