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String-net condensation: A physical mechanism for topological phases
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''
Detecting topological order in a ground state wave function.
A way to detect a kind of topological order using only the ground state wave function which directly measures the total quantum dimension D= Sum(id2i).
Doping a Mott insulator: Physics of high-temperature superconductivity
This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the
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
Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering
Quantum orders and symmetric spin liquids
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 the universality classes of
Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons
1. Introduction 2. Path integral formulation of quantum mechanics 3. Interacting boson systems 4. Free fermion systems 5. Interacting fermion systems 6. Quantum gauge theories 7. Theory of quantum
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
Topological orders and edge excitations in fractional quantum hall states
Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a completely new kind of ordering. We discuss the characterization and classification of the new