[1] Following his Postdoc, Sierra began his academic career as a Titular Professor at the University of Complutense de Madrid in 1984, a position he held for three years.

Townsend, he derived the magic square of Freudenthal, Rozenfeld, and Tits by utilizing the geometric principles found in a specific group of N=2 Maxwell-Einstein supergravity theories.

[35] He introduced a spin chain Hamiltonian that possesses integrability and invariance under 14 (sI(2)) transformations within nilpotent irreducible representations when r3 = 1.

[38] Furthermore, he explored spin-anisotropy commensurable chains, a class of 2D integrable models, and described their mathematics using quantum groups with the deformation parameter as an Nth root of unity.

[44] In addition, he applied the variational matrix product ansatz to determine the ground state of several ladder systems.

Román, introduced multiple models exhibiting a Russian doll renormalization group flow, featuring a cyclic nature instead of converging to a fixed point.

Among them was a BCS model with pairing scattering phases that break time-reversal symmetry,[18] which was later demonstrated to be solvable using the algebraic Bethe ansatz.

[59] Moreover, they put forward two scattering S-matrices exhibiting a cyclic renormalization group (RG) structure, which is related to both the cycle regime of the Kosterlitz-Thouless flow and an analytic extension of the massive sine-Gordon S matrix.

[73] The rainbow chain model, earlier proposed by J. I. Latorre in a separate joint work,[74] was examined using conformal field theory techniques[75][76] and was found to support symmetry-protected phases.

[77] In 2010, Sierra proposed a variational ansatz for the ground state of the XXZ spin chain using the chiral vertex operators of a CFT[24] to describe the critical region of this model, resulting in a matrix product state with an infinite bond dimension to capture logarithmic entanglement entropy.

[89] In 2022, Sierra, together with A. Bera and S. Singha Roy, demonstrated a connection between the ground state of a topological Hamiltonian and the optimal strategy in a causal order game, where the maximum violation of the classical bound is associated with a second-order quantum phase transition.

[26] Furthermore, working in conjunction with D. Centeno led to the development of several quantum versions of the Morra game, known as Chinos in Spain.