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Tensor-Network Methods: Structure, Applications and Holography: December 11 – 15, 2017

Organized by: Glen Evenbly (University of Sherbrooke), Roman Orus (Univ. of Mainz), David Perez-Garcia (Univ. Complutense de Marid), Tzu-Chieh Wei (Stony Brook University)

Attendee ListScheduleShuttle ScheduleView Videos

Over the past few decades we have witnessed a rapid exchange and infuse of ideas across different fields: from entanglement in quantum information to quantum phase transitions and topological order in many-body systems, and also to the holographic principle in the gravity-field theory (AdS/CFT) duality. A very useful framework that emerges from behind the curtain is that of tensor networks. Tensor Networks (TN) are rapidly evolving as an important tool and language and are employed by researchers of various different fields.

The simplest TN is the one-dimensional matrix product state (MPS) or finitely correlated state and is the fixed-point form that the density-matrix renormalization group (DMRG) converges to. DMRG and variational MPS algorithms are very efficient in dealing with one-dimensional and quasi-one-dimensional gapped quantum systems. Besides the algorithmic advantage, the MPS formulation has been utilized in the complete classification of one-dimensional gapped systems. The Mutli-scale Entanglement Renormalization Ansatz (MERA) and its generalization can cope with one-dimensional gapless systems and is able to obtain, for example, the central charge of a CFT, scaling dimensions of primary and quasi-primary operators, as well as the operator-product coefficients. The Projected Entangled Pair States (PEPS) or tensor-product states were a generalization of MPS to two and higher dimensions. They embody the entanglement area law and have been used variationally to approximate ground state wavefunctions. They can also be used to represent topologically ordered states, such eigenstates of the toric code and string-net models, as well as chiral topological states with a nonzero chiral central charge. In fact the classification of intrinsic topological order and symmetry-protected topological order can also be described in the same framework of PEPS. In order to compute physical properties, such as energy and other local observables, the corresponding tensor network needs to be contracted. Methods using real-space renormalization procedure, such as tensor renormalization group (TRG), higher-order TRG (HOTRG), corner transfer matrix (CTM), and more recently tensor network renormalization (TNR) have been proposed and were also successfully applied. Among many recent developments, the connection of TNs to holography is particularly interesting. It was proposed that MERA or a generalization of such tensor network is a discretized version of the AdS/CFT correspondence and a manifestation of the holographic nature entanglement, which may play a central role in a consistent theory of quantum gravity and emergence of spacetime. Other toy models for such bulk-boundary correspondence have been proposed using holographic quantum error-correcting codes, and using perfect and random tensors.

At such an exciting juncture, this proposed workshop aims to bring together experts in various related fields, and under such an embracing theme of tensor network the scientific activities and discussions in this workshop will generate further novel ideas linking different fields.

December 6-8, 2017 we will be hosting pre-workshop tutorials. These tutorials will be given by:

Lecturers:
Glen Evenbly (University of Sherbrooke): Introduction to entanglement renormalization and the MERA (notes -> WaveFree.pdf, code1 -> mera_exercises.jl, code2-> (binarymera.jl)
Ian McCulloch (University of Queensland): Introduction to MPS/DMRG (Code)
Norbert Schuch (Max Planck Institute for Quantum Optics): Tensor Network Theory — Symmetries, Entanglement, and Topological Order
Laurens Vanderstraeten (Ghent University): Tangent space methods for matrix product states (Notes, Code)

 

Dec. 6 (Wed)

9:30-10:30 Ian McCulloch (lecture)
10:30-11:00 break
11:00-12:00pm Laurens Vanderstraeten (lecture)
12:00pm-1:45pm lunch and free discussion
1:45pm-3:30pm Hands-on session [Ian] /problem discussions/Q&A
3:30pm-4:00pm break
4:00pm-5:00pm Glen Evenbly (lecture)

Dec. 7 (Thurs)

9:30-10:30 Ian McCulloch (lecture)
10:30-11:00 break
11:00-12:00 Laurens Vanderstraeten (lecture)
12:00-1:45 lunch and free discussion
1:45pm-3:30pm Hands-on session [Laurens] /problem discussions/Q&A
3:30pm-4:00pm break
4:00pm-5:00pm Norbert Schuch (lecture)

Dec. 8 (Friday)

9:30-10:30 Norbert Schuch (lecture)
10:30-11:00 break
11:00-12:00pm Glen Evenbly (lecture)
12:00-1:45 Lunch and free discussions
1:45pm-3:30pm Hands-on session [Glen]/problem discussions/Q&A
3:30pm-4:00pm end of tutorials and break

Talk Schedule


Time Title Presenter Location
9:30am Anyon condensation and topological phase transitions in tensor networks Norbert Schuch SCGP 102
10:30am Break Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
11:00am Matrix product states and symmetry Ian McCulloch SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Implicit Disentangling for Quantum Many-Body States Glen Evenbly SCGP 102
3:00pm Super vector spaces and fermionic tensor networks Nick Bultinck (short talk) SCGP 102
4:00pm Michael Zaletel SCGP 102

Time Title Presenter Location
9:15am Causal Structure of Emergent Geometries Thomas Hartman SCGP 102
10:15am Break Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
10:40am Holography and criticality in matchgate tensor networks Jens Eisert SCGP 102
11:40am Lunch N/A SCGP Cafe
1:00pm Frank Verstraete N/A
2:30pm Philippe Corborz SCGP 102
3:30pm Break N/A
4:00pm Laurens Vanderstraeten SCGP 102

Time Title Presenter Location
9:30am Shinsei Ryu SCGP 102
10:30am Break Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
11:00am Multiresolution decomposition of many-body Hilbert space using tensor networks Jutho Haegeman SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Ying-Jer Kao SCGP 102
3:00pm Break SCGP 102
3:30pm Sujeet Shukla (short talk) Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
4:10pm Nicholas Pomata SCGP 102

Time Title Presenter Location
9:30am Didier Poilblanc SCGP 102
10:30am Break Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
11:00am Shuo Yang SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Miles Stoudenmire SCGP 102
3:00pm Break Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
3:30pm Xiaoliang Qi SCGP 102
4:30pm Break Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
6:00pm Banquet SCGP Cafe

Time Title Presenter Location
9:30am Entanglement entropy of the boundary spin configuration of a random 2D statistical system Tomotoshi Nishino SCGP 102
10:30am Break Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794, USA
11:00am Mehmet Burak Sahinoglu (short talk) SCGP 102
11:40am Andrej Gendiar (short talk) SCGP 102
12:20pm Lunch and Departure N/A SCGP Cafe