Topological phase transitions in glassy quantum matter
Amorphous systems have rapidly gained attention as promising platforms for topological matter. In this work, we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topologic...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.013053 |
| _version_ | 1797211607730749440 |
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| author | Isac Sahlberg Alex Westström Kim Pöyhönen Teemu Ojanen |
| author_facet | Isac Sahlberg Alex Westström Kim Pöyhönen Teemu Ojanen |
| author_sort | Isac Sahlberg |
| collection | DOAJ |
| description | Amorphous systems have rapidly gained attention as promising platforms for topological matter. In this work, we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topological invariants averaged over discrete and continuum random geometries, we discover critical properties of Chern and Z_{2} glass transitions. Even for short-range hopping models, the Chern glass phase may persist down to the fundamental lower bound given by the classical percolation threshold. While the topological indices accurately satisfy the postulated one-parameter scaling, they do not generally flow to the closest integer value in the thermodynamic limit. Furthermore, the value of the critical exponent describing the diverging localization length varies continuously along the phase boundary and is not fixed by the symmetry class of the Hamiltonian. We conclude that the critical behavior of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of interesting research directions. |
| first_indexed | 2024-04-24T10:29:11Z |
| format | Article |
| id | doaj.art-6b0e10f0b5e7447c944d7b721b40ab80 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:29:11Z |
| publishDate | 2020-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-6b0e10f0b5e7447c944d7b721b40ab802024-04-12T16:48:48ZengAmerican Physical SocietyPhysical Review Research2643-15642020-01-012101305310.1103/PhysRevResearch.2.013053Topological phase transitions in glassy quantum matterIsac SahlbergAlex WestströmKim PöyhönenTeemu OjanenAmorphous systems have rapidly gained attention as promising platforms for topological matter. In this work, we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topological invariants averaged over discrete and continuum random geometries, we discover critical properties of Chern and Z_{2} glass transitions. Even for short-range hopping models, the Chern glass phase may persist down to the fundamental lower bound given by the classical percolation threshold. While the topological indices accurately satisfy the postulated one-parameter scaling, they do not generally flow to the closest integer value in the thermodynamic limit. Furthermore, the value of the critical exponent describing the diverging localization length varies continuously along the phase boundary and is not fixed by the symmetry class of the Hamiltonian. We conclude that the critical behavior of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of interesting research directions.http://doi.org/10.1103/PhysRevResearch.2.013053 |
| spellingShingle | Isac Sahlberg Alex Westström Kim Pöyhönen Teemu Ojanen Topological phase transitions in glassy quantum matter Physical Review Research |
| title | Topological phase transitions in glassy quantum matter |
| title_full | Topological phase transitions in glassy quantum matter |
| title_fullStr | Topological phase transitions in glassy quantum matter |
| title_full_unstemmed | Topological phase transitions in glassy quantum matter |
| title_short | Topological phase transitions in glassy quantum matter |
| title_sort | topological phase transitions in glassy quantum matter |
| url | http://doi.org/10.1103/PhysRevResearch.2.013053 |
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