Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach
We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-s...
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Nature Publishing Group
2015
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4286789/ |
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pubmed-42867892015-01-16 Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach Shi, Qian-Qian Zhou, Huan-Qiang Batchelor, Murray T. Article We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-size scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two H-orthogonal states and the energy gap between the ground state and low-lying excited states in the finite-size system. The physical information encoded in this gap arising from finite-size fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the one-dimensional quantum formulation of the q-state Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finite-size data obtained from the density matrix renormalization group algorithm. Nature Publishing Group 2015-01-08 /pmc/articles/PMC4286789/ /pubmed/25567585 http://dx.doi.org/10.1038/srep07673 Text en Copyright © 2015, Macmillan Publishers Limited. All rights reserved http://creativecommons.org/licenses/by-nc-nd/4.0/ This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Shi, Qian-Qian Zhou, Huan-Qiang Batchelor, Murray T. |
| spellingShingle |
Shi, Qian-Qian Zhou, Huan-Qiang Batchelor, Murray T. Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach |
| author_facet |
Shi, Qian-Qian Zhou, Huan-Qiang Batchelor, Murray T. |
| author_sort |
Shi, Qian-Qian |
| title |
Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach |
| title_short |
Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach |
| title_full |
Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach |
| title_fullStr |
Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach |
| title_full_unstemmed |
Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach |
| title_sort |
universal order parameters and quantum phase transitions: a finite-size approach |
| description |
We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-size scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two H-orthogonal states and the energy gap between the ground state and low-lying excited states in the finite-size system. The physical information encoded in this gap arising from finite-size fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the one-dimensional quantum formulation of the q-state Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finite-size data obtained from the density matrix renormalization group algorithm. |
| publisher |
Nature Publishing Group |
| publishDate |
2015 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4286789/ |
| _version_ |
1613174112055721984 |