2018
DOI: 10.1088/1367-2630/aadf67
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Qsymm: algorithmic symmetry finding and symmetric Hamiltonian generation

Abstract: Symmetry is a guiding principle in physics that allows us to generalize conclusions between many physical systems. In the ongoing search for new topological phases of matter, symmetry plays a crucial role by protecting topological phases. We address two converse questions relevant to the symmetry classification of systems: is it possible to generate all possible single-body Hamiltonians compatible with a given symmetry group? Is it possible to find all the symmetries of a given family of Hamiltonians? We prese… Show more

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Cited by 46 publications
(36 citation statements)
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“…However, the full symmetry group is much larger. Using the Qsymm software package [59], we find that our quasicrystal HOTI model has a symmetry group with 64 elements. It is generated by C 8 M , a mirror plane orthogonal to the plane of the system M x , particle-hole symmetry P, and an effective time reversal symmetry T .…”
Section: Effect Of Other Symmetriesmentioning
confidence: 99%
“…However, the full symmetry group is much larger. Using the Qsymm software package [59], we find that our quasicrystal HOTI model has a symmetry group with 64 elements. It is generated by C 8 M , a mirror plane orthogonal to the plane of the system M x , particle-hole symmetry P, and an effective time reversal symmetry T .…”
Section: Effect Of Other Symmetriesmentioning
confidence: 99%
“…By making use of the Python package Qsymm, 55 we generate all symmetry-allowed SOC terms up to nearest neighbors and also include symmetry-allowed, next-…”
Section: B Spin-orbit Coupling From Symmetriesmentioning
confidence: 99%
“…[H, S] = 0 for all S symmetries above. This can be easily implemented in using the Qsymm Python's package [37]. Splitting the resulting terms as H = H 0 + H A + H Z + H ft , we obtain…”
Section: Acknowledgementsmentioning
confidence: 99%
“…The band structures from the effective Hamiltonians are compared with ab initio results obtained from density functional theory (DFT). The effective Hamiltonians are obtained with support from Qsymm python's package [37], and the tight-binding models are implemented with Kwant python's package [38]. All codes, input and data files are available as Supplemental Material [39].…”
Section: Introductionmentioning
confidence: 99%