Related papers: Detecting two dimensional symmetry protected topol…
We present an experimentally feasible and efficient method for detecting entangled states with measurements that extend naturally to a tomographically complete set. Our detection criterion is based on measurements from subsets of a quantum…
We propose a set of constraints on the ground-state wavefunctions of fracton phases, which provide a possible generalization of the string-net equations used to characterize topological orders in two spatial dimensions. Our constraint…
Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. We consider topological phase…
We study anomalies of discrete internal global symmetry $G$ in two-dimensional rational conformal field theories based on twisted torus partition functions. The anomaly of $G$ can be seen from the noncommutativity of two symmetry lines…
We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it…
Through the study of the Rep($D_8$) non-invertible symmetry, we show how non-invertible symmetries manifest in dynamics. By considering the effect of symmetry preserving disorder, the non-invertible symmetry is shown to give rise to…
We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…
We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that…
Topological invariants are conventionally known to be responsible for protection of extended states against disorder. A prominent example is the presence of topologically protected extended-states in two-dimensional (2D) quantum Hall…
We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition $(A,B)$ of the lattice…
We explore the states of matter arising from the spontaneous symmetry breaking (SSB) of $\mathbb{Z}_2$ non-onsite symmetries. In one spatial dimension, we construct a frustration-free lattice model exhibiting SSB of a non-onsite symmetry,…
We introduce exactly solvable gapless quantum systems in $d$ dimensions that support symmetry protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as…
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…
Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static…
The two-dimensional cluster state, a universal resource for measurement-based quantum computation, is also the gapped ground state of a short-ranged Hamiltonian. Here, we examine the effect of perturbations to this Hamiltonian. We prove…
We consider SPT-phases with on-site finite group $G$ symmetry for two-dimensional Fermion systems.We derive an invariant of the classification.
Decoherence in realistic quantum platforms motivates a mixed-state notion of topological phases of matter, including average symmetry-protected topological (ASPT) phases. Alongside this progress, generalized symmetries--notably…
A symmetry-preserving, reduced-order state observer is presented for the unmeasured part of a system's state, where the nonlinear system dynamics exhibit symmetry under the action of a Lie group. Leveraging this symmetry with a moving…
We present a new approach to the analysis of entanglement in smooth bipartite continuous-variable states. One or both parties perform projective filterings via preliminary measurements to determine whether the system is located in some…
We introduce an order parameter for symmetry-protected phases in one dimension which allows to directly identify those phases. The order parameter consists of string-like operators and swaps, but differs from conventional string order…