Abstract The properties of the bound states on a lattice is an interesting problem related to the properties of superconductivity and Bose–Einstein condensation in a given model. By means of the exact solution of the Schrödinger equation the properties of the bound pairs on a frustrated, triangular lattice are examined within extended Hubbard model. Dispersion curves and mobilities are calculated for both positive and negative sign of the hopping integral. The possibility of increasing the mobility with increasing intersite Coulomb interaction is found. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)Abstract The properties of the bound states on a lattice is an interesting problem related to the properties of superconductivity and Bose–Einstein condensation in a given model. By means of the exact solution of the Schrödinger equation the properties of the bound pairs on a frustrated, triangular lattice are examined within extended Hubbard model. Dispersion curves and mobilities are calculated for both positive and negative sign of the hopping integral. The possibility of increasing the mobility with increasing intersite Coulomb interaction is found. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)Apr 12, 200711 citations

The Ground State for the Hubbard Model on Finite Frustrated Lattices

Kazuhiro Sano, Ken'ichi Takano

The Hubbard Hamiltonian with infinite on-site repulsion and negative transfer is diagonalized numerically on 3×3 frustrated lattices, such as the square lattice with next-nearest-neighbor transfer and the triangular lattice. The number of electrons is chosen to be less by just one electron than that in the exactly half-filled band. When the strength of the frustration is sufficiently large, a singlet state appears as the ground state. Then, the total spin of the lowest excited state is unity. There is an excitation gap for the square lattice but not for the triangular lattice.The Hubbard Hamiltonian with infinite on-site repulsion and negative transfer is diagonalized numerically on 3×3 frustrated lattices, such as the square lattice with next-nearest-neighbor transfer and the triangular lattice. The number of electrons is chosen to be less by just one electron than that in the exactly half-filled band. When the strength of the frustration is sufficiently large, a singlet state appears as the ground state. Then, the total spin of the lowest excited state is unity. There is an excitation gap for the square lattice but not for the triangular lattice.

Journal of the Physical Society of JapanDec 15, 19878 citations

Hubbard Model on a Triangular Lattice at Finite Temperatures

A. Sherman

arXiv:2406.13289Journal of Low Temperature PhysicsAug 4, 20240 citations

Site-resolved observables in the doped spin-imbalanced triangular Hubbard model

Davis Garwood, Jirayu Mongkolkiattichai, Liyu Liu +2 more

The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a numerical linked-cluster expansion algorithm. We investigate the Mott insulator transition finding a critical interaction ${U}_{c}/t=7.0(2)$ and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a numerical linked-cluster expansion algorithm. We investigate the Mott insulator transition finding a critical interaction ${U}_{c}/t=7.0(2)$ and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.

arXiv:2205.12233Physical Review AJul 11, 202216 citations

Attractive Hubbard pairing in a triangular lattice

Oracio Navarro, Luis Antonio Pérez, C. Wang

Physica C SuperconductivityDec 1, 19941 citation

{U}_{c}/t=7.0(2)

and use spatial two- and three-point correlation functions to explore doped and imbalanced systems. Our results demonstrate that many interesting features occur at temperatures previously obtained for ultracold fermions in optical lattices and are accessible by upcoming experiments. Our calculations will be helpful for thermometry in ultracold atom quantum simulators and can guide experimental searches for exotic quantum phases in atomic triangular Hubbard quantum simulators.