講演者：Sung G. Chung 氏（Western Michigan University）
日時：６月　１２日（金）　午後４時３０分から
場所： 青山学院大学　理工学部（相模原キャンパス）Ｌ棟６階　Ｌ６０３室

題目： 「Entanglement perturbation theory : 
a novel many-body method in statistical mechanics and 
strong correlation physics」



要旨：
　Since the very beginning of quantum theory, to calculate 
the partition functions and solve the Schro"dinger equation
for macroscopic quantum systems have been a fundamental task 
of theoretical physics. It would not be an exaggeration
to say that due to lack of such methods, a tremendous effort 
of theoretical physicists has been devoted to the development 
of a variety of approximate methods and numerical simulations. 
While we have seen a considerable progress in rigorous 
treatment of quantum 1D and classical 2D systems over the last 
several decades, these rigorous methods cannot handle 
non-integrable models nor generalizable to higher dimensions. 
On the other hand, the method of numerical renormalization 
group has seen a remarkable success in quantum 1D systems and 
in finite Fermi systems.
However, in spite of a huge effort, this approach has not 
been quite successful for macroscopic 2D quantum systems,
indicating the very idea of Hilbert space truncation breaks 
down in two dimensions. Over the recent years, we have been 
developing a novel many-body method, entanglement perturbation 
theory (EPT), for calculating partition functions and solve 
the Schro"dinger equation, particularly in the strongly 
correlated condensed matter systems. The method is simple, 
general, and exact. The current status of EPT is this:
(a) The ground states of 1D quantum systems with finite-range 
interactions and translational symmetry can be handled.
(b) The elementary excitation in 1D quantum systems can be calculated.
(c) The partition functions of 2,3D classical systems can be calculated.
(d) After a long struggle, we have started to see a clear evidence 
that EPT can also handle the quantum ground states in 2D.
In this talk, I will give an overview of this new theoretical 
endeavor: what was done, what is currently underway and 
what I am dreaming of.


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