Related papers: A staggered six-vertex model with non-compact cont…
New solvable vertex models can be easily obtained by staggering the spectral parameter in already known ones. This simple construction reveals some surprises: for appropriate values of the staggering, highly non-trivial continuum limits can…
We study the emergence of non-compact degrees of freedom in the low energy effective theory for a class of $\mathbb{Z}_2$-staggered six-vertex models. In the finite size spectrum of the vertex model this shows up through the appearance of a…
We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine $D_2^2$ Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic…
Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically…
The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general…
The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as…
We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An…
For a class of Hamiltonians of $XXZ$ spin chains in a uniform external magnetic field that are small quantum perturbations of an Ising Hamiltonian, it is shown that the spectral gap above the ground-state energy remains strictly positive…
We study the square-lattice three-state Potts model with the ferromagnetic next-nearest-neighbor coupling at finite temperature. Using the level-spectroscopy method, we numerically analyze the excitation spectrum of the transfer matrices…
We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small…
In this thesis, I study a two-dimensional extended Hubbard model in the weak coupling limit. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons. However in the special case of a…
We study a model of a spin S = 1/2 Heisenberg antiferromagnet on a one dimensional lattice with the local symmetry of the two dimensional kagom{\'e} lattice. Using three complementary approaches, it is shown that the low energy spectrum can…
This paper is concerned with the study of properties of the exact solution of the fundamental integrable $G_2$ vertex model. The model $R$-matrix and respective spin chain are presented in terms of the basis generators of the $G_2$ Lie…
We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice four-Fermi or Gross-Neveu model in $d+1$ space-time dimensions ($d=1,2,3$) and with $N$-component fermions. Let $\kappa>0$ be the hopping parameter, $\lambda>0$…
We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of…
We show that the one-dimensional lattice model proposed by Lipatov to describe the high energy scattering of hadrons in multicolor QCD is completely integrable. We identify this model as the XXX Heisenberg chain of noncompact spin $s=0$ and…
Microscopic models of quantum antiferromagnets are investigated on the basis of a mapping onto effective low energy hamiltonians. Lattice effects are carefully taken into account and their role is discussed. We show that the presence of an…
Using group theoretical and numerical methods we have calculated the exact energy spectrum of the two-dimensional Hubbard model on square lattices with four electrons for a wide range of the interaction strength. All known symmetries, i.e.\…
We show that, in certain circumstances, exact excitation energies appear as locally site-independent (or flat) modes if one records the excitation spectrum of the effective Hamiltonian while sweeping through the lattice in the variational…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…