Related papers: The Quantum Toda Lattice Revisited
Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for…
In this paper we consider the Toda lattice $(\boldsymbol{p}(t); \boldsymbol{q}(t))$ at thermal equilibrium, meaning that its variables $(p_i)$ and $(e^{q_i-q_{i+1}})$ are independent Gaussian and Gamma random variables, respectively. We…
A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium…
The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of…
We review some surprising links which have been discovered in the last few years between the theory of certain ordinary differential equations, and particular integrable lattice models and quantum field theories in two dimensions. An…
We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model. We apply our variational…
The asymmetric exclusion process on a ring in one-dimension is considered with a single defect particle. The steady state has previously been solved by a matrix product method. Here we use the Bethe ansatz to solve exactly for the long time…
In this paper we consider the Toda lattice $(\boldsymbol{p}(t); \boldsymbol{q}(t))$ at thermal equilibrium, meaning that its variables $(p_i)$ and $(e^{q_i-q_{i+1}})$ are independent Gaussian and Gamma random variables, respectively. This…
The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space…
We consider quantum quenches in the so-called $q$-boson lattice model. We argue that the Generalized Eigenstate Thermalization Hypothesis holds in this model, therefore the Generalized Gibbs Ensemble (GGE) gives a valid description of the…
We construct an effective Quantum Field Theory for the wrapping effects in 1+1 dimensional models of factorised scattering. The recently developed graph-theoretical approach to TBA gives the perturbative desctiption of this QFT. For the…
We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an…
I show how interaction corrections to the Bose condensation temperature of an atomic gas can be computed using a combination of perturbative effective field theory and lattice techniques.
We consider the D1Q3 lattice Boltzmann scheme with an acoustic scale for the simulation of diffusive processes. When the mesh is refined while holding the diffusivity constant, we first obtain asymptotic convergence. When the mesh size…
We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the…
We derive thermodynamic Bethe ansatz equations describing the vacuum energy of the SU(2N)/Sp(N) nonlinear sigma model on a cylinder geometry. The starting points are the recently-proposed amplitudes for the scattering among the physical,…
The traditional ambiguity about the bulk electrostatic potentials in crystals is due to the conditional convergence of Coulomb series. The classical Ewald approach turns out to be the first one resolving this task as consistent with a…
We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in coordinate representation. A diagrammatic approach is…
A new method based on the concept of probability distribution is proposed to analyze the finite volume energy spectrum in lattice QCD. Using synthetic lattice data, we demonstrate that for the channel with quantum numbers of the…
We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other…