Related papers: Topological order in an exactly solvable 3D spin m…
Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the…
Topological quantum field theory (TQFT) provides a unifying framework for describing topological phases of matter and for constructing quantum error-correcting codes, playing a central role across high-energy physics, condensed matter, and…
Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical…
We show that interactions can drive a class of higher order topological superconductors (HOTSC) into symmetry enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting…
Topologically-ordered phases of matter, although stable against local perturbations, are usually restricted to relatively small regions in phase diagrams. Their preparation requires thus a precise fine tunning of the system's parameters, a…
Topological configurations, monopoles and vortices, successfully describe quark confinement and the spontaneous breakdown of chiral symmetry. Despite their infinite action, these configurations are relevant due to a subtle cancellation…
One of the most striking features of quantum phases that exhibit topological order is the presence of long range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a…
In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The…
Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such "rotors" are found in the natural world spanning vastly disparate length scales - from the rotor proteins…
We propose a general construction of commuting projector lattice models for 2D and 3D topological phases enriched by U(1) symmetry, with finite-dimensional Hilbert space per site. The construction starts from a commuting projector model of…
We propose and study a generalization of Kitaev's $\mathbb Z_2$ toric code on a square lattice with an additional global $U(1)$ symmetry. Using Quantum Monte Carlo simulation, we find strong evidence for a topologically ordered ground state…
We develop a non planar topological vertex formalism and we use it to study the A-model partition function $\mathcal{Z}_{top}$ of topological string on the class of toric Calabi-Yau threefolds (CY3) in large complex structure limit. To that…
We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct bond-ordered phases for spin-1, spin-$\tfrac{3}{2}$, and spin-2 models. In all cases, we find translational symmetry…
It is shown that unification of strong and Electroweak interactions at Tev scale may lead to appearance of topologically stable monopoles with masses of the order of 40 Tev. Those monopoles may play an important role in the early Universe,…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
The Z2 topological invariant is defined in the chiral d-wave superconductor having a triangular lattice in the presence of the 120 degrees magnetic ordering. By analyzing the Z2 invariant, we determine the conditions of implementing…
The quest for new realizations of higher-order topological system has garnered much recent attention. In this work, we propose a paradigmatic brick lattice model where corner modes requires protection by nonsymmorphic symmetry in addition…
We study interaction-induced bound states in a system of ultracold bosons loaded into the states with orbital angular momentum in a one-dimensional staggered lattice of rings. We consider the hard-core limit and strong nearest-neighbour…
This thesis addresses whether it is possible to build a robust memory device for quantum information. A three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…