Corrections to Wigner–Eckart Relations by Spontaneous Symmetry Breaking

Abstract

<jats:p>The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.</jats:p>

Discrete time crystal in a finite chain of Rydberg atoms without disorder

“…Inspired by the concept of crystal order in space, in 2012 Wilczek first proposed the idea of a timecrystal phase, corresponding to spontaneous time-translationsymmetry breaking [2], whereby time-periodic properties, i.e., a clock, emerge in a time-invariant dynamical system. This intriguing idea was found to be unfeasible [3,4] at thermal equilibrium, though it can be suitably generalized [5,6]. It was soon realized, however, that periodically driven (i.e., Floquet) systems may enter a discrete time-crystal (DTC) phase [7][8][9][10][11], in which the dynamics is governed by a periodicity that is different (typically a subharmonic) from that of the Hamiltonian.…”