Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles

Abstract

As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of deltatype interactions which include different kinds of momentum dependent terms, and we determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe Ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta-and (so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulas for all eigenfunctions.

Gravitational waves propagation in nondynamical Chern–Simons gravity

“…(ii) The second condition for an operator to be self-adjoint is that both the domain and the action of the operator acting on the right are equal to the domain and the action of the adjoint operator acting on the left. In this case, we have only one matrix U for both type of functions ψ and ϕ, and the condition (A.4) translates into 46,47 U † JU = J , J = 0 1 −1 0 .…”

Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line

“…which obviously is the most general hermitian Hamiltonian with interactions localized in x = 0 and containing only derivatives up to second order (higher derivatives than that do not lead to physically acceptable boundary conditions). This Hamiltonian is formally self-adjoint for arbitrary parameters c, λ ∈ R and γ ∈ C, and it indeed corresponds to the 4-parameter family of local interactions mentioned above [14]. All these models have natural generalizations to the manybody case, but there is only one case where these latter models are known to be exactly solvable even for distinguishable particles by the coordinate Bethe Ansatz: (c, λ, γ) = (c, 0, 0).…”

“…It would be interesting to know if there are other exactly solvable cases. We plan to come back to this question elsewhere [14]. We only mention here that the many-body generalization of the Hamiltonian in Eq.…”

Non relativistic limit of integrable QFT with fermionic excitations

“…Interestingly, the duality between the Thirring model and the purely bosonic Sine Gordon model [27] is reflected also in their NR limits [4,26,28], being the NR limit of the Sine Gordon the attractive Lieb Liniger model [4,29]. The purpose of the present investigation is to enlarge the landscape of the known NR limits, in particular we consider the supersymmetric Sinh-Gordon model (SShG) [30,31], the O(N ) Gross-Neveu model (GN) [21,32,33] and 1 In Ref.…”