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  1. M

    Spin liquid states and conductors

    I guess my main problem was, to go into the specifics now, how it might be reasoned that a state with exotic properties like emergent gauge structure or topological order or fractionalisation of charge - as you point out - is equivalent to another standard definition of quantum SL (QSL) i.e. a...
  2. M

    Spin liquid states and conductors

    Hi, All articles on spin liquids I've seen treat them as insulators. This is understandable in the context in which they were first introduced i.e. the resonating valence bond state in which every electron is singlet-ed with every other, and thus essentially blocking conduction. Given...
  3. M

    U(1) symmetry breaking within the superluid phase

    Yes, this is clear. My question was how does one see, mathematically or heuristically just with the BHH expression being given, that the hopping-terms prefer a state with a broken symmetry? For example, the ferromagnetic Heisenberg Hamiltonian has -S.S term which favours parallel alignment of...
  4. M

    U(1) symmetry breaking within the superluid phase

    Well, as I mentioned before and to be more explicit, I can argue phenomenologically that the U(1) is broken in the SF phase as follows: since U(1) symmetry is nothing but charge conservation (see for e.g. Fradkin's book "Field theories on Condensed matter") and since there is spontaneous...
  5. M

    Ising ang heisenberg model

    That is not entirely correct. There are classical and quantum versions of the Ising model. Mavi
  6. M

    U(1) symmetry breaking within the superluid phase

    Hi With the Bose-Hubbard Hamiltonian (BHH) being invariant under a U(1)\equivO(2) symmetry transformation, it is said that the hopping-term in the BHH tends to break the U(1) symmetry as the system leaves the insulating phase. This is not clear to me. However within the mean-field...
  7. M

    Singlet sharing

    The answer comes from the AKLT hamiltonian, wherein at each site, the spin 1 is decomposed into 2 spin-1'2's. This is the ground state of the said hamiltonian and can be best understood within the Schwinger boson formalism.
  8. M

    Singlet sharing

    Hello I have come across this inexplicable fact mentioned in somewhere that for a chain of S = 1 spins, the adjacent bonds can all be in a singlet state i.e. singlets can be shared in this case (forming valence bond solids) but not, for example, for |S| = 1/2, the latter point being clear. I...
  9. M

    Tight binding model

    What cgk meant by the "totally symmetric representation" is actually the trivial representation. Landau & Lifgarbagez:Volume 3 explains in simple terms why this wonderful theorem is true (sort of like the Kraemers degeneracy theorem). Mavi
  10. M

    Question on universailty classes

    Guessing another part of the answer: it seems that since the continuum limit or the lattice limit must yield the same critical exponents (due to scaling invariance after graining), the lattice structure itself must not matter for the exponents. I wonder if this reasoning is correct. Mavi
  11. M

    Question on universailty classes

    I found out one part of the answer: changing the dimensionality of the lattice will change the critical exponents for the same model (say Ising). So the modified question would be whether the exponents change while changing the lattice structure (say square to triangle) for the same model in a...
  12. M

    Question on universailty classes

    Hi When a particular model (say Ising) is solved on a particular lattice (say 2D triangular), do the critical exponents of the same model fall within the same universality class (have same critical exponents) as when solved on a different lattice (say 3D cubic)? Thanks, Mavi
  13. M

    Tight binding model

    Quantum theory of solids, Kittel Solid state physics, Ashcroft and Mermin Mavi
  14. M

    Opening up of spin gap

    So if there is a continuous band of energies connecting the ground and excited state of the d-wave superconductor (because it is gapless), why should the superconductivity be stable, since arbitrarily small thermal fluctuations can excite it? This should be true even if we consider large...
  15. M

    Instability of Fermi surface

    Right that makes sense; I guess its something similar to a p-n junction where the Fermi levels between the p and n sides develop a gap between each other.
  16. M

    Diffrence between Normal mode and phonons

    Phonons are more correctly known as collective-excitations rather than quasiparticles. Collective excitations occur when the interaction between the particles of the unexcited system is strong, so that one cannot really identify a single-particle to describe the dynamics of the system, but...
  17. M

    Instability of Fermi surface

    rizzodex/stephenhky Can you explain the mechanism as to how the Fermi surface of different spin sites depart from each other, thus opening up a gap?
  18. M

    Instability of Fermi surface

    What do you mean by Fermi surfaces of particles with different spins? Fermi surface applies to the entire solid and not for individual particles.
  19. M

    Opening up of spin gap

    Now I think maybe I misinterpreted your initial statement: " ... it does not require too much energy to excite modes of lower values of momenta (k) ... ". I initially presumed that you were referring to excitations between different degenerate levels with momentum being preserved, but after your...
  20. M

    Opening up of spin gap

    That makes sense; so isn't the unfortunate nomenclature ("gapless excitation") an oxymoron of some sort? Because if it is multiply-degenerate, why call it an excitation?
  21. M

    Physical origin of different phase velocities.

    Light propagates as a wave-packet (mixture of different monochromatic frequencies); each frequency of oscillation interacts differently with the material (constituting its dispersion relation). This gives rise to various components of the wave-packet travelling with different velocities...
  22. M

    Opening up of spin gap

    Hi Can somebody explain what is a "gapless excitation"? If it is an excitation, why does it require no energy (gapless) to excite the system? Thanks, Mavi
  23. M

    Instability of Fermi surface

    Hi Can somebody explain the meaning of the following sentence which is from Wikipedia: "Solids with a large density of states at the Fermi level become unstable at low temperatures and tend to form ground states where the condensation energy comes from opening a gap at the Fermi surface e.g...
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