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Kosterlitz-Thouless Phase Transition and Ground State Fidelity: a Novel Perspective from Matrix Product States
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wang, Hong-Lei Zhao, Jian-Hui Zhou, Huan-Qiang |
| Copyright Year | 2009 |
| Abstract | The Kosterlitz-Thouless transition is studied from the representation of the systems's ground state wave functions in terms of Matrix Product States for a quantum system on an infinite-size lattice in one spatial dimension. It is found that, in the critical regime for a one-dimensional quantum lattice system with continuous symmetry, the newly-developed infinite Matrix Product State algorithm automatically leads to infinite degenerate ground states, due to the finiteness of the truncation dimension. This results in \textit{pseudo} continuous symmetry spontaneous breakdown, which allows to introduce a pseudo-order parameter that must be scaled down to zero, in order to be consistent with the Mermin-Wegner theorem. We also show that the ground state fidelity per lattice site exhibits a \textit{catastrophe point}, thus resolving a controversy regarding whether or not the ground state fidelity is able to detect the Kosterlitz-Thouless transition. |
| File Format | PDF HTM / HTML |
| DOI | 10.1088/1742-5468/2011/10/L10001 |
| Alternate Webpage(s) | https://arxiv.org/pdf/0902.1670v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1088/1742-5468%2F2011%2F10%2FL10001 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
