# DMRG studies of ferromagnetic phase diagram of infinite-U hubbard ladders

## Abstract/Contents

- Abstract
- The Hubbard model is one of the most important models in theoretical condensed matter physics. The model, which captures the strong interactions among the electrons, has not been solved analytically in more than one dimension. Therefore, over the past tens of year, there has been a tremendous analytic and computational effort to understand the parameter dependent ground state of this model, especially for intermediate strengths of the on-site repulsion U - the regime of parameters relevant to the properties of real material. Possible approaches to understand this model includes perturbative methods which start with the non-interacting kinetic term and treats the potential to low order in an expansion in powers of the interaction strength. A less intuitive approach is to attack the problem from the opposite extreme U> > t, where t is the electron hopping matrix element. In my thesis, I present the results concerning the ground-state phase diagram of Hubbard model in the infinite-U limit with an emphasis on the 2-leg ladder and the extrapolation of these results to the 2D limit. We will show that there is a half metallic ferromagnetic ground state when the density of electrons per site n> =n_c ~ 0.80. When n=0.75, the ground state is a commensurate anti-ferromagnetically ordered plaquette phase with bond density order. We show evidence that in the range of n between n_c and 0.75, the ground state is phase separated between these two states. These properties hold not only for the two-leg ladder, but wider ladders as well, which we assume implies that they continue smoothly to the fully 2D limit. However for 0.75 > n > 0.5 while the ground state is found to be unpolarized for wider ladders, the two leg ladder exhibits a partially polarized ferromagnetic ground state , with a peak in the magnetization density occurring at around n=2/3 where we have demonstrated the existence of another commensurate phase. The ground state of the 2-leg ladder when n=0.5 is an anti-ferromagnetic dimerized phase. A study of the charge carrying elementary excitations in the various commensurate phases suggests that there are further intermediate phases rather than direct first order transitions between them. Moving from infinite to large but finite U, we trace out the boundary of half metallic ferromagnetic phase of the 2-leg ladder as a function of n and U. As the transition seems to be everywhere first order, we propose that outside this phase gives way to a phase-separated ground state between such boundary and the two commensurate phases at n=1 and n=3/4 respectively. The plaquette phase is observed to be stable down to at least values of U~20t, but below a smaller critical value of U/t the ground state enters a stripe ordered phase. We also test the correspondence between Hubbard and t-J at least down to values of U~100t.

## Description

Type of resource | text |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Publication date | 2014 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Liu, Li | |
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Associated with | Stanford University, Department of Physics. | |

Primary advisor | Kivelson, Steven | |

Thesis advisor | Kivelson, Steven | |

Thesis advisor | Qi, Xiaoliang | |

Thesis advisor | Raghu, Srinivas, 1978- | |

Advisor | Qi, Xiaoliang | |

Advisor | Raghu, Srinivas, 1978- |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Li Liu. |
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Note | Submitted to the Department of Physics. |

Thesis | Thesis (Ph.D.)--Stanford University, 2014. |

Location | electronic resource |

## Access conditions

- Copyright
- © 2014 by Li Liu
- License
- This work is licensed under a Creative Commons Attribution Share Alike 3.0 Unported license (CC BY-SA).

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