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2d
comment Equivalence of nonlinear sigma model and the $CP^1$ model
@TuhinSubhraMukherjee There are two kinds of $Z_2$ RVB state, one called toric code, the other called double semion. The toric code state has Majorana fermions.
Apr
28
comment Equivalence of nonlinear sigma model and the $CP^1$ model
@TuhinSubhraMukherjee They actually mean RVB state = condensate of spinon Cooper pairs, but not the condensate of spinons themselves. BCS condensate of some quasiparticles actually means to condense the Cooper pairs of those quasiparticles. By such a BCS condensation, the U(1) gauge structure is Higgs down to $Z_2$, which leads to $Z_2$ topological ordered RVB spin liquid. But in the $Z_2$ spin liquid, spinons are still deconfined and not condensed.
Apr
28
comment Elementary question about the quantization of Hall conductivity
@TuhinSubhraMukherjee Right, the level crossing does not occur in the bulk.
Apr
27
comment Equivalence of nonlinear sigma model and the $CP^1$ model
@TuhinSubhraMukherjee No, RVB state is not a condensate of spinons. RVB state is a deconfined state, where both spinons and visons are not condensed. Spinon condensation will lead to anti-ferromagnetic (AFM) state, and vison condensation will lead to the valence bond solid (VBS) state. I believe what people talked about is the VBS state as vison condensation.
Apr
27
comment Elementary question about the quantization of Hall conductivity
@TuhinSubhraMukherjee Yes, there is a level crossing during the process. But at the level crossing point, the two degenerated states are differed from each other by one unit of charge transfer, but since the bulk is insulating, it is exponentially unlikely to resonance between the two degenerated states to avoid the level cross, or in other words, the crossing is topologically protected. So after the flux threading, the final state is inevitably an excited state.
Apr
25
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Apr
22
comment Symmetries in physics (specifically condensed matter physics)
@Marnix The issue is subtle for particle-hole. In the many-body basis, particle-hole symmetry is a unitary symmetry. But for single-particle free fermion systems, particle-hole symmetry "looks like" an antiunitary symmetry, because complex conjugation of the single-particle wave function is involved. That is why particle-hole symmetry is also "special" for free fermion systems, even though it is a unitary symmetry in the many-body sense.
Apr
21
answered Symmetries in physics (specifically condensed matter physics)
Apr
21
answered Super conductivity and energy gap in fermionic/bosonic subspaces
Apr
9
revised Why we call the ground state of Kitaev model a Spin Liquid?
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Apr
9
revised Why we call the ground state of Kitaev model a Spin Liquid?
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Mar
28
comment General properties of Matsubara frequency summations
@leongz The key point is to find poles and calculate residuals. Mathematica is good at these stuff.
Mar
27
answered How can wavefunction degeneracy be incoperated into a tight binding model?
Mar
26
comment MFT Approximation for Dilute Bose Gas
What you have heard about the relative $1/\sqrt{N_0}$ fluctuation about $b_0$ may be wrong. For coherent state where $\langle b_0\rangle=\sqrt{N_0}$ holds, there is actually no fluctuation of $\langle b_0\rangle$, because coherent state is an eigenstate of $b_0$.
Mar
26
comment What is the magnetic-ordering wave vector?
@ZJX The trick is to imagine the pattern of spin as a wave. Up spin = + and down spin = -. Then the wave vector can be read off directly by looking at the wave. Or you can measure the wavelength $\lambda$ as the up-spin-to-up-spin distance and calculate the wave number as $2\pi/\lambda$, and the direction of the wave vector is perpendicular to the equal-spin plane (or line).
Mar
25
revised What is the magnetic-ordering wave vector?
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Mar
25
answered What is the magnetic-ordering wave vector?
Mar
25
revised Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?)
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Mar
25
comment Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?)
@JohnM $|G|$ is the group order. I have updated my answer with a detailed example of how to implement the general construction for a specific group $T_d$. I have also provided a useful link at the end of the answer.
Mar
25
revised Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?)
Add a detailed example.