We present an exact diagonalization study of the low-energy singlet and triplet states for both the one-dimensional (1D) and 2D t-J models. A scan of the parameter ratio J/t shows that for most low-energy states in both 1D and 2D the excitation energy takes the form E(t,J)=a\ensuremath{\cdot}t+b\ensuremath{\cdot}J. In 1D this is the natural consequence of the factorization of the low-energy wave functions, i.e., spin-charge separation. Examination of the low-energy eigenstates in 2D shows that most of these are collective modes, which for larger J correspond to a periodic modulation of the hole density. The modulation is well reproduced by treating holes as hard-core bosons with an attractive interaction.We present an exact diagonalization study of the low-energy singlet and triplet states for both the one-dimensional (1D) and 2D t-J models. A scan of the parameter ratio J/t shows that for most low-energy states in both 1D and 2D the excitation energy takes the form E(t,J)=a\ensuremath{\cdot}t+b\ensuremath{\cdot}J. In 1D this is the natural consequence of the factorization of the low-energy wave functions, i.e., spin-charge separation. Examination of the low-energy eigenstates in 2D shows that most of these are collective modes, which for larger J correspond to a periodic modulation of the hole density. The modulation is well reproduced by treating holes as hard-core bosons with an attractive interaction.

Physical review. B, Condensed matterMay 1, 19978 citations

Single Particle Excitations in the t-J Model

Michael Brunner, C. Lavalle, Fakher F. Assaad +1 more

Springer eBooksJan 1, 20010 citations

Ground state and low-lying excitations in a Heisenberg spin-glass model in three dimensions

Fumitaka Matsubara, Takayuki Shirakura, S. Takahashi +1 more

We developed a hybrid genetic algorithm and studied the ground state and low-lying excitations of the $\ifmmode\pm\else\textpm\fi{}J$ Heisenberg model on a three-dimensional $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L(L\ensuremath{\leqslant}11)$ lattice. Our results suggest occurrence of a Parisi state. That is, there exists a metastable state with a finite energy of $\ensuremath{\Delta}E\ensuremath{\sim}O(J)$ in the thermodynamic limit and the energy barrier $\ensuremath{\Delta}W$ between the metastable state and the ground state is $\ensuremath{\Delta}W\ensuremath{\propto}J{L}^{\ensuremath{\theta}}$ with $\ensuremath{\theta}\ensuremath{\sim}0.53$. Our results also suggest that the energy $\ensuremath{\Delta}E$ of small scale excitations are related to a scale of the excitation $V$ in a similar manner to those of the ferromagnetic model, i.e., $\ensuremath{\Delta}E\ensuremath{\propto}J{L}^{{\ensuremath{\theta}}_{L}}{V}^{{\ensuremath{\theta}}_{v}}$ with ${\ensuremath{\theta}}_{L}\ensuremath{\sim}\ensuremath{-}4.7$ and ${\ensuremath{\theta}}_{v}\ensuremath{\sim}2.0$. This fact suggests that similarity exists in the ground state structure between the $\ifmmode\pm\else\textpm\fi{}J$ and the ferromagnetic Heisenberg models, though the spin directions of those two models differ greatly from one another.We developed a hybrid genetic algorithm and studied the ground state and low-lying excitations of the $\ifmmode\pm\else\textpm\fi{}J$ Heisenberg model on a three-dimensional $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L(L\ensuremath{\leqslant}11)$ lattice. Our results suggest occurrence of a Parisi state. That is, there exists a metastable state with a finite energy of $\ensuremath{\Delta}E\ensuremath{\sim}O(J)$ in the thermodynamic limit and the energy barrier $\ensuremath{\Delta}W$ between the metastable state and the ground state is $\ensuremath{\Delta}W\ensuremath{\propto}J{L}^{\ensuremath{\theta}}$ with $\ensuremath{\theta}\ensuremath{\sim}0.53$. Our results also suggest that the energy $\ensuremath{\Delta}E$ of small scale excitations are related to a scale of the excitation $V$ in a similar manner to those of the ferromagnetic model, i.e., $\ensuremath{\Delta}E\ensuremath{\propto}J{L}^{{\ensuremath{\theta}}_{L}}{V}^{{\ensuremath{\theta}}_{v}}$ with ${\ensuremath{\theta}}_{L}\ensuremath{\sim}\ensuremath{-}4.7$ and ${\ensuremath{\theta}}_{v}\ensuremath{\sim}2.0$. This fact suggests that similarity exists in the ground state structure between the $\ifmmode\pm\else\textpm\fi{}J$ and the ferromagnetic Heisenberg models, though the spin directions of those two models differ greatly from one another.

Physical Review BNov 11, 20047 citations

Excitations and superconductivity in the two-dimensional t-J model

Y. Ohta, Tomohiro Shimozato, R. Eder +1 more

Physica C SuperconductivityDec 1, 19940 citations

Spin and Charge Excitations in the 2D t-J Model

W. O. Putikka, Marco U. Luchini, R. R. P. Singh

APSMar 1, 20000 citations

t−t′−J model in one dimension using extremely correlated Fermi-liquid theory and time-dependent density matrix renormalization group

Peizhi Mai, Steven R. White, B. Sriram Shastry

We study the one-dimensional $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e., the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.We study the one-dimensional $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e., the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong quantum fluctuations inherent in one dimension. The momentum distribution function, the spectral function, and the excitation dispersion of these two methods also compare well.

arXiv:1712.05396Physical review. B./Physical review. BJul 6, 20187 citations

V

in a similar manner to those of the ferromagnetic model, i.e., $\ensuremath{\Delta}E\ensuremath{\propto}J{L}^{{\ensuremath{\theta}}_{L}}{V}^{{\ensuremath{\theta}}_{v}}$ with ${\ensuremath{\theta}}_{L}\ensuremath{\sim}\ensuremath{-}4.7$ and ${\ensuremath{\theta}}_{v}\ensuremath{\sim}2.0$. This fact suggests that similarity exists in the ground state structure between the $\ifmmode\pm\else\textpm\fi{}J$ and the ferromagnetic Heisenberg models, though the spin directions of those two models differ greatly from one another.