Berry’s geometric phase can be defined for a single Bloch band, or for a group of bands, and allows for integer characterization of topological phases via the TKNN (Chern) numbers. \u00a0An extension of Berry’s phase to density matrices, first discussed by Uhlmann [Rep. Math. Phys. 24, 229 (1986)], generalizes Berry’s phase in such a way that finite temperature can be accommodated. \u00a0Topological phases at finite temperature can thereby be characterized by one or more integers in such a way that reduces to the conventional TKNN description at T=0, yet change discretely at one or more critical temperatures. \u00a0We demonstrate these ideas, and their limitations, in detail, using Haldane’s honeycomb lattice model, and comment on their generalization to multi-band Chern insulators and Z_2 topological insulators.<\/p>\n
Authors:
Zhoushen Huang
Daniel Arovas<\/p>\n","protected":false},"excerpt":{"rendered":"
Daniel Arovas Berry’s geometric phase can be defined for a single Bloch band, or for a group of bands, and allows for integer characterization of topological phases via the TKNN (Chern) numbers. \u00a0An extension of Berry’s phase to density matrices, first discussed by Uhlmann [Rep. Math. Phys. 24, 229 (1986)], generalizes Berry’s phase in such …<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-17","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-uncategorized","7":"entry"},"yoast_head":"\n