Related papers: Something interacting and solvable in 1d
We introduce a new type of models for two-component systems in one dimension subject to exact solutions by Bethe ansatz, where the interspecies interactions are tunable via Feshbach resonant interactions. The applicability of Bethe ansatz…
We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an…
We present an exact solution of an experimentally realizable and strongly interacting one-dimensional spin system which is a limiting case of a quantum Ising model with long range interaction in a transverse and longitudinal field.…
The Lieb-Liniger model describes one-dimensional bosons interacting through a repulsive contact potential. In this work, we introduce an extended version of this model by replacing the contact potential with a decaying exponential. Using…
We analyze a family of two-dimensional BCS Hamiltonians with general l-wave pairing interactions, classifying the models in this family that are Bethe-ansatz solvable in the finite-size regime. We show that these solutions are characterized…
We develop an alternative description to solve the problem of the ground-state energy of the Lieb-Liniger model that describes one-dimensional bosons with contact repulsion. For this integrable model we express the Lieb integral equation in…
In this chapter we will present the one-dimensional (1d) quantum degenerate Bose gas (1d superfluid) as a testbed to experimentally illustrate some of the key aspects of quantum thermodynamics. Hard-core bosons in one-dimension are…
Recent exact solutions of the 1D Kardar-Parisi-Zhang equation make use of the 1D integrable Lieb-Liniger model of interacting bosons. For flat initial conditions, it requires the knowledge of the overlap between the uniform state and…
In this paper we introduce a solvable two-orbital/band model with infinite-range Hatsugai-Kohmoto interaction, which serves as a modified periodic Anderson model. Its solvability results from strict locality in momentum space, and is valid…
The integrability of one dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) $\delta$-function interaction there is another…
Two-particle lattice states are important for physics of magnetism, superconducting oxides, and cold quantum gases. The quantum-mechanical lattice problem is exactly solvable for finite-range interaction potentials. A two-body Schroedinder…
For a large class of finite-range quantum spin models with half-integer spins, we prove that uniqueness of the ground state implies the existence of a low-lying excited state. For systems of linear size L, of arbitrary finite dimension, we…
We derive the large particle number limit of the Bethe equations for the ground state of the attractive one-dimensional Bose gas (Lieb-Liniger model) on a ring and solve it for arbitrary coupling. We show that the ground state of this…
Exactly solved models provide rigorous understanding of many-body phenomena in strongly correlated systems. In this article, we report a breakthrough in uncovering universal many-body correlated properties of quantum integrable Lieb-Liniger…
A new family of exactly solvable one dimensional models with a hard-core repulsive potential is solved by the Bethe Ansatz for an arbitrary hard-core radius. The exact ground state phase diagrams in a plane 'electron density - on-site…
We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a…
We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave…
Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…
Degenerate spinor Bose gases with repulsive density-density interaction and anti-ferromagnetic spin-spin coupling in one spatial dimension are shown to be described by a quantum integrable matrix extension of the nonlinear Schr\"odinger…
We review recent results obtained for a class of one-dimensional quantum models with $1/r^2$ long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum…