Tensor Network

This series consists of biweekly seminars on Tensor Networks, ranging from algorithms to their application in condensed matter, quantum gravity, or high energy physics. Each seminar starts with a gentle introduction to the subject under discussion. Everyone is strongly encouraged to participate with questions and comments.

Seminar Series Events/Videos

Currently there are no upcoming talks in this series.
 

 

Thursday Apr 18, 2019
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Computing vacuum expectation values is paramount in studying Quantum Field Theories (QFTs) since they provide relevant information for comparing the underlying theory with experimental results.

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Monday Apr 08, 2019
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We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is shown the emergence of a CDL fixed point structure. In the massless limit, we reproduce the results of conformal field theory including a precise value of the central charge.

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Thursday Mar 28, 2019
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Adiabatic evolution is a common strategy for manipulating quantum states. However, it is inherently slow and therefore susceptible to decoherence. Shortcuts to adiabaticity are methods of achieving faster adiabatic evolution, in order to maintain high fidelity in the presence of decoherence and noise. In this talk I will review recent progress on counter-diabatic (CD) driving for many-body systems. In particular, we will discuss a variational principle that allows to systematically compute approximate CD Hamiltonians. Two recent experiments will be discussed. 

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Tuesday Oct 16, 2018
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We discuss some algebraic quantum field theory (AQFT) ingredients that should be useful in defining a tensor network describing a Lorentzian space-time.

We look into toy models that approximate Minkowski space and show how Lorentz boosts are approximately recovered, and obtain Rindler modes that can be compared with the entanglement spectrum. 

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Tuesday Oct 09, 2018
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Abstract TBD.

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Tuesday Sep 04, 2018
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Simplicial complexes naturally describe discrete topological spaces. When their links are assigned a length they describe discrete geometries. As such simplicial complexes have been widely used in quantum gravity approaches that involve a discretization of spacetime. Recently they are becoming increasingly popular to describe complex interacting systems such a brain networks or social networks. In this talk we present non-equilibrium statistical mechanics approaches to model large simplicial complexes.

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Tuesday Aug 07, 2018

Three fundamental factors determine the quality of a statistical learning algorithm: expressiveness, generalization and optimization.  The classic strategy for handling these factors is relatively well understood.  In contrast, the radically different approach of deep learning, which in the last few years has revolutionized the world of artificial intelligence, is shrouded by mystery.  This talk will describe a series of works aimed at unraveling some of the mysteries revolving expressiveness, arguably the most prominent factor behind the success of deep learning.  I will begin b

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Thursday Dec 07, 2017

In this talk, I will discuss how to assign geometries, such as metric tensors, to certain tensor networks using quantum entanglement and tensor Radon transform. In addition, we show that behaviour similar to linearized gravity can naturally emerge in said tensor networks, provided a modified version of Jacobson's entanglement equilibrium is satisfied. Since the aforementioned properties can be reached without relying on AdS/CFT, the approach also shows promise towards constructing tensor network models for cosmological spacetimes. 

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Thursday Dec 07, 2017
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A great deal of progress has been made toward a classification of bosonic topological orders whose microscopic constituents are bosons. Much less is known about the classification of their fermionic counterparts. In this talk I will describe a systematic way of producing fermionic topological orders using the technique of fermion condensation.

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Thursday Nov 30, 2017

The construction of trial wave functions has proven itself to be very useful for understanding strongly interacting quantum many-body systems. Two famous examples of such trial wave functions are the resonating valence bond state proposed by Anderson and the Laughlin wave function, which have provided an (intuitive) understanding of respectively spin liquids and fractional Quantum Hall states. Tensor network states are another, more recent, class of such trial wave functions which are based on entanglement properties of local, gapped systems.

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