Typicality in random matrix product states

Details Typicality in random matrix product states Typicality in random matrix product states

2009-08-26

arxiv.org/abs/0908.3877v2

Phys. Rev. A 81, 032336 (2010)

Physics

Quantum Physics

9 pages, 6 figures; accepted for publication in PRA

Scientific paper

10.1103/PhysRevA.81.032336

Recent results suggest that the use of ensembles in Statistical Mechanics may not be necessary for isolated systems, since typically the states of the Hilbert space would have properties similar to the ones of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are non-physical and not good descriptions of realistic systems. Therefore, to better understand the actual power of typicality it is important to ask if it is also a property of a set of physically relevant states. Here we address this issue, studying if and how typicality emerges in the set of matrix product states. We show analytically that typicality occurs for the expectation value of subsystems' observables when the rank of the matrix product state scales polynomially with the size of the system with a power greater than two. We illustrate this result numerically and present some indications that typicality may appear already for a linear scaling of the rank of the matrix product state.

Affiliated with

Also associated with

No associations

Rating

Typicality in random matrix product states does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Typicality in random matrix product states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Typicality in random matrix product states will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-625728