Matrix product states algorithms and continuous systems

Iblisdir, S., Roman Orus Lacort and Latorre, J. I. (2007) Matrix product states algorithms and continuous systems. Physical Review B, 75 10: 104305-1-104305-15. doi:10.1103/PhysRevB.75.104305

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Author Iblisdir, S.
Roman Orus Lacort
Latorre, J. I.
Title Matrix product states algorithms and continuous systems
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
Publication date 2007-03-23
Year available 2007
Sub-type Article (original research)
DOI 10.1103/PhysRevB.75.104305
Open Access Status File (Publisher version)
Volume 75
Issue 10
Start page 104305-1
End page 104305-15
Total pages 15
Editor P.D. Adams
Place of publication United States
Publisher American Physical Society
Collection year 2008
Language eng
Subject 240202 Condensed Matter Physics - Structural Properties
C1
780102 Physical sciences
Abstract A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS's) and the algorithms thereof. The method is quite versatile and can be applied to a wide variety of situations. As a first test, we show how it provides reliable results in the computation of fundamental properties of a chain of quantum harmonic oscillators achieving off-critical and critical relative errors of the order of 10(-8) and 10(-4), respectively. Next, we use it to study the ground-state properties of the quantum rotor model in one spatial dimension, a model that can be mapped to the Mott insulator limit of the one-dimensional Bose-Hubbard model. At the quantum critical point, the central charge associated with the underlying conformal field theory can be computed with good accuracy by measuring the finite-size corrections of the ground-state energy. Examples of MPS computations both in the finite-size regime and in the thermodynamic limit are given. The precision of our results is found to be comparable to that previously encountered in the MPS studies of, for instance, quantum spin chains. Finally, we present a spin-off application: an iterative technique to efficiently get numerical solutions of partial differential equations of many variables. We illustrate this technique by solving Poisson-like equations with precisions of the order of 10(-7).
Keyword Physics, Condensed Matter
Q-Index Code C1
Q-Index Status Confirmed Code

 
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Created: Wed, 09 Apr 2008, 15:53:11 EST by Jo Hughes on behalf of School of Mathematics & Physics