Renormalization and tensor product states in spin chains and lattices

By J. I. Cirac, Frank Verstraete. 2009

378 citations recorded by the source corpus.

We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and show that they naturally arise in that context. We concentrate on matrix product states, tree tensor states, multiscale entanglement renormalization ansatz and projected entangled pair states. We highlight some of their properties, and show how they can be used to describe a variety of systems.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/27044bc85b77e716ce61693cbbd43ce594d6a634

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Sahel Ashhab
2. Franco Nori
3. I. Georgescu
4. Frank Verstraete
5. J. I. Cirac
6. Norbert Schuch
7. J. Haegeman
8. T. Takayanagi

In Atomic and Molecular Physics, and Optics

1. Frank Verstraete
2. Norbert Schuch
3. Sahel Ashhab
4. J. Haegeman
5. I. Georgescu
6. Franco Nori
7. I. Cirac
8. David Pérez-García

Citations in the corpus

• Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains (2014, background): “A general discussion of tensor networks and their use in numerical simulations for quantum spin systems can be found in [71,72].”
• The mass spectrum of the Schwinger model with matrix product states (2013, background): “The dashed line corresponds to the fit of the whole computed range, x ∈ [15, 600], to a cubic function in 1/ √ x.”
• Quantum Simulation (2013, background): “For more details we direct the reader to the two reviews (Cirac and Verstraete, 2009; Verstraete et al., 2008) and the references therein.”
• Holographic local quenches and entanglement density (2013, methodology): “reviews [44]) and has been recently used to prepare a candidate of approximate ground states based on the variational principle, optimized by a number of parameters.”
• Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, background): “While there are many reviews on that topic (Biamonte, 2019; Bridgeman and Chubb, 2017; Cirac and Verstraete, 2009; Hallberg, 2006; Orus, 2014; Schollwöck, 2005, 2011; Verstraete et al., 2008) the vast majority focus on the practical aspects of tensor networks; in particular, on how to use them in…”
• Quantum spin liquid states (2016, methodology): “Readers can refer to references (Cirac and Verstraete, 2009; Orus, 2014; Verstraete et al., 2008) for details.”