Quantum Order: a Quantum Entanglement of Many Particles

Abstract

It is pointed out that quantum states, in general, contain a new kind of orders that cannot be characterized by symmetry. A concept of quantum order is introduced to describe such orders. As two concrete examples, we discussed quantum orders in free fermion systems and in 2D spin-1/2 systems. We generalize the Landau's theory for the classical orders and introduce projective symmetry group and Fermi surface topology to characterize different quantum orders.

4 pages, 1 figures, RevTeX4, homepage: http://dao.mit.edu/~wen

References in corpus (3)

• Quantum Orders and Symmetric Spin Liquids
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Origin of Light

Cited by in corpus (65)

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Quantum orders in an exact soluble model
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Quantum order from string-net condensations and origin of light and massless fermions
• String and Membrane condensation on 3D lattices
• Formation of Electronic Nematic Phase in Interacting Systems
• Two-component Structure in the Entanglement Spectrum of Highly Excited States
• The Spinon Fermi Surface U(1) Spin Liquid in a Spin-Orbit-Coupled Triangular Lattice Mott Insulator YbMgGaO4
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Artificial light and quantum order in systems of screened dipoles
• A classification of 2D fermionic and bosonic topological orders
• Doping the chiral spin liquid -- topological superconductor or chiral metal?
• Spectroscopic signatures of crystal momentum fractionalization
• The Spectral Periodicity of Spinon Continuum in Quantum Spin Ice
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• Entanglement and majorization in (1+1)-dimensional quantum systems
• Fermi surface reconstruction in hole-doped t-J models without long-range antiferromagnetic order
• Gapless Fermions and Quantum Order
• Structure of Quasiparticles and Their Fusion Algebra in Fractional Quantum Hall States
• Chiral spin density wave, spin-charge-Chern liquid and d+id superconductivity in 1/4-doped correlated electronic systems on the honeycomb lattice
• Relating the entanglement spectrum of noninteracting band insulators to their quantum geometry and topology
• Entanglement properties of topological color codes
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Density matrix renormalization group boosted by Gutzwiller projected wave functions
• Quantum entanglement in states generated by bilocal group algebras
• Edge excitations and Topological orders in rotating Bose gases
• Quantum Disentanglement in Long-range Orders and Spontaneous Symmetry Breaking
• Symmetry protected topological orders of 1D spin systems with D2+T symmetry
• Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models
• Fractionalization of Coset Non-Invertible Symmetry and Exotic Hall Conductance
• Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis
• Classical and quantum order in hyperkagome antiferromagnets
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Possible chiral spin liquid state in the $S=1/2$ kagome Heisenberg model
• An architecture for two-qubit encoding in neutral ytterbium-171 atoms
• Non-Kitaev spin liquids in Kitaev materials
• Inaccessible entanglement in symmetry protected topological phases
• Long-range entanglement and topological excitations
• Area Law from Loop Quantum Gravity
• Topological $Z_2$ invariant in Kitaev spin liquids: Classification of gapped spin liquids beyond projective symmetry group
• 2D Superconductivity: Classification of Universality Classes by Infinite Symmetry
• Topological order in Josephson junction ladders with Mobius boundary conditions
• Superconducting Topological Fluids in Josephson Junction Arrays
• 2D Multipartite Valence Bond States in Quantum Antiferromagnets
• Numerical detection of symmetry enriched topological phases with space group symmetry
• Classification of Fermionic Topological Orders from Congruence Representations
• Tensor-product representations for string-net condensed states
• Theory of quantum kagome ice and vison zero modes
• Classification and emergence of quantum spin liquids in chiral Rydberg models
• Fully frustrated Josephson junction ladders with Mobius boundary conditions as topologically protected qubits
• Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Topologically protected qubits as minimal Josephson junction arrays with non trivial boundary conditions: a proposal
• Bosonic Fractional Quantum Hall States in Rotating Optical Lattices: Projective Symmetry Group Analysis
• Modular extension of topological orders from congruence representations
• Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator
• Jordan-Wigner composite-fermion liquids in 2D quantum spin-ice
• Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem
• Majorana Diagrammatics for Quantum Spin-1/2 Models
• Topological Quantum Phase Transitions in Topological Superconductors
• Few-particle systems: An analysis of some strongly correlated states
• Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature