Hi all,
I will be defending my thesis and it would be great to see you
there. The details are:
Space-time coordinates : Monday, April 23, 2012 at 11 am in room 4-159.
Title : Eigenvalues and Eigenvectors of QMBS
Abstract:
The first part is devoted to eigenvalues of quantum many-body systems
(QMBS). I introduce Isotropic Entanglement (IE) and show that the
distribution of QMBS with generic interactions can be accurately
obtained using IE. Next, I discuss the eigenvalue distribution of one
particle hopping random Schr\"{o}dinger operator in one dimension
from free probability theory.
The second part is devoted to ground states and gap of QMBS. I first
give the necessary background on frustration free Hamiltonians, real
and imaginary time evolution of quantum spin systems on a line within
MPS representation and the numerical implementation. I then prove the
degeneracy and unfrustration condition for quantum spin chains with
generic local interactions. Lastly, I discuss a measure zero example
(i.e., $d=3$) which is a frustration free translation-invariant spin-1
chain that has a unique highly entangled ground state and exhibits
some signatures of a critical behavior.
See you then and there!
Ramis
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