# I Quantum spin liquid

1. Apr 5, 2016

### Kevin McHugh

I just read an article stating physicists have discovered a new state of matter. What is a quantum spin liquid?

2. Apr 5, 2016

3. Apr 5, 2016

4. Apr 5, 2016

### vanhees71

5. Apr 5, 2016

A spin liquid is a spin state which breaks no symmetries down to zero temperature. Furthermore it has an emergent gauge theory with topological excitations and long range entanglement. It occurs in Mott insulators at half filling which are "frustrated" i.e. have competing interactions. The gauge theories are usually Z2 or U(1) but only the former is stable in two dimensions.

You can construct a SL from a resonating valence bond state with nearby spins (not always just nearest neighbors) paired in spin singlets (you have all of the possible dimer coverings.) You can construct a mean field theory description from the Heisenberg model using Schwinger bosons (or fermions but this is quite complicated). Excitations above the MF ground state are called spinons which are unpaired spins. In the SL phase they are "deconfined" and can separate as fractionalized excitations with spin =1/2 (this is actually quite similar to the idea of confinement in QCD).

In the MF construction you do not really have an order parameter since you have broken no symmetries. Instead you want to impose single occupancy at all times. Here is where the gauge theory comes in: since mean field theory just imposes the constraint on average, you must find a way to account for this. MF theory can give you states with two or no spins and you need to project out those states. You do this by identifying some emergent gauge field (it comes from a Lagrange multiplier in the Hamiltonian). So the spinons actually interact via this gauge field like charges (there are also monopole like excitations).

Another way to see this is that since you want only one bond coming from each site, you get a "Gauss's law" constraint from considering the RVB state and hence get an emergent gauge theory.

Quantum Field Theory of Many-Body Systems has a whole chapter on SLs.