相关论文: Localized endomorphisms in Kitaev's toric code on …
Understanding the behaviour of topologically ordered lattice systems at finite temperature is a way of assessing their potential as fault-tolerant quantum memories. We compute the natural extension of the topological entanglement entropy…
Product code construction is a powerful tool for constructing quantum stabilizer codes, which serve as a promising paradigm for realizing fault-tolerant quantum computation. Furthermore, the natural mapping between stabilizer codes and the…
We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of nonlinearities.…
We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified…
Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are…
We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin-chain. For the latter, we developed a numerical application of…
We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-D real Ginzburg-Landau equation. While for local coupling the fronts are always…
We introduce a new representation of an integer spin $S$ via bosonic operators which is useful in describing the paramagnetic phase and transitions to magnetically ordered phases in magnetic systems with large single-ion easy-plane…
In this work we calculate the entanglement entropy of certain excited states of the quantum Lifshitz model. The quantum Lifshitz model is a 2 + 1-dimensional bosonic quantum field theory with an anisotropic scaling symmetry between space…
While local unitary transformations are used for identifying quantum states which are in the same topological class, non-local unitary transformations are also important for studying the transition between different topological classes. In…
The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of…
Combined with Laughlin's argument on the quantized Hall conductivity, Lieb-Schultz-Mattis argument is extended to quantum many-particle systems (including quantum spin systems) with a conserved particle number, on a periodic lattice in…
This paper starts by describing the dynamics of the electron-monopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are…
Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality…
The magnetic properties and electronic structure of the ground and excited states of two recently characterized endohedral metallo-fullerenes, [Gd$_2$@C$_{78}$]$^{-}$ (1) and [Gd$_2$@C$_{80}$]$^{-}$ (2), have been studied by theoretical…
The construction of the topologically protected code space of Kitaev's model for fault-tolerant quantum computation is extended from complex semisimple to arbitrary finite-dimensional Hopf algebras admitting pairs in involution. One input…
Kitaev's lattice models are usually defined as representations of the Drinfeld quantum double $D(H)=H\bowtie H^{*\text{op}} $, as an example of a double cross product quantum group. We propose a new version based instead on…
The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated. The ribbon operators and the classification of…
We introduce the notion of polynomial-depth duality transformations, which relates two sets of operator algebras through a conjugation by a poly-depth quantum circuit, and make use of this to construct efficient Gibbs samplers for a variety…
We show that the one-dimensional extended Hubbard model has saturated ferromagnetic ground states with the spin-triplet electron pair condensation in a certain range of parameters. The ground state wave functions with fixed electron numbers…