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

  title={Tensor network simulation of QED on infinite lattices: Learning from (1+1)d , and prospects for (2+1)d},
  author={Kai Zapp and Rom{\'a}n Or{\'u}s},
  journal={Physical Review D},
The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in $(3+1)$ dimensions in regimes difficult for other methods. So far, however, TN methods have mostly simulated lattice gauge theories in $(1+1)$ dimensions. The aim of this paper is to explore the simulation of quantum electrodynamics (QED) on infinite lattices with TNs, i.e., fermionic matter fields coupled… 

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Preface 1. Introduction 2. Path integral and lattice regularisation 3. O(n) models 4. Gauge field on the lattice 5. U(1) and SU(n) gauge theory 6. Fermions on the lattice 7. Low mass hadrons in QCD

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A more detailed analysis and justification of this truncation can be found in Ref

    Recall that an occupied positron or electron state corresponds to sn = 1 or sn = −1, respectively, and that positrons/electrons live on even

      We choose A as the center site for the mixed canonical form of the MPS

        JHEP 11 (2013) 158; B

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        Ln |pn = pn |pn with pn = 0, ±1


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          This is what is meant by local : one can redefine the phase of the fermionic field locally at every point in space-time