[en] We obtain the exceptional part of the eigenspectrum of the generalized Rabi model, also known as the driven Rabi model, in terms of the roots of a set of algebraic equations. This approach provides a product form for the wavefunction components and allows an explicit connection with recent results obtained for the wavefunction in terms of truncated confluent Heun functions. Other approaches are also compared. For particular parameter values the exceptional part of the eigenspectrum consists of doubly degenerate crossing points. We give a proof for the number of roots of the constraint polynomials and discuss the number of crossing points. (paper)

[en] We examine the energy surfaces of the driven Rabi model, also known as the biased or generalized Rabi model, as a function of the coupling strength and the driving term. The energy surfaces are plotted numerically from the known analytic solution. The resulting energy landscape consists of an infinite stack of sheets connected by conical intersection points located at the degenerate Juddian points in the eigenspectrum. Trajectories encircling these points are expected to exhibit a nonzero geometric phase. (letter)

[en] This paper employs Schramm-Loewner evolution to obtain intersection exponents for several chordal SLE_8/3 curves in a wedge. As SLE_8/3 is believed to describe the continuum limit of self-avoiding walks, these exponents correspond to those obtained by Cardy, Duplantier and Saleur for self-avoiding walks in an arbitrary wedge-shaped geometry using conformal invariance-based arguments. Our approach builds on work by Werner, where the restriction property for SLE(κ, ρ) processes and an absolute continuity relation allow the calculation of such exponents in the half-plane. Furthermore, the method by which these results are extended is general enough to apply to the new class of hiding exponents introduced by Werner

[en] The fully anisotropic two-leg spin-$\frac{1}{2}$ XXZ ladder model is studied in terms of an algorithm based on the tensor network (TN) representation of quantum many-body states as an adaptation of projected entangled pair states to the geometry of translationally invariant infinite-size quantum spin ladders. The TN algorithm provides an effective method to generate the groundstate wave function, which allows computation of the groundstate fidelity per lattice site, a universal marker to detect phase transitions in quantum many-body systems. The groundstate fidelity is used in conjunction with local order and string order parameters to systematically map out the groundstate phase diagram of the ladder model. The phase diagram exhibits a rich diversity of quantum phases. These are the ferromagnetic, stripe ferromagnetic, rung singlet, rung triplet, Néel, stripe Néel and Haldane phases, along with the two XY phases XY1 and XY2. (paper)

[en] The asymmetric quantum Rabi model (AQRM) exhibits level crossings in the eigenspectrum for the values $\mathrm{ϵ<!--\; ??\; -->}\in <!--\; ???\; -->\frac{1}{2}\mathbb{Z}$ of the bias parameter ϵ. Such level crossings are expected to be associated with some hidden symmetry of the model. The origin of this hidden symmetry is established by finding the operators which commute with the AQRM Hamiltonian at these special values. The construction is given explicitly for the first several cases $\mathrm{ϵ<!--\; ??\; -->}=0,\frac{1}{2},1$ and can be applied to other related light–matter interaction models for which similar level crossings have been observed in the presence of a bias term. (letter)

[en] The symmetry operators generating the hidden ${\mathbb{Z}}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) at bias $\mathrm{ϵ<!--\; ??\; -->}\in <!--\; ???\; -->\frac{1}{2}\mathbb{Z}$ have recently been constructed by Mangazeev et al (2021 J. Phys. A: Math. Theor. 54 12LT01). We start with this result to determine symmetry operators for the N-qubit generalisation of the AQRM, also known as the biased Dicke model, at special biases. We also prove for general N that the symmetry operators, which commute with the Hamiltonian of the biased Dicke model, generate a ${\mathbb{Z}}_2$ symmetry. (paper)

[en] The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data are in perfect agreement with the remarkable field theory results obtained by Fonseca and Zamolodchikov, as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with analytic results for the magnetic susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general, the high precision of the numerical results underlines the potential and full power of the variational corner transfer matrix approach. (fast track communication)

No abstract available

[en] The Hamiltonian of the N-state superintegrable chiral Potts (SICP) model is written in terms of a coupled algebra defined by N − 1 types of Temperley–Lieb generators. This generalises a previous result for N = 3 obtained by Fjelstad and Månsson (2012 J. Phys. A: Math. Theor. 45 155208). A pictorial representation of a related coupled algebra is given for the N = 3 case which involves a generalisation of the pictorial presentation of the Temperley–Lieb algebra to include a pole around which loops can become entangled. For the two known representations of this algebra, the N = 3 SICP chain and the staggered spin-1/2 XX chain, closed (contractible) loops have weight $\sqrt{3}$ and weight 2, respectively. For both representations closed (non-contractible) loops around the pole have weight zero. The pictorial representation provides a graphical interpretation of the algebraic relations. A key ingredient in the resolution of diagrams is a crossing relation for loops encircling a pole which involves the parameter ρ = e ^2πi/3 for the SICP chain and ρ = 1 for the staggered XX chain. These ρ values are derived assuming the Kauffman bracket skein relation. (letter)

[en] The Yang–Baxter equation has long been recognised as the masterkey to integrability, providing the basis for exactly solved models which capture the fundamental physics of a number of realistic classical and quantum systems. In this article we provide an introductory survey of the impact of Yang–Baxter integrable models on experiments in condensed matter physics and ultracold atoms. A number of prominent examples are covered, including the hard-hexagon model, the Heisenberg spin chain, the transverse quantum Ising chain, a spin ladder model, the Lieb–Liniger Bose gas, the Gaudin–Yang Fermi gas and the two-site Bose–Hubbard model. The review concludes by pointing to some other recent developments with promise for further progress. (review)