Split Fermi seas in one-dimensional Bose fluidsFokkema, T.B.; Eliëns, I.S.; Caux, J.S. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly excited states obtained by giving a finite momentum to subgroups of particles. These states, which correspond to "splitting" the ground-state Fermi-sea-like quantum number configuration, are zero-entropy states which display interesting properties more normally associated with ground states. Using a numerically exact method based on integrability, we study these states' excitation spectrum, density correlations, and momentum distribution functions. These correlations display power-law asymptotics and are shown to be accurately described by an effective multicomponent Tomonaga-Luttinger liquid theory whose parameters are obtained from the Bethe ansatz. The nonuniversal correlation prefactors are moreover obtained from integrability, yielding a completely parameter-free fit of the correlator asymptotics.

We analyse a class of 1D lattice models, known as M k models, which are characterised by an orderk clustering of spin-less fermions and by N = 2 lattice supersymmetry. Our main result is the identification of a class of (bulk or edge) defects, that are in one-to-one correspondence with socalled spin fields in a corresponding Z k parafermion CFT. In the gapped regime, injecting such defects leads to ground state degeneracies that are protected by the supersymmetry. The defects, which are closely analogous to quasi-holes over the fermionic Read-Rezayi quantum Hall states, display characteristic fusion rules, which are of Ising type for k = 2 and of Fibonacci type for k = 3.

A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice N = 2 supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the N = 1 super-sine-Gordon model at a particular coupling where an additional N = (2, 2) supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model. arXiv:1408.4403v1 [cond-mat.stat-mech]

The M k models for 1D lattice fermions are characterised by = 2 supersymmetry and by an order-k clustering property. This paper highlights connections with quantum field theories (QFTs) in various regimes. At criticality the QFTs are minimal models of = 2 supersymmetric conformal field theory (CFT) -we analyse finite size spectra on open chains with a variety of supersymmetry preserving boundary conditions. Specific staggering perturbations lead to a gapped regime corresponding to massive = 2 supersymmetric QFT with Chebyshev superpotentials. At 'extreme staggering' we uncover a simple physical picture with degenerate supersymmetric vacua and mobile kinks. We connect this kink-picture to the Chebyshev QFTs and use it to derive novel CFT character formulas. For clarity the focus in this paper is on the simplest models, M 1 , M 2 and M 3 . 5 Off-critical M k models at extreme staggering 15 5.1 M 1 model 15 5.2 M 2 model 15 5.2.1 Kinks and anti-kinks 16 5.2.2 Multiple (anti-)kinks 16 5.3 M 3 model 17 6 Counting of M 2 model kink states and CFT character formulas 17 6.1 Analogy with MR state in thin torus limit 18 6.2 Example 20 6.3 Open/open BC, fusion degeneracies and correspondence to MR quasi-hole state counting 21 6.4 Open/σ BC 22 6.5 σ/σ BC 23 7 M 2 model versus supersymmetric sine-Gordon theory -action of the supercharges 24 7.1 Kinematics 25 7.2 M 2 model supercharges 25 7.3 Supercharges in supersymmetric sine-Gordon theory 26 7.4 M 2 model vs. supersymmetric sine-Gordon theory 26 8 M 2 model versus supersymmetric sine-Gordon theory -finite chains 27 8.1 Mobile M 2 model kinks on open chains 28 8.2 Boundary scattering and kink-spectrum in supersymmetric sine-Gordon theory 29 A Integrable Field Theory 31 A.1 The sine-Gordon theory 31 A.1.1 Sine-Gordon theory with = 2 supersymmetry as a perturbed superconformal field theory 32 A.1.2 Particles in sine-Gordon theory with = 2 supersymmetry 32 A.1.3 Commutation of supercharges with the scattering of solitons 33 A.2 Supersymmetric sine-Gordon theory 33 A.2.1 Particles in supersymmetric sine-Gordon theory 34 A.2.2 = 1 supersymmetry 35 A.2.3 = 3 supersymmetric sine-Gordon as a perturbed conformal field theory 35 A.2.4 Particles in = 3 supersymmetric sine-Gordon theory 36 A.3 Superfields and superpotentials 37 A.3.1 Integrable massive field theories with a Chebyshev superpotential 37 A.3.2 Comparison of k = 1 Chebyshev QFT with sine-Gordon theory 38 References 38The action of the SU(2) currents on the kinks is J + K ±,0 =K ±,0 , J + K 0,± = ±K 0,± , J − K ±,0 = 0, J − K 0,± = 0, J 0 K ±,0 = − 1 2 K ±,0 , J 0 K 0,± = − 1 2 K 0,± , J +K ±,0 = 0, J +K 0,± = 0, J −K ±,0 = K ±,0 , J −K 0,± = ±K 0,± , J 0K ±,0 =