Week 2
July 27
11:00- (A615, 6th floor of the main building)

E. Jeckelmann (Institute for Theoretical Physics, University of Hannover)
Recent Developments in DMRG

In this second talk, I will first present the variational formulation of DMRG based on matrix- and tensor-product states. Then I will briefly discuss the relationship to quantum information and entanglement. Recent developments in generalizing the DMRG to calculate the spectral properties and the full time evolution of quantum systems (transport, dissipation, ...) will be discussed in detail and some new algorithms based on matrix- and tensor-product states will be outlined.
14:00- (A615, 6th floor of the main building)

K. Okunishi (Department of Physics, Niigata University)
Is DMRG a renormalization group ? --unconventional introduction to DMRG--

Density matrix renormalization group has been established as one of the most reliable numerical tools to investigate the ground state of 1D quantum many body systems. In fact, a lot of interesting properties of 1D quantum spin/correlated electron systems have been clarified by DMRG. Moreover, a variety of extensions of DMRG is recently developing, such as dynamical DMRG, time dependent DMRG....etc. Of course, these are fascinating and important topics. In my talk, however, I want to focus on some fundamental ideas behind DMRG rather than recent algorithmic/technical developments. This is partly because the theoretical back ground of DMRG seems to have connections to a wide area of physics such as quantum imformation, integrable systems, .... I think that a review of the theoretical background becomes potentially important in considering such connections to other fields in physics. Another reason is that a certain part of my interest is now toward some fundamental question that has been attracting me since begining of my research on DMRG: Is DMRG a renormalization group in the Wilson's sense?

Plan of my talk is following:
1 matrix product eigenvector and variational approximation for a transfer
matrix in 2D classical systems
2 connection to the ground state of a quantum Hamiltonian(White's DMRG)
3 matrix product wavefunction in the Hamiltonian problem
4 "critical phenomena" in the reduced density matrix
5 Is DMRG a renormalization group? a comparison to the Wilson's NRG
....

In the first half, I try an unconventional introduction to DMRG, starting from the transfer matrix in a 2D classical system. Then I want to explain recent my consideration about DMRG. Thus the latter half may include not established but trial contents.