Some spectral equivalences between Schrodinger operators

Spectral equivalences of the quasi-exactly solvable sectors of two classes of Schrodinger operators are established, using Gaudin-type Bethe ansatz equations. In some instances the results can be extended leading to full isospectrality. In this manner we obtain equivalences between PT-symmetric problems and Hermitian problems. We also find equivalences between some classes of Hermitian operators.Comment: 14 page

Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry

The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model describes local interactions between non-Abelian anyons, with fusion rules given by the tensor product decompositions of the irreducible representations of D(D_3). The Bethe ansatz equations which characterise the exact solution are found through the use of functional relations satisfied by a set of mutually commuting transfer matrices.Comment: 19 page

A variational approach for the Quantum Inverse Scattering Method

We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability through the existence of a set of conserved operators. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC). The Hamiltonians considered describe systems with interacting Cooper pairs and a bosonic degree of freedom. We obtain general exact solvability requirements which include seven subcases which have previously appeared in the literature.Comment: 18 pages, no eps figure

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models.Comment: 17 pages, RevTe

Deconfined quantum criticality and generalised exclusion statistics in a non-hermitian BCS model

We present a pairing Hamiltonian of the Bardeen-Cooper-Schrieffer form which exhibits two quantum critical lines of deconfined excitations. This conclusion is drawn using the exact Bethe ansatz equations of the model which admit a class of simple, analytic solutions. The deconfined excitations obey generalised exclusion statistics. A notable property of the Hamiltonian is that it is non-hermitian. Although it does not have a real spectrum for all choices of coupling parameters, we provide a rigorous argument to establish that real spectra occur on the critical lines. The critical lines are found to be invariant under a renormalisation group map.Comment: 7 pages, 1 figure. Stylistic changes, results unchange

Transfer matrix eigenvalues of the anisotropic multiparametric U model

A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1)) superalgebraic structure which introduces the additional free parameters that arise in the model. Three forms of Bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent.Comment: 26 pages, no figures, LaTe

Ground-state properties of the attractive one-dimensional Bose-Hubbard model

We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties like the gap between the ground and first excited energy levels, and the incremental ground-state wavefunction overlaps are used to locate different regimes. Using mean-field theory we predict that there are two distinct crossovers connected to spontaneous symmetry breaking of the ground state. The first crossover arises in an analysis valid for large L with finite N, where L is the number of lattice sites and N is the total particle number. An alternative approach valid for large N with finite L yields a second crossover. For small system sizes we numerically investigate the model and observe that there are signatures of both crossovers. We compare with exact results from Bethe ansatz methods in several limiting cases to explore the validity for these numerical and mean-field schemes. The results indicate that for finite attractive systems there are generically three ground-state phases of the model.Comment: 17 pages, 12 figures, Phys.Rev.B(accepted), minor changes and updated reference

Berry phase and fidelity susceptibility of the three-qubit Lipkin-Meshkov-Glick ground state

Berry phases and quantum fidelities for interacting spins have attracted considerable attention, in particular in relation to entanglement properties of spin systems and quantum phase transitions. These efforts mainly focus either on spin pairs or the thermodynamic infinite spin limit, while studies of the multipartite case of a finite number of spins are rare. Here, we analyze Berry phases and quantum fidelities of the energetic ground state of a Lipkin-Meshkov-Glick (LMG) model consisting of three spin-1/2 particles (qubits). We find explicit expressions for the Berry phase and fidelity susceptibility of the full system as well as the mixed state Berry phase and partial-state fidelity susceptibility of its one- and two-qubit subsystems. We demonstrate a realization of a nontrivial magnetic monopole structure associated with local, coordinated rotations of the three-qubit system around the external magnetic field.Comment: The title of the paper has been changed in this versio

State of the art and future directions in the systemic treatment of medullary thyroid cancer

PURPOSE OF REVIEW: Systemic treatment is the only therapeutic option for patients with progressive, metastatic medullary thyroid cancer (MTC). Since the discovery of the rearranged during transfection (RET) proto-oncogene (100% hereditary, 60-90% sporadic MTC), research has focused on finding effective systemic therapies to target this mutation. This review surveys recent findings. RECENT FINDINGS: Multikinase inhibitors are systemic agents targeting angiogenesis, inhibiting growth of tumor cells and cells in the tumor environment and healthy endothelium. In the phase III EXAM and ZETA trials, cabozantinib and vandetanib showed progression-free survival benefit, without evidence of prolonged overall survival. Selpercatinib and pralsetinib are kinase inhibitors with high specificity for RET; phase I and II studies showed overall response rates of 73% and 71% in first line, and 69% and 60% in second line treatment, respectively. Although resistance mechanisms to mutation-driven therapy will be a challenge in the future, phase III studies are ongoing and neo-adjuvant therapy with selpercatinib is being studied. SUMMARY: The development of selective RET-inhibitors has expanded the therapeutic arsenal to control tumor growth in progressive MTC, with fewer adverse effects than multikinase inhibitors. Future studies should confirm their effectiveness, study neo-adjuvant strategies, and tackle resistance to these inhibitors, ultimately to improve patient outcomes

Quantum dynamics of a model for two Josephson-coupled Bose--Einstein condensates

In this work we investigate the quantum dynamics of a model for two single-mode Bose--Einstein condensates which are coupled via Josephson tunneling. Using direct numerical diagonalisation of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalised and self-trapping phases. We show that these behaviours are dependent on both the initial state of the system as well as regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.Comment: 15 pages, 8 eps figures, accepted in J. Phys.