123 research outputs found
Universal correlations of one-dimensional interacting electrons in the gas phase
We consider dynamical correlation functions of short range interacting
electrons in one dimension at finite temperature. Below a critical value of the
chemical potential there is no Fermi surface anymore, and the system can no
longer be described as a Luttinger liquid. Its low temperature thermodynamics
is that of an ideal gas. We identify the impenetrable electron gas model as a
universal model for the gas phase and present exact and explicit expressions
for the asymptotics of correlation functions at small temperatures, in the
presence of a magnetic field.Comment: 4 pages, Revte
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On the absence of simultaneous reflection and transmission in integrable impurity systems
The Hubbard chain: Lieb-Wu equations and norm of the eigenfunctions
We argue that the square of the norm of the Hubbard wave function is
proportional to the determinant of a matrix, which is obtained by linearization
of the Lieb-Wu equations around a solution. This means that in the vicinity of
a solution the Lieb-Wu equations are non-degenerate, if the corresponding wave
function is non-zero. We further derive an action that generates the Lieb-Wu
equations and express our determinant formula for the square of the norm in
terms of the Hessian determinant of this action.Comment: 11 pages, Late
Correlations in the impenetrable electron gas
We consider non-relativistic electrons in one dimension with infinitely
strong repulsive delta function interaction. We calculate the long-time,
large-distance asymptotics of field-field correlators in the gas phase. The gas
phase at low temperatures is characterized by the ideal gas law. We calculate
the exponential decay, the power law corrections and the constant factor of the
asymptotics. Our results are valid at any temperature. They simplify at low
temperatures, where they are easily recognized as products of free fermionic
correlation functions with corrections arising due to the interaction.Comment: 17 pages, Late
Fourth-neighbour two-point functions of the XXZ chain and the Fermionic basis approach
We give a descriptive review of the Fermionic basis approach to the theory of correlation functions of the XXZ quantum spin chain. The emphasis is on explicit formulae for short-range correlation functions which will be presented in a way that allows for their direct implementation on a computer. Within the Fermionic basis approach a huge class of stationary reduced density matrices, compatible with the integrable structure of the model, assumes a factorized form. This means that all expectation values of local operators and all two-point functions, in particular, can be represented as multivariate polynomials in only two functions and and their derivatives with coefficients that are rational in the deformation parameter of the model. These coefficients are of `algebraic origin'. They do not depend on the choice of the density matrix, which only impacts the form of and . As an example we work out in detail the case of the grand canonical ensemble at temperature and magnetic field for in the critical regime. We compare our exact results for the fourth-neighbour two-point functions with asymptotic formulae for and for finite and
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