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.
Tensor network/spacetime correspondences explore the exciting idea that geometric information about a quantum state might be related to the actual geometry that the state describes in a quantum gravitational setting. I will give an overview of a new type of correspondence between global de Sitter spacetime and the MERA. This simple correspondence is already enough to see several features of de Sitter gravity emerge, such as cosmic no-hair and horizon complementarity. I will also comment on some more speculative topics like complexity = action and possible future directions.
I will describe our recent work from 1709.07460, where we introduce a new renormalization group algorithm for tensor networks. The algorithm is based on a novel understanding of local correlations in a tensor network, and a simple method to remove such correlations from any network.
We study 't Hooft anomalies of discrete groups in the framework of (1+1)-dimensional multiscale entanglement renormalization ansatz states on the lattice. Using matrix product operators, general topological restrictions on conformal data are derived. An ansatz class allowing for optimization of MERA with an anomalous symmetry is introduced. We utilize this class to numerically study a family of Hamiltonians with a symmetric critical line.
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 this first part of this talk, I will discuss entanglement properties of models of topological crystalline insulators and spin liquids and show how to incorporate topological order, symmetry fractionalization, and lattice symmetry protected topological order into tensor network wave functions.
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.