Pietro Silvi, Ferdinand Tschirsich, Matthias Gerster, Johannes Jünemann, Daniel Jaschke, Matteo Rizzi, Simone Montangero
SciPost Phys. Lect. Notes 8 (2019) ·
published 18 March 2019

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We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of manybody quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with lowdimension physical setups, from a computational physics perspective. We focus on symmetries and closedsystem simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loopfree network geometries, discussing their advantages, and presenting in detail algorithms to simulate lowenergy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a selfcontained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.
Ferdinand Tschirsich, Simone Montangero, Marcello Dalmonte
SciPost Phys. 6, 028 (2019) ·
published 6 March 2019

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We investigate the ground state phase diagram of square ice  a U(1) lattice
gauge theory in two spatial dimensions  using gauge invariant tensor network
techniques. By correlation function, Wilson loop, and entanglement diagnostics,
we characterize its phases and the transitions between them, finding good
agreement with previous studies. We study the entanglement properties of string
excitations on top of the ground state, and provide direct evidence of the fact
that the latter are described by a conformal field theory. Our results pave the
way to the application of tensor network methods to confining, twodimensional
lattice gauge theories, to investigate their phase diagrams and lowlying
excitations.
Mr Tschirsich: "We thank the referee for her/h..."
in Report on Phase Diagram and Conformal String Excitations of Square Ice using Gauge Invariant Tensor Networks