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Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture…
Quantum spin models find applications in many different areas, such as spintronics, high-Tc superconductivity, and even complex optimization problems. However, studying their many-body behaviour, especially in the presence of frustration,…
Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly…
Symmetry-protected topological phases (SPTs) characterized by short-range entanglement include many states essential to understanding of topological condensed matter physics, and the extension to gapless SPTs provides essential…
The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels.…
There have been considerable efforts devoted to the study of topological phases in certain non-Hermitian systems that possess real eigenfrequencies in the presence of gain and loss. However, it is challenging to experimentally realize such…
Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal…
We introduce and study dynamical probes of band structure topology in the post-quench time-evolution from mixed initial states of quantum many-body systems. Our construction generalizes the notion of dynamical quantum phase transitions…
We report the observation of a symmetry-protected topological time crystal, which is implemented with an array of programmable superconducting qubits. Unlike the time crystals reported in previous experiments, where spontaneous breaking of…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
The classification of symmetry-protected topological (SPT) phases in one dimension has been recently achieved, and had a fundamental impact in our understanding of quantum phases in condensed matter physics. In this framework, SPT phases…
We show how combining a discrete symmetry with topological Hilbert space fragmentation can give rise to exponentially many topologically stable qubits protected by a single discrete symmetry. We illustrate this explicitly with the example…
Gapped interfaces (and boundaries) of two-dimensional (2D) Abelian topological phases are shown to support a remarkably rich sequence of 1D symmetry-protected topological (SPT) states. We show that such interfaces can provide a physical…
Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected topological (SPT) phases in interacting…
Harnessing topological phases with their dissipationless edge-channels coupled with the effective engineering of quantum phase transitions is a spinal aspect of topological electronics. The accompanying symmetry protection leads to…
Topological phases have been extensively studied over the past two decades, primarily in quantum pure states, where they are protected by exact symmetries. Recently, numerous studies have theoretically demonstrated the existence of average…
The program of classifying symmetry protected topological (SPT) phases in 1D has been recently completed and has opened the doors to study closely the properties of systems belonging to these phases. It was recently found that being able to…
A higher-order (HO) symmetry-protected topological (SPT) state can be realized in a plaquette-modulated square lattice antiferromagnet, which hosts a spin-$1/2$ degenerate mode on each corner of the lattice with open boundaries. In this…
The interplay between topology and non-Hermiticity gives rise to exotic dynamic phenomena that challenge conventional wave-packet propagation and entanglement dynamics. While recent studies have established the non-Hermitian skin effect…
Decades of research have revealed a deep understanding of topological quantum matter with protected edge modes. We report that even richer physics emerges when tuning between two topological phases of matter whose respective edge modes are…