Fracton Topological Order

Out-of-Time-Ordered Correlator

Symmetry protected topological (SPT) phases

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Symmetry protected topological phases have the exotic property of hosting gapless / nontrivial edge states around an otherwise ‘normal’ looking bulk. The non-trivialness of the phases is protected by certain global symmetry of the system, like time reversal, charge conservation, spin rotation, etc. Such phases lie outside the conventional symmetry breaking paradigm of Landau and generalize the special properties of topological insulators and superconductors from free fermion systems to general interacting boson, fermion and spin systems. We did a series of work on constructing models with nontrivial SPT orders, exploring their physical properties (exotic edge states), and classifying all possible SPT phases. Related publications can be found here.

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Symmetry fractionalization

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Quantum phases with intrinsic topological order host anyonic excitations which posses fractional statistics. In addition to that, when the system has global symmetries, the anyonic excitations can also transform in a fractional way under the symmetry action. For example, they can carry fractional charges of charge conservation symmetry or be Kramer doubles under time reversal symmetry. This is the phenomenon of symmetry fractionalization. Our work tries to understand what symmetry fractionalization patterns are possible and how they can be realized. In particular, it was realized that there exists a set of consistent looking symmetry fractionalization patterns which are actually anomalous and cannot be realized on their own. We proposed various methods to for their detection and demonstrated that they can be realized as the surface state of a system in one higher dimension. Related publications can be found here.

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Tensor network representation

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The tensor network formalism provides an efficient representation of many-body entangled wave functions satisfying an area law and therefore has become a powerful tool in both the analytical and numerical study of strongly interacting condensed matter systems. We are interested in using the tensor network representation to study systems with nontrivial topological order. In particular, we focus on questions like: what kind of topological order can be represented with tensors, how to extract the topological order encoded in local tensors and in general how to simulate strongly interacting systems in a more efficient way. Related publications can be found here.

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Other Projects

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We are generally interested in topics in condensed matter / quantum information theory, especially in many-body entangled strongly interacting systems and how that entanglement can give rise to nontrivial physical properties or be useful for quantum information processing. Related publications can be found here.

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