Dear Itensor,

I have some questions on how one can compute the ground state energy in a given symmetry sector. For some reason, I was not able to obtain these results from a google search, so I decided to ask them here.

1) For the transverse-field Ising chain, with

H = \sum*i \sigma^z*i \sigma^z*{i+1} + h \sum*i \sigma^x*i
When h < h*c, is there anyway for DMRG to obtain the ground state polarized along the +z direction? What about the ground state with even/odd parity?

What about the imaginary-time TEBD or the VUMPS algorithm?

2) For systems with global U(1) symmetry, such as the Bose-Hubbard model,

H =\sum*i (a*i^\dag a*{i+1} + a*i a*{i+1}^\dag + \gamma n*i n*{i+1}) - \mu sum*i n*i
where a*i and n_i are respectively the annihilation and number operators of the bosons.

Is there anyway for DMRG to obtain the ground state of H with a given particle number? (I know one can shift the chemical potential \mu to make the full ground state have any given particle number. But I'm curious whether one can do this directly by exploiting symmetries of the MPS) Is it enough to use an initial state with a definite particle number in the DMRG? Is so, why?

What about the imaginary-time TEBD or the VUMPS algorithm?

I would also be very grateful for any pointers to references that talk about these issues. (I find this reference ("Tensor network states and algorithms in the presence of a global U(1) symmetry" PRB 83 115125) very helpful. But unfortunately, it focuses on MERA instead of MPSes).

Thanks very much!

Yantao