Related papers: Correlation Critical Exponents for the Six-Vertex …
We present a new exact renormalization approach for quantum lattice models leading to long-range interactions. The renormalization scheme is based on wavelets with an infinite support in such a way that the excitation spectrum at the fixed…
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a $\delta$…
We extract an exact formula relating the number of lattice points in an expanding region of a complex semi-simple symmetric space and the automorphic spectrum from a spectral identity, which is obtained by producing two expressions for the…
We consider interacting theories with a compact internal symmetry group on a regular lattice. We show that the spectrum is necessarily vector-like provided the following conditions are satisfied: (a)~weak form of locality, (b)~relativistic…
We survey the connections between the six-vertex (square ice) model of 2d statistical mechanics and random matrix theory. We highlight the same universal probability distributions appearing on both sides, and also indicate related open…
For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general, this discretization destroys the rotational or…
We present a theoretical study on the response properties to an external electric field of strongly correlated one-dimensional metals. Our investigation is based on the recently developed Bethe-Ansatz local density approximation (BALDA) to…
We present a detailed numerical study of the orthogonality catastrophe exponent for a one-dimensional lattice model of spinless fermions with nearest neighbor interaction using the density matrix remormalization group algorithm. Keeping up…
We present in this paper a comprehensive introduction to the algebraic Bethe Ansatz, taking as examples the six-vertex model with periodic and non-periodic boundary conditions. We propose a diagrammatic representation of the commutation…
It is shown that the percolation model of hydrogen-bonded crystals, which is a 6-vertex model with bond defects, is completely equivalent with an 8-vertex model in an external electric field. Using this equivalence we solve exactly a…
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems,…
The six-vertex model is an important toy-model in statistical mechanics for two-dimensional ice with a natural parameter $\Delta$. When $\Delta = 0$, the so-called free-fermion point, the model is in natural correspondence with domino…
Isoscaling is derived within a recently proposed modified Fisher model where the free energy near the critical point is described by the Landau O(m^6) theory. In this model m = (N-Z)/A is the order parameter, a consequence of (one of) the…
Conventional lattice Boltzmann models only satisfy moment isotropy up to fourth order. In order to accurately describe improtant physical effects beyond the isothermal Navier-Stokes fluid regime, higher order isotropy is required. In this…
Quantum systems on a one-dimensional lattice are ubiquitous in the study of models exactly-solved by Bethe Ansatz techniques. Here it is shown that including global-range interaction opens scope for Bethe Ansatz solutions that are not…
Following the paradigm of Boltzmann-BBGKY we propose a correlation entropy (of the nth order) for an interacting quantum field, obtained by `slaving' (truncation with causal factorization) of the higher (n+1 th) order correlation functions…
Exact expressions for correlation functions are known for the large-$N$ (planar) limit of the $(1+1)$-dimensional ${\rm SU}(N)\times {\rm SU}(N)$ principal chiral sigma model. These were obtained with the form-factor bootstrap, an entirely…
Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the $k\times k$ fusion eight-vertex model in terms of the corresponding fusion SOS model. Here $k\in Z_{>0}$. A general formula…
The exact perturbation approach is used to derive the elementary correlation lengths $\xi_i$ and related mass gaps $m_i$ of the two-dimensional dilute A_L lattice model in regimes 1 and 2 for L odd from the Bethe Ansatz solution. In regime…
Using the algebraic Bethe ansatz, we derive a matrix product representation of the exact Bethe-ansatz states of the six-vertex Heisenberg chain (either XXX or XXZ and spin-$\frac{1}{2}$) with open boundary conditions. In this…