相关论文: Algebras of order parameters in one-dimensional sp…

In this paper, we construct strange correlators and string order parameters for non-invertible symmetry protected topological phases (NISPTs) in 1+1d quantum lattice spin models. The strange correlator exhibits long-range order when…

We present three Lagrangian algebras in the modular 2-category associated to the 3+1D $\mathbb{Z}_2$ topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps…

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 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…

We study the anomalies of non-invertible symmetries in 1+1D QFTs using gapped boundaries of its SymTFT. We establish the explicit relation between Lagrangian algebras which determine gapped boundaries of the SymTFT, and algebras which…

In this dissertation, we detail an operator algebraic approach to studying topological order in the infinite volume setting. We give a thorough and self-contained review of the DHR-style approach on quantum spin systems, which builds a…

Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold. A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory,…

One-dimensional gapped spin chains with symmetry PSU(N) = SU(N)/Z_N are known to possess N different topological phases. In this paper, we introduce a non-local string order parameter which characterizes each of these N phases…

We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category…

We show that the existence of string order in a given quantum state is intimately related to the presence of a local symmetry by proving that both concepts are equivalent within the framework of finitely correlated states. Once this…

We propose entropic order parameters that capture the physics of generalized symmetries and phases in QFT's. We do it through an analysis of simple properties (additivity and Haag duality) of the net of operator algebras attached to…

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are…

Contrary to canonical expectations we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomena by studying a spinless-fermion model on a square latttice with…

In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…

We investigate spatial reflection and associated nonlocal order in spin chain quantum systems. The proposed string order parameters, e.g., reflected via operations of the spatial reflection or combinations of it with spin reflection, are…

We apply the twisted order parameter (TOP) for dimerized quantum spin ladders to locate the critical phases that separate gapped phases representing quantum spin liquids of various types. Using the DMRG, method we find that the TOP is a…

The phase diagram and the order parameters of the exactly solvable quantum 1D model are analysed. The model in its spin representation is the dimerized XY spin chain in the presence of uniform and staggered transverse fields. In the…

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot…

For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in…

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…