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Symmetry protected topological orders and the group cohomology of their symmetry group
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the
Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped
Classification of gapped symmetric phases in one-dimensional spin systems
Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for
Quantum Information Meets Quantum Matter
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We
Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model
Three dimensional topological superconductors (TScs) protected by time reversal (T) symmetry are characterized by gapless Majorana cones on their surface. Free fermion phases with this symmetry
Fracton Models on General Three-Dimensional Manifolds
Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some 'topological' features: they support fractional bulk excitations
Symmetry-Protected Topological Orders in Interacting Bosonic Systems
Just as group theory allows us to construct 230 crystal structures in three-dimensional space, group cohomology theory is used to systematically construct different interacting bosonic SPT phases in any dimension and with any symmetry, leading to the discovery of bosonic topological insulators and superconductors.
Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations
Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected
Complete classification of one-dimensional gapped quantum phases in interacting spin systems
Quantum phases with different orders exist with or without breaking the symmetry of the system. Recently, a classification of gapped quantum phases which do not break time reversal, parity or on-site
Symmetry-protected topological phases from decorated domain walls.
It is shown that symmetry-protected topological phases are realized when these domain walls are decorated, that is, are themselves symmetries in one lower dimension, both for unitary Z2 and anti-unitary time reversal symmetry.