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Symmetry-protected topological (SPT) phases are short-range entangled quantum phases with symmetry, which have gapped excitations in the bulk and gapless modes at the edge. In this paper, we study the SPT phases in the spin-1 Heisenberg…

We explore 1+1 dimensional (1+1D) gapped phases in systems with non-invertible symmetries, focusing on symmetry-protected topological (SPT) phases (defined as gapped phases with non-degenerate ground states), as well as SPT orders (defined…

The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained (in part) from momentum space. Recently, Real Space…

We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…

Quantum many-body systems undergoing phase transitions have been proposed as probes enabling beyond-classical enhancement of sensing precision. However, this enhancement is usually limited to a very narrow region around the critical point.…

Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order…

We study several aspects of the realization of global symmetries in highly entangled phases of quantum matter. Examples include gapped topological ordered phases, gapless quantum spin liquids and non-fermi liquid phases. An insightful…

We propose a new theoretical method to describe the monitored dynamics of bosonic many-body systems based on the concept of the most likely trajectory. We show how such trajectory can be identified from the probability distribution of…

Quantum entanglement is a powerful quantum resource for enhancing measurement precision beyond classical limit. % Here we propose an entanglement-enhanced symmetry-protected destructive many-body Ramsey interferometry for precise parameter…

Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the symmetry. It has been shown that a large…

Identifying topological properties is a major challenge because, by definition, topological states do not have a local order parameter. While a generic solution to this challenge is not available yet, a broad class of topological states,…

We propose an order parameter for the Symmetry-Protected Topological (SPT) phases which are protected by Abelian on-site symmetries. This order parameter, called the "SPT-entanglement", is defined as the entanglement between A and B, two…

We investigate the influence of local decoherence on a symmetry-protected topological (SPT) phase of the two-dimensional (2D) cluster state. Mapping the 2D cluster state under decoherence to a classical spin model, we show a topological…

We propose a diagnostic tool for detecting non-trivial symmetry protected topological (SPT) phases protected by a symmetry group $G$ in 2+1 dimensions. Our method is based on directly studying the 1+1-dimensional anomalous edge conformal…

Entanglement entropy has become an important theoretical concept in condensed matter physics, because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental…

We propose that ultracold alkaline-earth-like atoms confined in one-dimensional optical lattice can realize a Kondo lattice model which hosts a symmetry-protected topological (SPT) phase and an associated quantum phase transition in a…

We investigate topological signatures in the short-time non-equilibrium dynamics of symmetry protected topological (SPT) systems starting from initial states which break the protecting symmetry. Na\"ively, one might expect that topology…

Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group…

In quantum multiparameter estimation, multiple to-be-estimated parameters are encoded in a quantum dynamics system by a unitary evolution. As the parameters vary, the system may undergo a topological phase transition (TPT). In this paper,…

Symmetry protected topological (SPT) phases with unusual edge excitations can emerge in strongly interacting bosonic systems and are classified in terms of the cohomology of their symmetry groups. Here we provide a physical picture that…