Symmetry Protected Topological phases of Quantum Matter

By T. Senthil. 2014

500 citations recorded by the source corpus.

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting many particle systems, known as Symmetry Protected Topological (SPT) phases. In common with the topological band insulators these states have a bulk gap and no exotic excitations but have non-trivial surface states that are protected by symmetry. We describe the various possible such phases and their properties in three dimensional systems with realistic symmetries. We develop many key ideas of the theory of these states using simple examples. The emphasis is on physical rather than mathematical properties. We survey insights obtained from the study of SPT phases for a number of other theoretical problems.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/0fe5a2d3f31ad4ac6135f76407a723b22d3f7907

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016, background): “[28] is suitable for the context of probing the global-symmetry protected states, so-called Symmetry Protected Topological states [45] (SPTs, see [10, 46, 47] for recent reviews).”
Generalized Symmetries in Condensed Matter (2022, unknown): “One way to define (48) a Symmetry-Protected Topological (SPT) phase is as a nontrivial phase of matter (with some symmetry G) without topological order (for a review, see (49)).”
Topological bands for ultracold atoms (2018, unknown): “Hence these states have a unique ground state on a periodic geometry, and the many-body ground state has only short-range entanglement (Senthil, 2015).”
Three-dimensional all-dielectric photonic topological insulator (2016, background): “Following the footsteps of condensed matter topological systems, a significant progress has been recently made in understanding and realizing topological states for bosons [ 1, 2, 3, 4, 5] and in classical systems [ 6, 7, 8, 9, 10, 11, 12, 13, 14 15, 16, 17, 18, 19, 20, 21, 22, 23].”
Self-induced topological transitions and edge states supported by nonlinear staggered potentials (2015, unknown): “Driven by recent advances in understanding topological phases in condensed matter physics [1]-[10], there has been a significant interest in engineering or emulating topological states in classical [11]-[17] and bosonic [18]-[22] systems.”
Many-Body Quantum Magic (2020, background): “[95, 96] for introductions) and in particular, been studied as a useful type of many-body resource states useful for MBQC (see, e.”
Classification of topological quantum matter with symmetries (2015, methodology): “…Metlitski et al., 2013; Vishwanath and Senthil, 2013; Wang and Senthil, 2013), a. Application to class DIII TSC Let us now discuss how the vortex condensation approach works for the 3d class DIII TSC with an even number ν of Majorana surface cones (Metlitski et al., 2014; Wang and Senthil, 2014).”