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.
In recent years there has been quite some effort to apply Matrix Product States (MPS) and more general Tensor Networks (TN) to lattice gauge theories. Contrary to the standard Euclidean-time Monte Carlo approach, which faces a major obstacle in the sign problem, numerical methods based on TN are free from the sign problem and allow to some extent simulating time evolution. Moreover, TN are also a suitable tool to explore proposals for potential future quantum simulators for lattice gauge theories.
In this talk I will give a short introduction into Projected Entangled-Pair States (PEPS), and their infinite variant iPEPS, a class of tensor network Ansatz targeted at the simulation of 2D strongly correlated systems. I will present work on two recent
In order to create ansatz wave functions for models that realize topological or symmetry protected topological phases, it is crucial to understand the entanglement properties of the ground state and how they can be incorporated into the structure of the wave function.
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study local quantum many-body systems at low energies.
I discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. I review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state.
Entanglement is fundamental to quantum mechanics. It is central to the EPR paradox and Bell’s inequality. Tensor network states constructed with explicit entanglement structures have provided powerful new insights into many body quantum mechanics. In contrast, the saddle points of conventional Feynman path integrals are not entangled, since they comprise a sequence of classical field configurations.
In the rst part of this talk I will give a brief introduction to the variational class of continuous
matrix product states (cMPS). Then I will present a time evolution algorithm for cMPS with periodic
boundary conditions. In the second part, I will explain how to apply this method to simulate
atomtronic circuits. In particular, I will show results for persistent currents in an interacting bose
gas rotating in a ring shaped trap in the presence of an arti cial U(1) gauge potential.
In this talk, I present a new framework for topologically ordered gapped ground states in 2+1 spacetime dimensions (which generalizes to higher dimensions) using tensor networks. We will see that topological order can exist in tensor network states (TNS), if the local tensor satisfies certain axioms which we call MPO (matrix product operator)-injectivity and pulling through. We then continue with examples, and see how renormalization fixed point models in the literature (Levin-Wen models, etc.) can be covered in this framework.
I will describe how to define a proper RG flow in the space of
tensor networks, with applications to the evaluation of classical
partition functions, euclidean path integrals, and overlaps of tensor
network states.