Chasing infinity with matrix product states by embracing divergences

Crosswhite, Gregory M. (2014) Chasing infinity with matrix product states by embracing divergences. Journal of Physics A: Mathematical and Theoretical, 47 6: . doi:10.1088/1751-8113/47/6/065303


Author Crosswhite, Gregory M.
Title Chasing infinity with matrix product states by embracing divergences
Journal name Journal of Physics A: Mathematical and Theoretical   Check publisher's open access policy
ISSN 1751-8113
1751-8121
Publication date 2014-02-14
Year available 2014
Sub-type Article (original research)
DOI 10.1088/1751-8113/47/6/065303
Open Access Status
Volume 47
Issue 6
Total pages 19
Place of publication Bristol, United Kingdom
Publisher Institute of Physics Publishing
Collection year 2015
Language eng
Formatted abstract
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products, expectations, etc, as maps from natural numbers to complex numbers which contain information about how these quantities diverge, and in particular whether they scale linearly, quadratically, exponentially, etc with the size of the system. We build our formalism on a variant of matrix product states, as this class of states has a structure that naturally provides a way to obtain the scaling function. We show that the states in our formalism form a module over the ring of functions that are made up of sums of exponentials times polynomials and delta functions. We analyze properties of this formalism and show how it works for selected systems. Finally, we discuss how our formalism relates to other work.
Keyword Quantum mechanics
Mathematical physics
Matrix product states
Infinite systems
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article no.: 065303

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2015 Collection
 
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