Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 063039 |
| Fachzeitschrift | New Journal of Physics |
| Jahrgang | 17 |
| Ausgabenummer | 6 |
| Publikationsstatus | Veröffentlicht - 29 Juni 2015 |
Abstract
Anatural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentzinvariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
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in: New Journal of Physics, Jahrgang 17, Nr. 6, 063039, 29.06.2015.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Continuum tensor network field states, path integral representations and spatial symmetries
AU - Jennings, David
AU - Brockt, Christoph
AU - Haegeman, Jutho
AU - Osborne, Tobias J.
AU - Verstraete, Frank
N1 - Funding information: Helpful discussions with H Verschelde are gratefully acknowledged. This work was supported by EU grants QUERG and QFTCMPS, FWF SFB grants FoQuS and ViCoM, and by the cluster of excellence EXC 201 Quantum Engineering and Space-Time Research. DJ is supported by the Royal Society. Helpful discussions withHVerschelde are gratefully acknowledged. This work was supported by EU grants QUERGand QFTCMPS,FWFSFB grants FoQuS and ViCoM, and by the cluster of excellence EXC 201 Quantum Engineering and Space-Time Research. DJ is supported by the Royal Society.
PY - 2015/6/29
Y1 - 2015/6/29
N2 - Anatural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentzinvariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.
AB - Anatural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentzinvariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.
KW - Many-body physics
KW - Quantum fields
KW - Quantum information theory
UR - http://www.scopus.com/inward/record.url?scp=84983445899&partnerID=8YFLogxK
U2 - 10.1088/1367-2630/17/6/063039
DO - 10.1088/1367-2630/17/6/063039
M3 - Article
AN - SCOPUS:84983445899
VL - 17
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
IS - 6
M1 - 063039
ER -