Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

Understand

It has been established that Matrix Product States can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit.

• However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group.
• We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavour QED$_2$, with a uniform electric background field.
• We compute the two-site reduced density matrix of the ground state and the weight of each of the representations.