Related papers: Symmetry-deformed toric codes and the quantum dime…
Topological phase transitions beyond anyon condensation remain poorly understood. A notable example is the transition between the toric code (TC) and double semion (DS) phases, which has two distinct $\mathbb{Z}_2$ topological orders in (2…
Symmetry and topology are essential principles in topological physics. Recently, the idea of sub-symmetry-protected topology -- where some of the original symmetries are broken while a remaining subset, called sub-symmetries, continues to…
Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum…
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…
We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations.…
We study a class of anomalies associated with time-reversal and spatial reflection symmetry in (2+1)D topological phases of matter. In these systems, the topological quantum numbers of the quasiparticles, such as the fusion rules and…
We demonstrate that field theories involving explicit breaking of continous symmetries, incorporate two generic classes of topological defects each of which is stable for a particular range of parameters. The first class includes defects of…
The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding…
Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on a special subclass of such symmetries, known as higher-form…
We consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between…
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…
The classical cubic-lattice dimer model undergoes an unconventional transition between a columnar crystal and a dimer liquid, in the same universality class as the deconfined quantum critical point in spin-1/2 antiferromagnets but with very…
Rank-2 toric code (R2TC), a prototypical archetype of the discrete rank-2 symmetric gauge theory, has properties that differ from those of the standard toric code. Specifically, it features a blending of UV and IR in its ground state,…
Two new quantum anti-de Sitter so(4,2) and de Sitter so(5,1) algebras are presented. These deformations are called either time-type or space-type according to the dimensional properties of the deformation parameter. Their Hopf structure,…
We construct an artificial U(1) gauge field in the cold atom system to form a monopole along with vortices. It is supposed that the cold atoms are confined on a spherical surface, and two sets of identical laser beams in the opposite…
This paper introduces a new class of error-correcting codes constructed from the ideal lattices of finite commutative ternary Gamma-semirings (TGS). Unlike classical linear or ring-linear codes, which rely on binary operations, TGS codes…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. In a recent paper [arXiv:0907.2994v1] we discussed how to…
Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…