Related papers: Modular transformations through sequences of topol…
The theory of anyon systems, as modular functors topologically and unitary modular tensor categories algebraically, is mature. To go beyond anyons, our first step is the interplay of anyons with conventional group symmetry due to the…
We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling…
A simple algebraic model for charged particle moving in two dimensional space under influence of singular magnetic field is given. The fundamental assumption for the model is that every charged particle coupled to the magnetic field is…
Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing…
We demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum…
A condition of geometric modular action is proposed as a selection principle for physically interesting states on general space-times. This condition is naturally associated with transformation groups of partially ordered sets and provides…
We study topological transitions in one dimensional superconductors that can harbor multiple edge Majorana bound states protected by chiral symmetry. The chiral symmetry arises due to the structure of the internal spin degrees of freedom of…
Nontrivial topology in physical systems is the driving force behind many phenomena. Notably, phases of matter must be classified in part by their topological properties. Phases with topological order (TO), such as the fractional quantum…
We propose an exactly solvable Hamiltonian for topological phases in $3+1$ dimensions utilising ideas from higher lattice gauge theory, where the gauge symmetry is given by a finite 2-group. We explicitly show that the model is a…
We investigate nonlinear aggregation dynamics of phase elements distributed on the unit circle under parametrically modulated external fields. Our model, inspired by flaky particle rotation in fluids, employs the equation ${d\alpha/dt} =…
Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed…
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition of a quantum state gets destroyed by the interaction with…
Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the quantization of the algebra of functions on the…
Topological materials hold immense promise for exhibiting exotic quantum phenomena, yet achieving controllable topological phase transitions remains challenging. Here, we demonstrate a structurally driven, reversible topological phase…
Topological phases of matter are commonly understood as emerging either from crystalline symmetry and intrinsic spin-orbit coupling or from disorder-driven electronic renormalization. In realistic materials, however, structural defects…
Recently, generative machine-learning models have gained popularity in physics, driven by the goal of improving the efficiency of Markov chain Monte Carlo techniques and of exploring their potential in capturing experimental data…
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.
In the tensor network representation, a deformed $Z_{2}$ topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller (AT) model. Then the topological (toric code) phase…
We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $\mathbb{Z}_K$ or $\mathbb Z_K \times \mathbb Z_K $ symmetry. We argue that modular…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…