Some questions about DMRG
Posted: 31 Jan 2019, 09:56
Hi, I would like to clarify questions about DMRG. Am I right to say that DMRG works very well for gapped Hamiltonians because of the area law and the fact that entanglement in the ground states of such Hamiltonians are minimised? When we extend the method to gapless Hamiltonians, as gapless systems are considered as critical and thus do not obey the area law, it is also computationally more expensive to obtain the correct ground state.
I am asking this because when I am performing finite size effects calculations on the S=1 Heisenberg chain in a uniform magnetic field, the "gap" between the ground state and the lowest excited state increases with system size at B > \Delta{B}_c where \Delta{B}_c > 0.41. The exact parameter used is B=2.0. At this field strength, one expects the Luttinger liquid phase which is gapless. Looking at the entanglement entropy, I can see that entanglement actually increased in the Luttinger liquid phase from the Haldane phase. I suspect that this increase in entanglement coupled with the fact that we are working in the gapless regime, it makes DMRG very inefficient to calculate the ground state energies correctly and accurately with minimal chi states needed to be kept. Is this correct?
However, if the entanglement entropy were to decrease in the gapless phase due to breaking of some symmetry, can we now expect to calculate the ground states efficiently once again?
On a side note, the calculation of excited energies in iDMRG is not trivial right?
I am asking this because when I am performing finite size effects calculations on the S=1 Heisenberg chain in a uniform magnetic field, the "gap" between the ground state and the lowest excited state increases with system size at B > \Delta{B}_c where \Delta{B}_c > 0.41. The exact parameter used is B=2.0. At this field strength, one expects the Luttinger liquid phase which is gapless. Looking at the entanglement entropy, I can see that entanglement actually increased in the Luttinger liquid phase from the Haldane phase. I suspect that this increase in entanglement coupled with the fact that we are working in the gapless regime, it makes DMRG very inefficient to calculate the ground state energies correctly and accurately with minimal chi states needed to be kept. Is this correct?
However, if the entanglement entropy were to decrease in the gapless phase due to breaking of some symmetry, can we now expect to calculate the ground states efficiently once again?
On a side note, the calculation of excited energies in iDMRG is not trivial right?