Related papers: Characterizing Topological Order with Matrix Produ…
It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped…
I propose to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient is the use of parametric amplifiers in the random network which can in turn be used to…
Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of…
The ground states encode the information of the topological phases of a 2-dimensional system, which makes them crucial in determining the associated topological quantum field theory (TQFT). Most numerical methods for detecting the TQFT…
Mathematical foundation of the novel concept of quantum tensor product by Zanardi et al is rigorously established. The concept of relative quantum entanglement is naturally introduced and its meaning is made clear both mathematically and…
Multipartite entanglement offers a powerful framework for understanding the complex collective phenomena in quantum many-body systems that are often beyond the description of conventional bipartite entanglement measures. Here, we propose a…
Quantum entanglement marks a definitive feature of topological states. However, the entanglement spectrum remains insufficiently explored for topological states without a bulk energy gap. Using a combination of field theory and numerical…
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…
In this paper a duality between the d=2 Wen-plaquette model in a transverse field and the d=1 Ising model in a transverse field is used to learn the nature of the quantum phase transition (QPT) between a spin-polarized phase and a…
A large class of quantum phase transitions for quantum lattice systems are characterized by local order parameters. It is shown that local order parameters may be systematically constructed from tensor network representations of quantum…
Topological semimetals are a class of many-body systems exhibiting novel macroscopic quantum phenomena at the interplay between high energy and condensed matter physics. They display a topological quantum phase transition (TQPT) which…
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…
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…
Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…
We introduce a many-body topological invariant, called the topological disorder parameter (TDP), to characterize gapped quantum phases with global internal symmetry in (2+1)d. TDP is defined as the constant correction that appears in the…
We study the entanglement structure of Abelian topological order described by $p$-form BF theory in arbitrary dimensions. We do so directly in the low-energy topological quantum field theory by considering the algebra of topological surface…
For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at…
Quantifying entanglement is one of the most important tasks in the entanglement theory. In this paper, we establish entanglement monotones in terms of an operational approach, which is closely connected with the state conversion from pure…
Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When…
Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the…