his second pedagogical lecture, Cenke Xu told me there were many
questions about spin liquids and deconfined quantum criticality. To
guide my last pedagogical lecture, I'd like to ask for your questions
on these topics - or others if you think we could answer them. So:
please add your questions here.
- Is there a simple definition of a spin liquid?
- Can quantum or thermal order by disorder split an accidental degeneracy and stabilize a gapped spin liquid?
- Relation between spin-liquids and topological states?
important is it to find a spin-liquid ground state (as opposed to, say,
an intermediate-temperature regime that's disordered because of
spin-liquid physics, followed by more conventional ordering at very low
T)? Could one have exotic finite-temperature excitations in such a
- Are spinon Fermi surfaces unstable to BCS pairing via the Kohn-Luttinger effect?
easy is it to make mesoscopic samples of potential spin-liquid
materials? In principle, could one force a mesoscopic system into a
spin-liquid state by playing with boundary conditions to maximize
- How to distinguish a quantum spin-liquid
(either gapped or gapless) from a classical one at finite temperatures
(theoretically and experimentally)? How low temperature is low enough
to make the distinction?
- [Question emailed by S. Sorella,
entered by L. Balents] We have now a beatiful classification of spin
liquids in spin models, SU(2), U(1), Z2, based on the SU(2) invariance
of the electronic degrees of freedom in any spin model. My question is
, is there any stability argument why this classification should hold
when charge fluctuations are allowed? In particular I am referring to
the Z2 SPS (sublattice pairing state) spin liquid recently supported by
PSG classification of Heisenberg model on the honeycomb lattice. In
this case before projection the mean field state breaks sublattice
symmetry and time reversal, that is fully recovered after projection
(due to PSG). In Hubbard like models, such symmetries should be really
broken and a simple dimer state should be left. Or there is some field
theory stability argument that SU(2) is somehow a well defined symmetry
also in Hubbard model for large U/t? I spoke very long time ago with X.
G. Wen, and, as far as I remember, he replied ''yes it should be...'',
but I have not understood why. In the framework of variational
wavefunctions, it is very difficult to define a Jastrow factor that
allows to recover a spin liquid starting from a broken symmetry mean
field state, as it happens in spin models for the exact Gutzwiller
- [Question emailed by C. Lhuillier, entered by
S. Trebst] About deconfined quantum criticality. Could it be explained
in rather pedestrian terms what makes the transition from the colinear
Ne'el state to the columnar VBC so different from the transition from
the same colinear state to the staggered VBC?
- Would the
transition from a Ne'el state, in which SU(2) is broken to Z2, to a
phase with an U(1) invariant order parameter be an exotic phase
transition? ( I have in mind the phase diagram of the J-K model on the
- Would spin liquids have technological applications?