Bethe Ansatz for XXX chain with negative spin

Abstract

XXX spin chain with spin s = −1 appears as an effective theory of Quantum Chromodynamics. It is equivalent to lattice nonlinear Schroediger's equation: interacting chain of harmonic oscillators [bosonic]. In thermodynamic limit each energy level is a scattering state of several elementary excitations [lipatons]. Lipaton is a fermion: it can be represented as a topological excitation [soliton] of original [bosonic] degrees of freedom, described by the group Z 2 . We also provide the CFT description (including local quenches) and Yang-Yang thermodynamics of the model. * haoke72@163.com

Analytic continuation of Bethe energies and application to the thermodynamic limit of the SL(2, ℂ) non-compact spin chains

“…Let us show first that the equations (3.2) only have real solutions. The proof is identical to that of the same property for the repulsive Lieb-Liniger model [55,61], and can be formulated as follows. Let us denote λ + the root with the largest imaginary part.…”

“…being the spin of the representation to which the state belongs, where N denotes the number of Bethe roots. However, since s is negative the structure of the Bethe roots changes dramatically [51][52][53][54][55]. Moreover, since N has to be obviously a non-negative integer, the ABA construction can only provide eigenstates for which Ls − u is a non-negative integer, and continuous series representations for a real arbitrary u cannot be obtained directly this way [56].…”

“…To show that with this constraint (3.6) a solution to (3.5) does exist and is unique, we follow again [55,61] and introduce…”

Entanglement entropy production in deep inelastic scattering

“…Here ρ t (λ) is the sum of the numbers of particles ρ p (λ) and holes ρ h (λ). Their proofs follow from [11,15,25]. All λ j are different [15] (Pauli principle in the momentum space).…”

“…The chain was mapped to the spin (−1) [10] and to lattice nonlinear Schrödinger model [11]. Here we will use nonlinear Schrödinger (NLS) equation [12][13][14][15] to describe the entanglement entropy evolution in DIS.…”