Location:
Erwin Schrödinger lecture hall
Faculty of Physics, Strudlhofgasse 4/Boltzmanngasse 5, 5th floor
Title:
Field tensor network states
Abstract:
Tensor networks (TNS) can provide exact representative ground-states for a wide variety of systems that possess an entanglement area law. However, states which demand an entanglement structure beyond that, such as critical states in one-dimensional systems, lack an exact analytical description in terms of matrix product states (MPS). Furthermore, there are states in two-dimensional systems that can also not be exactly expressed as projected entangled pair states (PEPS), such as chiral gapped states like the Laughlin state. In order to provide exact descriptions for these states, we construct a field theory generalization of tensor network states known as field tensor network states (fTNS). These are by construction infinite dimensional tensor networks whose virtual space is described by a conformal field theory (CFT). To better understand this ansatz, we first aim to understand which theorems of standard TNS theory translate to fTNS. We prove an analogous relation about symmetry protected topological (SPT) order classification for the case of fMPS, by studying the interplay between symmetry representations of the physical and virtual space for a critical spin system. We use this result to distinguish the two ground states of the critical Majumdar-Ghosh point according to their critical SPT classification. In two dimensions, we use fPEPS to provide an exact and analytically contractible tensor network representation of a chiral gapped state, the Laughlin state on a plane and a recipe for the Kalmeyer-Laughlin state on a torus.
Host:
Norbert Schuch
You are welcome to join this talk without prior registration.
This talk is part of the Quantum Information and Quantum Many-Body Physics seminar. For information on further talks in this series, please visit our seminar page.