Read-Green resonances in a topological superconductor coupled to a bath

Abstract

We study a topological superconductor capable of exchanging particles with an environment. This additional interaction breaks particle-number symmetry and can be modelled by means of an integrable Hamiltonian, building on the class of Richardson-Gaudin pairing models. The isolated system supports zero-energy modes at a topological phase transition, which disappear when allowing for particle exchange with an environment. However, it is shown from the exact solution that these still play an important role in system-environment particle exchange, which can be observed through resonances in low-energy and -momentum level occupations. These fluctuations signal topologically protected Read-Green points and cannot be observed within traditional mean-field theory.Comment: 7 pages, 4 figure

Ground-state energies of the open and closed p + ip-pairing models from the Bethe Ansatz

“…The conserved operator eigenvalue approach was then extended to accommodate the open case based on results from [8,9,21]. Again, it was found that the result for the ground-state energy is in agreement with mean-field calculations.…”

“…and {T j } is a set of mutually commuting conserved operators. These operators have been shown [9] to satisfy the following quadratic identities…”

Variational method for integrability-breaking Richardson-Gaudin models

“…A common approach, known as the eigenvaluebased method, maps the Richardson-Gaudin equations (3) to an equivalent set of equations for the variables 13,14,25,52,[93][94][95][96][97][98][99]…”

Ground-state energy of a Richardson-Gaudin integrable BCS model

“…In particular, the exact Bethe Ansatz solutions provide insight into the topological behaviour of the system through the peculiar behaviour of Bethe roots [7,9,14]. Topological properties of the open model have been studied in [15,16].…”

“…This technique was shown to be generalizable in [22,23]. It was subsequently shown for some systems that the conserved operator eigenvalues (COE), satisfying quadratic relations, are inherited from the same relations at the operator level [15,24]. The generalized model considered below also shares this property of underlying conserved operators satisfying quadratic relations [17,18].…”