Abstract
Using matrix product states, we explore numerically the phenomenology of string breaking in a non-Abelian lattice gauge theory, namely 1+1 dimensional SU(2). The technique allows us to study the static potential between external heavy charges, as traditionally explored by Monte Carlo simulations, but also to simulate the real-time dynamics of both static and dynamical fermions, as the latter are fully included in the formalism. We propose a number of observables that are sensitive to the presence or breaking of the flux string, and use them to detect and characterize the phenomenon in each of these setups.
Highlights
A promising approach is the application of tensor networks (TN) to the Hamiltonian formulation of LGT [13,14,15,16,17,18,19,20,21,22,23,24]
Using matrix product states, we explore numerically the phenomenology of string breaking in a non-Abelian lattice gauge theory, namely 1+1 dimensional SU(2)
The technique allows us to study the static potential between external heavy charges, as traditionally explored by Monte Carlo simulations, and to simulate the real-time dynamics of both static and dynamical fermions, as the latter are fully included in the formalism
Summary
The model we consider is the Hamiltonian formulation of a 1+1 dimensional SU(2) lattice gauge theory with dynamical fermions, in which the gauge symmetry is exactly realized with finite-dimensional link variables [47]. Rnα are the generators of left and right gauge transformations acting on link n, which correspond to the left and right electric field on the link and fulfill the commutation relations [Lαn, Lβm] = −iδnm γ εαβγLγn, [Rnα, Rmβ ] = iδnm γ εαβγRnγ and [Lαn, Rmβ ] = 0 They are related to the operator for the electric flux energy as J2n = α LαnLαn = α RnαRnα. The Gauss Law components do not commute among themselves, as [Gαn, Gβm] = −iδnm γ εαβγGγn, and cannot be diagonalized simultaneously They all commute with the Hamiltonian, [H, Gαn] = 0, so that the Hilbert space is a direct sum of sectors characterized by their configuration of external charges, {qnα} [47]. The fermionic part of this state corresponds to the Dirac sea, and it is easy to check that it fulfills Gauss Law with Gαn|φSC = 0 ∀n, α Applying on this state the gauge invariant string operator. We consider the model corresponding to the simplest non-trivial truncation of the full theory, meaning that only the trivial and the fundamental representation are kept, resulting in dimension 5 for the links
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