Tensor Networks for Quantum Field Theories Conference
In this second presentation, we will revisit Feynman's first argument and discuss how it still strongly influences variational studies of relativistic field theories with MPS or cMPS. However, as we explain, this argument can be completely overcome by introducing different variational parameters for the different length scales in the system, a strategy that naturally results in the MERA for lattice systems, or its continuous version for field theories.
In this talk I will describe how to generalize the multiscale entanglement renormalization ansatz to quantum fields. The resulting variational class of wavefunctions, cMERA, arising from this RG flow are translation invariant and exhibit an entropy-area law. I'll illustrate the construction for some example fields, and describe how to cover the case of interacting theories.
Topological Quantum field theories(TQFTs) are a special class of QFTs. Their actions do not depend on the metric of the background space-time manifold. Thus, it is very natural to define TQFTs on an arbitrary triangulation of the space-time manifold and they are independent on the triangulation. More importantly, TQFTs defined on triangulations are always a finite theory associated with a well defined cut-off. A well known example is the Turaev-Viro states sum invariants. Essentially, the Turaev-Viro constructions are (local) tensor network representations of a special class of 1+2D TQFTs.
The MERA offers a powerful variational approach to quantum field theory. While the continuous MERA may allow us to directly address field theories in the continuum, the MERA on the lattice has already demonstrated its ability to characterize conformal field theories. In this talk I will explain how to extract the conformal data (central charge, primary fields, and their scaling dimensions and OPE) of a CFT from a quantum spin chain at a quantum critical point.
One might be confused by the proliferation of tensor network states, such as MPS, PEPS, tree tensor networks [TTN], MERA, etc. What is the main difference between them? In this talk I will argue that the geometry of a tensor network determines several properties of the state that is being represented, such as the asymptotic scaling of correlations and of entanglement entropy. I will also describe the relation between the MERA and the Renormalization Group, and will review Brian Swingle
In 1987, Feynman devoted one of his last lectures to highlighting three serious objections against the usefulness of the variational principle in the theory of relativistic quantum fields. In that same year, in a different branch of physics, Affleck, Kennedy, Lieb and Tasaki devised a quantum state that resulted in the development of a handful of different variational ansÃ¤tze for lattice models over the last two decennia. These quantum states are known as tensor network states and invalidate at least two of Feynman's arguments.
I will talk about matrix product states and their suitability for simulating quantum many-body systems in the continuum.
In this talk, I will present a first principle construction of a holographic dual for gauged matrix models that include gauge theories. The dual theory is shown to be a closed string field theory coupled with an emergent two-form gauge field defined in one higher dimensional space. The bulk space with an extra dimension emerges as a well defined classical background only when the two-form gauge field is in the deconfinement phase. Based on this, it is shown that critical phases that admit holographic descriptions form a novel universality class with a non-trivial quantum order.
The study of fermionic and frustrated systems in two dimensions is one of the biggest challenges in condensed matter physics. Among the most promising tools to simulate these systems are 2D tensor networks, including projected entangled-pair states (PEPS) and the 2D multi-scale entanglement renormalization ansatz (MERA), which have been generalized to fermionic systems recently.
This introductory talk aims to answer a few basic questions (What is a tensor network? Under which circumstance is a tensor network useful?) and describe the tensor network states that will be discussed during the workshop (matrix product state [MPS], projected entangled pair states [PEPS], and the multi-scale entanglement renormalization ansatz [MERA]). I will then briefly describe the recent developments that motivated this workshop on