Related papers: Duality between string and computational order in …
We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken…
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…
In this paper, we explore topological quantum computation augmented by subphases and phase transitions. We commence by investigating the anyon tunneling map, denoted as $\varphi$, between subphases of the quantum double model…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order.…
We give a pedagogical introduction to topologically ordered states of matter, with the aim of familiarizing the reader with their axiomatic topological quantum field theory description. We introduce basic noninteracting topological phases…
We discuss the problem of characterizing "quantum disordered" ground states, obtained upon loss of antiferromagnetic order on general lattices in two spatial dimensions, with arbitrary electronic band structure. A key result is the response…
The existence of topological order is frequently associated with strongly coupled quantum matter. Here, we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
Topological quantum computing is believed to be inherently fault-tolerant. One mathematical justification would be to prove that ground subspaces or ground state manifolds of topological phases of matter behave as error correction codes…
Topological order (long-range entanglement) is a new type of order that beyond Landau's symmetry breaking theory. This concept plays important roles in modern condensed matter physics. The topological entanglement entropy provides a…
The holographic duality relates a field theory to a theory of (quantum) gravity in one dimension more. The extra dimension represents the scale of the RG transformation in the field theory. It has been conjectured that the tensor networks…
This work explores a deformation of the Kitaev toric code that induces a phase transition out of the topologically ordered phase. By placing the model on a cylinder, the bulk global 1-form symmetries separate into distinct boundary…
Enhancing robustness of topological orders against perturbations is one of the main goals in topological quantum computing. Since the kinetic of excitations is in conflict with the robustness of topological orders, any mechanism that…
The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states had received only quite recently attention in the literature. In…
We present a numerical study of a quantum phase transition from a spin-polarized to a topologically ordered phase in a system of spin-1/2 particles on a torus. We demonstrate that this non-symmetry-breaking topological quantum phase…
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…
Motivated by the limited understanding of entanglement entropy in non-asymptotically AdS spacetimes, we develop a framework in which a circular string is embedded as a quantum probe in a spherically symmetric curved spacetime, and its…
In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases,…
A natural way to generalise tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product…