On the phase diagram of Spin-1 cases

[JerryChen97]

I spent some days improving the phase diagram of spin-1 cases but there has been no significant change.

Here is a diagram just as usual, where we calculate the correlation length (logarithm) for each phase point at two different bond dimensions 64 and 128.

The main part is still composed of gapped points that have no change in the correlation length, which is fine; but for certain points gathered in the center of two diagonal directions, they seemed gapless but also sometimes calculated inaccurately, which seems quite creepy.

Then, I look closer into the line Jx=Jy, do the DMRG in a series (iteratively using the previous psi as the input of the next DMRG engine), and here is an interesting figure for the correlation length (the original value, not log)

The two peak points correspond to Jx=Jy=.84 and Jx=Jy=1.40 respectively.

[JerryChen97]

Here is a fig for the finite-scaling of entanglement entropy w.r.t. the log of correlation length at Jx=Jy=1.4, Jz=1

[JerryChen97]

Here is a fig for the finite-scaling of entanglement entropy w.r.t. the log of correlation length at Jx=Jy=1.4, Jz=1

A fitting gives the central charge to be 0.5 here.

[JerryChen97]

Here is a fig for the finite-scaling of entanglement entropy w.r.t. the log of correlation length at Jx=Jy=1.4, Jz=1

A fitting gives the central charge to be 0.5 here.

chi_list = [16, 32, 64, 128, 256]

[JerryChen97]

The .84 point seems a little bit not so typical. I will try finding a 'more gapless' point.

[JerryChen97]

Here is a rough phase diagram given by directly calculating the correlation length of each point.

It seems that there is a rocket-shaped gapless circle lying in the center.

[JerryChen97]

Here is a much more precise phase diagram given by log xi (all the log below zero were trimmed to be just zero). @aaronszasz How do you like it?

[JerryChen97]

Here is the original version:

[JerryChen97]

I got a feeling that maybe the real phase diagram is much more complicated and elegant than I've thought

[aaronszasz]

This looks really interesting! So it looks like there are really three phases, maybe?

[JerryChen97]

This looks really interesting! So it looks like there are really three phases, maybe?

Yeah that's my current guess.

[JerryChen97]

And the shape of the left-below region seems really unusual; also I am curious about what happened to the border between the left-below region and the central region.

[JerryChen97]

Some other figs along the line Jx=Jy, where the resolution is 0.01

[JerryChen97]

Next: fDMRG for the critical points

[JerryChen97]

Here is a map for XY local order parameter using the same dataset of spin-1 case