Matrix product state renormalization

Autor(en)

M. Bal, M. M. Rams, Valentin Zauner, J. Haegeman, F. Verstraete

Abstrakt

The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this compression as an application of Wilson's numerical renormalization group along the imaginary time direction appearing in the path integral representation of the state. The location of the physical index is considered as an impurity in the transfer matrix and static MPS correlation functions are reinterpreted as dynamical impurity correlations. Coarse-graining the transfer matrix is performed using a hybrid variational ansatz based on matrix product operators, combining ideas of MPS and the multiscale entanglement renormalization ansatz. Through numerical comparison with conventional MPS algorithms, we explicitly verify the impurity interpretation of MPS compression, as put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015)NJOPFM1367-263010.1088/1367-2630/17/5/053002] for the transverse-field Ising model. Additionally, we motivate the conceptual usefulness of endowing MPS with an internal layered structure by studying restricted variational subspaces to describe elementary excitations on top of the ground state, which serves to elucidate a transparent renormalization group structure ingrained in MPS descriptions of ground states.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Ghent University , Jagiellonian University in Krakow

Journal

Physical Review B

Band

94

Anzahl der Seiten

14

ISSN

1098-0121

DOI

https://doi.org/10.1103/PhysRevB.94.205122

Publikationsdatum

11-2016

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie

Schlagwörter

ASJC Scopus Sachgebiete

Electronic, Optical and Magnetic Materials, Condensed Matter Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/3d200b01-9597-4804-bd61-e1ab8f1d4eee