Related papers: Symmetry and Topological Order
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…
Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose…
Understanding quantum phases and phase transitions in the presence of symmetries is a central objective of quantum many-body physics. A powerful modern paradigm for investigating this problem is topological holography, which relates…
Symmetry packaging is the phenomenon whereby, upon particle creation, all the internal quantum numbers (IQNs) become locked into a single irreducible representation (irrep) block of the gauge group, as required by locality and gauge…
The quantum metric encodes the geometric structure of Bloch wave functions and governs a wide range of physical responses. Its Brillouin-zone integral, the quantum weight, appears in the structure factor and provides lower bounds on…
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding…
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…
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…
Symmetries in the Physical Laws of Nature lead to observable effects. Beyond regularities and conserved magnitudes, the last decades in Particle Physics have seen the identification of symmetries, and their well defined breaking, as the…
We discuss the Pauli Hamiltonian within a ${SU(2)}$ gauge theory interpretation, where the gauge symmetry is broken. This interpretation carries directly over to the structural inversion asymmetric spin-orbit interactions in semiconductors…
We establish an important duality correspondence between topological order in quantum many body systems and criticality in ferromagnetic classical spin systems. We show how such a correspondence leads to a classical and simple procedure for…
It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local…
We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on…
It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in $d$…
We study the spontaneous decoherence of the coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry breaking field or surrounding…
We discuss symmetries intermediate between global and local and formalize the notion of dimensional reduction adduced from such symmetries. We apply this generalization to several systems including liquid crystalline phases of Quantum Hall…
It is known that if gauge conditions have Gribov zero modes, then topological symmetry is broken. In this paper we apply it to topological gravity in dimension $n \geq 3$. Our choice of the gauge condition for conformal invariance is…
One-dimensional superlattices with periodic spatial modulations of onsite potentials or tunneling coefficients can exhibit a variety of properties associated with topology or symmetry. Recent developments of ring-shaped optical lattices…
As temperature drops, molecular systems may undergo spontaneous ordering, moving from random behavior to orderly structure. This research demonstrates a direct analogy between this type of thermodynamic ordering in molecular systems and the…