Regensburg 2019 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 3: Topological Insulators (joint session TT/MA)

TT 3.3: Vortrag

Montag, 1. April 2019, 10:00–10:15, Theater

Quantum Phase Transitions between Z_n×Z_n Symmetry Protected Topological Phases — •Julian Bibo¹, Ruben Verresen^1,2, and Frank Pollmann¹ — ¹Technische Universität München — ²Max-Planck-Institut für komplexe Systeme, Dresden

Symmetry protected topological (SPT) phases are phases of matter without local order parameters. Instead, they are characterized by how a global symmetry G acts projectively on the edges. The projective transformations at the boundaries are in turn classified by the second cohomology group H²(G,U(1)). Given this classification scheme, we can construct so called fixed-point models describing the universal features of these phases. For G = Z_n×Z_n, there are n−1 non-trivial SPT phases and hence n−1 fixed-point models. For n≤ 4, it has been proven that the corresponding fixed-point models have direct transitions between adjacent phases. For n≥ 5, however, the expectation was that there are intermediate gapless phases instead of direct transitions. Contrary to this expectation, we use local symmetries to construct a path, proving that there are indeed direct transitions in cases, where n is divisible by 2, 3 or 4. We numerically confirm these arguments and show that these transitions are not fine-tuned.