Quantum orders and symmetric spin liquids

By X. Wen. 2001

634 citations recorded by the source corpus.

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 states (described bycomplex ground-state wave functions) are much richer than classical orders that characterize the universality classes of finite-temperature classical states (described by positive probability distribution functions). Landau's theory for orders and phase transitions does not apply to quantum orders since they cannot be described by broken symmetries and the associated order parameters. We introduced a mathematical object-projective symmetry group-to characterize quantum orders. With the help of quantum orders and projective symmetry groups, we construct hundreds of symmetric spin liquids, which have SU(2), U(1), or Z 2 gauge structures at low energies. We found that various spin liquids can be divided into four classes: (a) Rigid spin liquid-spinons (and all other excitations) are fully gapped and may have bosonic, fermionic, or fractional statistics. (b) Fermi spin liquid-spinons are gapless and are described by a Fermi liquid theory. (c) Algebraic spin liquid-spinons are gapless, but they are not described by free fermionic-bosonic quasiparticles. (d) Bose spin liquid-low-lying gapless excitations are described by a free-boson theory. The stability of those spin liquids is discussed in detail. We find that stable two-dimensional spin liquids exist in the first three classes (a)-(c). Those stable spin liquids occupy a finite region in phase space and represent quantum phases. Remarkably, some of the stable quantum phases support gapless excitations even without any spontaneous symmetry breaking. In particular, the gapless excitations in algebraic spin liquids interact down to zero energy and the interaction does not open any energy gap. We propose that it is the quantum orders (instead of symmetries) that protect the gapless excitations and make algebraic spin liquids and Fermi spin liquids stable. Since high-T c superconductors are likely to be described by a gapless spin liquid, the quantum orders and their projective symmetry group descriptions lay the foundation for a spin liquid approach to high-T c superconductors.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/85eb78944c4bf578d53f48b2d4ef29df9ad8cff4

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Citations in the corpus

Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface (2015, background): “[44] Xiao-Gang Wen, “Quantum orders and symmetric spin liquids,” Phys.”
Doping a Mott insulator: Physics of high-temperature superconductivity (2004, methodology): “So it is not surprising that one can construct bosonic models on cubic lattice that have emergent gapless photons (U(1) gauge bosons) (Wen, 2002a; Motrunich and Senthil, 2002; Wen, 2003a).”
Quantum Information Meets Quantum Matter (2015, background): “f FQH states. We can even calculate the topological properties of the FQH states, such as the ground state degeneracy and the fractional charges, from the valid sequences. For more details, see Refs. [55,7,56,77,78,1, 53,57,8,3,54,4,5]. References 1.Eddy Ardonne, Emil J Bergholtz, Janik Kailasvuori,”
Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections (2017, methodology): “However, such a generalization should be taken with great care because 1D fractionalization is qualitatively different from D ≥ 2 fractionalization [49, 66].”
Topological Nematic States and Non-Abelian Lattice Dislocations (2011, background): “[27] Xiao-Gang Wen, Quantum Orders and Symmetric Spin Liquids, Phys.”
Fractional quantum Hall physics in topological flat bands (2013, positive): “…these also allows control of the hopping interference and permits bands with f (cid:4) 10 [32] Numerical studies of these models show a variety of phases at ν = 1 / 2, including fractional Chern insulators for a range of parameters that are not too far from current experimental capabilities [31”
Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors (2010, background): “Indeed, Wen classified hundreds of them for the square lattice (Wen, 2002).”