José María Román

Large-N limit of the exactly solvable BCS model: analytics versus numerics

Abstract We have studied the numerical solutions of Richardson equations of the BCS model in the limit of large number of energy levels at half-filling, and compare them with the analytic results derived by Gaudin and Richardson, which in turn leads to the standard BCS solution. We focus on the location and density of the roots, the eigenvalues of the conserved quantities, and the scaling properties of the total energy for the equally spaced and the two-level models.

Russian doll renormalization group and superconductivity

We show that a simple extension of the standard BCS Hamiltonian leads to an infinite number of BCS eigenstates with different energy gaps and self-similar properties, described by a cyclic renormalization group flow of the BCS coupling constant which returns to its original value after a finite renormalization group time.

Russian doll renormalization group and Kosterlitz–Thouless flows

We investigate the previously proposed cyclic regime of the Kosterlitz-Thouless renormalization group (RG) flows. The period of one cycle is computed in terms of the RG invariant. Using bosonization, we show that the theory has

Log-periodic behavior of finite size effects in field theories with RG limit cycles

U_q (\hat{sl(2)})

Elementary excitations of the BCS model in the canonical ensemble

quantum affine symmetry, with

The regulated four-parameter one-dimensional point interaction

q

Charge and spin quantum fluids generated by many-electron interactions

{\it real}. Based on this symmetry, we study two possible S-matrices for the theory, differing only by overall scalar factors. We argue that one S-matrix corresponds to a continuum limit of the XXZ spin chain in the anti-ferromagnetic domain

Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystalline Solids

\Delta<-1

The matrix product approach to quantum spin ladders

. The latter S-matrix has a periodicity in energy consistent with the cyclicity of the RG. We conjecture that this S-matrix describes the cyclic regime of the Kosterlitz-Thouless flows. The other S-matrix we investigate is an analytic continuation of the usual sine-Gordon one. It has an infinite number of resonances with masses that have a Russian doll scaling behavior that is also consistent with the period of the RG cycles computed from the beta-function. Closure of the bootstrap for this S-matrix leads to an infinite number of particles of higher spin with a mass formula suggestive of a string theory.

What are the elementary excitations of the BCS model in the canonical ensemble

Abstract We compute the finite size effects in the ground state energy, equivalently the effective central charge c eff , based on S-matrix theories recently conjectured to describe a cyclic regime of the Kosterlitz–Thouless renormalization group flows. The effective central charge has periodic properties consistent with renormalization group predictions. Whereas c eff for the massive case has a singularity in the very deep ultra-violet, we argue that the massless version is non-singular and periodic on all length scales.