English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The simulation of lattice gauge theories with tensor network (TN) methods isbecoming increasingly fruitful. The vision is that such methods will,eventually, be used to simulate theories in $(3+1)$ dimensions in regimesdifficult for other methods. So far, however, TN methods have mostly simulatedlattice gauge theories in $(1+1)$ dimensions. The aim of this paper is toexplore the simulation of quantum electrodynamics (QED) on infinite latticeswith TNs, i.e., fermionic matter fields coupled to a $U(1)$ gauge field,directly in the thermodynamic limit. With this idea in mind we first consider agauge-invariant iDMRG simulation of the Schwinger model -i.e., QED in$(1+1)d$-. After giving a precise description of the numerical method, webenchmark our simulations by computing the substracted chiral condensate in thecontinuum, in good agreement with other approaches. Our simulations of theSchwinger model allow us to build intuition about how a simulation shouldproceed in $(2+1)$ dimensions. Based on this, we propose a variational ansatzusing infinite Projected Entangled Pair States (PEPS) to describe the groundstate of $(2+1)d$ QED. The ansatz includes $U(1)$ gauge symmetry at the levelof the tensors, as well as fermionic (matter) and bosonic (gauge) degrees offreedom both at the physical and virtual levels. We argue that all thenecessary ingredients for the simulation of $(2+1)d$ QED are, a priori, alreadyin place, paving the way for future upcoming results.

Tensor network simulation of QED on infinite lattices: learning from (1+1)d, and prospects for (2+1)d