Related papers: The Six-Vertex Model with a Non-Standard Boundary …
The free fermion condition of the six-vertex model provides a 5 parameter sub-manifold on which the Bethe Ansatz equations for the wavenumbers that enter into the eigenfunctions of the transfer matrices of the model decouple, hence allowing…
In this contribution we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the…
In this paper we consider the existence and uniqueness of pure states with some fixed slope $(s, t) \in [0, 1]^2$ for a general ferroelectric six-vertex model. First, we show there is an open subset $\mathfrak{H} \subset [0, 1]^2$, which is…
We present the expressions for the monodromy matrix elements of the six-vertex model in the F-basis for arbitrary Boltzmann weights. The results rely solely on the property of unitarity and Yang-Baxter relations, avoiding any specific…
Based on the two-dimensional lattice fermion model, we discuss transitions between different pairing states. Each phase is labeled by an integer which is a topological invariant and characterized by vortices of the Bloch wavefunction. The…
Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary…
In this work we demonstrate that the Yang-Baxter algebra can also be employed in order to derive a functional relation for the partition function of the six vertex model with domain wall boundary conditions. The homogeneous limit is studied…
The main result of this paper is the construction of infinitely many conserved quantities (corresponding to commuting transfer-matrices) for the limit shape equation for the 6-vertex model on a cylinder. This suggests that the limit shape…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
The boundary states for a certain class of WZW models are determined. The models include all modular invariants that are associated to a symmetry of the unextended Dynkin diagram. Explicit formulae for the boundary state coefficients are…
We consider a new kind of straight and shifted plane partitions/Young tableaux --- ones whose diagrams are no longer of partition shape, but rather Young diagrams with boxes erased from their upper right ends. We find formulas for the…
Asymptotics of the eigenvalues can always be derived for self-adjoint boundary value problems. However, they can also be derived for boundary value problems that fail to be self-adjoint provided that they are Birkhoff regular. A regular…
The voter model is a paradigm of ordering dynamics. At each time step, a random node is selected and copies the state of one of its neighbors. Traditionally, this state has been considered as a binary variable. Here, we relax this…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on…
We study the fully entangled fraction of a quantum state. An upper bound is obtained for arbitrary bipartite system. This upper bound only depends on the Frobenius norm of the state.
We study the norms of the Bloch vectors for arbitrary $n$-partite quantum states. A tight upper bound of the norms is derived for $n$-partite systems with different individual dimensions. These upper bounds are used to deal with the…
We will show how it is possible to generate entangled states out of unentangled ones on a bipartite system by means of dynamical boundary conditions. The auxiliary system is defined by a symmetric but not self-adjoint Hamiltonian and the…
The recently introduced two-parameter eight-state $U_q[gl(3|1)]$ supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded…
We numerically study a particle in a box with moving walls. In the case where the walls are oscillating sinusoidally with small amplitude, we show that states up to the fourth state can be populated with more than 80 percent population,…