Related papers: Symmetry and Topological Order
We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The guiding principle behind our approach is that of symmetries and entanglement. We introduce the concept of low-dimensional…
High temperature is usually expected to destroy order: as the Gibbs state approaches the infinite-temperature limit, it becomes an equal-weight ensemble over all states and the system is generically disordered. Recent works showed that…
We broaden the scope of quantum field theory by introducing a general class of discrete gauge theories that realize either topological order or fracton behavior across dimensions. We start from translation-invariant systems endowed with…
A concept -- quantum order -- is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize universality classes of quantum states (described by {\em complex}…
We study topological order in a toric code in three spatial dimensions, or a 3+1D Z_2 gauge theory, at finite temperature. We compute exactly the topological entropy of the system, and show that it drops, for any infinitesimal temperature,…
Are systems that display Topological Quantum Order (TQO), and have a gap to excitations, hardware fault-tolerant at finite temperatures? We show that in surface code models that display low d-dimensional Gauge-Like Symmetries, such as…
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological…
We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of geometrically local commuting projectors on a…
In this work we explore the possibility of spontaneous breaking of global symmetries at all nonzero temperatures for conformal field theories (CFTs) in $D = 4$ space-time dimensions. We show that such a symmetry-breaking indeed occurs in…
We begin with an introduction to topological order using Wegner's quantum $Z_2$ gauge theory on the square lattice: the topological state is characterized by the expulsion of defects, carrying $Z_2$ magnetic flux. The interplay between…
In this work we demonstrate that linearized gravity exhibits gapless topological order with an extensive ground state degeneracy. This phenomenon is closely related both to the topological order of the pyrochlore U(1) spin liquid and to…
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…
Topological entanglement entropy is a topological invariant which can detect topological order of quantum many-body ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth…
Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…
We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the Toric Code Model and, after the quench, it…
Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as…
In two spatial dimensions, topological order is robust for static deformations at zero temperature, while it is fragile at any finite temperature. How robust is topological order after a quantum quench? In this paper we show that…
Understanding which physical processes are symmetric with respect to time inversion is a ubiquitous problem in physics. In quantum physics, effective gauge fields allow emulation of matter under strong magnetic fields, realizing the…
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call "Local Topological Quantum Order" and…
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…