One-dimensional symmetry protected topological phases and their transitions

By R. Verresen, Roderich Moessner, Frank Pollmann. 2017

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We present a unified perspective on symmetry protected topological (SPT) phases in one dimension and address the open question of what characterizes their phase transitions. In the first part of this work we use symmetry as a guide to map various well-known fermionic and spin SPTs to a Kitaev chain with coupling of range $\alpha \in \mathbb Z$. This unified picture uncovers new properties of old models --such as how the cluster state is the fixed point limit of the Affleck-Kennedy-Lieb-Tasaki state in disguise-- and elucidates the connection between fermionic and bosonic phases --with the Hubbard chain interpolating between four Kitaev chains and a spin chain in the Haldane phase. In the second part, we study the topological phase transitions between these models in the presence of interactions. This leads us to conjecture that the critical point between any SPT with $d$-dimensional edge modes and the trivial phase has a central charge $c \geq \log_2 d$. We analytically verify this for many known transitions. This agrees with the intuitive notion that the phase transition is described by a delocalized edge mode, and that the central charge of a conformal field theory is a measure of the gapless degrees of freedom.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/e40ea00e9f403707adc832c908857de7e222ec6a

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, background): “[54] Ruben Verresen, Roderich Moessner, and Frank Pollmann, “One-dimensional symmetry protected topological phases and their transitions,” Phys.”