Truncating an exact matrix product state for the XY model: Transfer matrix and its renormalization

Autor(en)

Marek M. Rams, Valentin Zauner, Matthias Bal, Jutho Haegeman, Frank Verstraete

Abstrakt

We discuss how to analytically obtain an essentially infinite matrix product state (MPS) representation of the ground state of the XY model. On one hand this allows us to illustrate how the Ornstein-Zernike form of the correlation function emerges in the exact case using standard MPS language. On the other hand we study the consequences of truncating the bond dimension of the exact MPS, which is also part of many tensor network algorithms, and analyze how the truncated MPS transfer matrix is representing the dominant part of the exact quantum transfer matrix. In the gapped phase we observe that the correlation length obtained from a truncated MPS approaches the exact value following a power law in effective bond dimension. In the gapless phase we find a good match between a state obtained numerically from standard MPS techniques with finite bond dimension and a state obtained by effective finite imaginary time evolution in our framework. This provides a direct hint for a geometric interpretation of finite entanglement scaling at the critical point in this case. Finally, by analyzing the spectra of transfer matrices, we support the interpretation put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015)] that the MPS transfer matrix emerges from the quantum transfer matrix though the application of Wilson's numerical renormalization group along the imaginary-time direction.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Jagiellonian University in Krakow, Tadeusz Kościuszko University of Technology, Ghent University

Journal

Physical Review B

Band

92

Anzahl der Seiten

13

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.92.235150

Publikationsdatum

12-2015

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Electronic, Optical and Magnetic Materials, Condensed Matter Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/41841853-7d50-48ab-934e-7e8a42c09b41