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Haldane phase, non-interacting topological insulator/superconductor, and SPT phase
The essence of Haldane phase is its energy gap. It is known that anti-ferromagnetic spin-1/2 chain has quasi long rang order and is gapless. This…
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Continuous anomaly
In many cases, an anomaly corresponds to a SPT order or a topological order in one higher dimension.[1][2] This kind of anomalies are labelled by…
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A dopon theory of high Tc superconductor
A dopon theory is an all-fermion slave-particle mean field theory for Cu high Tc superconductors, which was developed by Ribeiro and Wen in 2004 .…
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Topological non-linear σ-model, higher gauge theory, and a systematic construction of 3+1D topological orders for boson systems
A summary of arXiv:1808.09394 DOI: 10.1103/PhysRevB.100.045105 Topological order describes a new kind of quantum phases of matter at zero temperature. This paper describes a systematic…
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Quantum spin Hall state and 2+1D topological insulator
What is quantum spin Hall effect? According to Bernevig-Zhang and Kane-Mele, quantum spin Hall effect refers to quantized transverse Sz-spin current induced by force acting…
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Non-Abelian statistics in condensed matter systems
The particles in our world can be divided into two classes: those with Bose statistics (such as photons, Hydrogen atom, etc) and those with Fermi…
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A solution to chiral fermion problem, or not
In 2013, I wrote a paper (arXiv:1305.1045) claiming solved the chiral fermion problem. It is known that some gauge-anomalous chiral fermion theory cannot be put…
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Topological order (two macroscopic definitions/characterizations)
For a long time, people thought Landau symmetry breaking theory can describe all phase transitions and all phases of matter. When encounter a new phase…
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Spin-1/2 J1-J2 model on square lattice
Peolpe have been working on J1-J2 model for 30 years. Here is a recent tensor network calculation. Comparing with the following meanfield result may give…
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Are we living in a quantum noodle soup?
The following picture has mountain, lake, trees, snow,… …, and light. If we look closer, we see atoms, protons, electrons, quarks, photons, … If we…
Neither nonbeing nor bing, nonbing produce being. Both illusive and real, illusive become real.