Related papers: Duality between string and computational order in …
Topological quantum phases of quantum materials are defined through their topological invariants. These topological invariants are quantities that characterize the global geometrical properties of the quantum wave functions and thus are…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…
We prove numerically and by dualities the existence of modulated, commensurate and incommensurate states of topological quantum matter in simple systems of parafermions, motivated by recent proposals for the realization of such systems in…
It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
We investigate the anisotropic quantum orbital compass model on an infinite square lattice by means of the infinite projected entangled-pair state algorithm. For varying values of the $J_x$ and $J_z$ coupling constants of the model, we…
In two-dimensional topological phases, quasiparticle excitations can carry fractional symmetry quantum numbers. We generalize this notion of symmetry fractionalization to three-dimensional topological phases, in particular to loop…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
In primary school, we were told that there are four states of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four states of matter. For example, there are ferromagnetic states as revealed by the…
Quantum resources exist in a hierarchy of multiple levels. At order zero, quantum states are transformed by linear maps (channels, or gates) in order to perform computations or simulate other states. At order one, gates and channels are…
The field of quantum metrology promises measurement devices that are fundamentally superior to conventional technologies. Specifically, when quantum entanglement is harnessed the precision achieved is supposed to scale more favourably with…
Entanglement is known to serve as an order parameter for true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors.…
The Kitaev surface-code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy…
We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a…
Programmable quantum simulators such as superconducting quantum processors and ultracold atomic lattices represent rapidly developing emergent technology that may one day qualitatively outperform existing classical computers. Yet, apart…
A thought experiment is formulated to unify quantum mechanics and general relativity in a topological manner. An analysis of the interactions in Nature is then presented. The universal ground state of the constructed theory derives from the…
A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic…
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…
Topological phases are exotic quantum phases which are lacking the characterization in terms of order parameters. In this paper, we develop a unified framework based on variational iPEPS for the quantitative study of both topological and…