224 research outputs found

### Partition function of the trigonometric SOS model with reflecting end

We compute the partition function of the trigonometric SOS model with one
reflecting end and domain wall type boundary conditions. We show that in this
case, instead of a sum of determinants obtained by Rosengren for the SOS model
on a square lattice without reflection, the partition function can be
represented as a single Izergin determinant. This result is crucial for the
study of the Bethe vectors of the spin chains with non-diagonal boundary terms.Comment: 13 pages, improved versio

### Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field

Using algebraic Bethe ansatz and the solution of the quantum inverse
scattering problem, we compute compact representations of the spin-spin
correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field. At
lattice distance m, they are typically given as the sum of m terms. Each term n
of this sum, n = 1,...,m is represented in the thermodynamic limit as a
multiple integral of order 2n+1; the integrand depends on the distance as the
power m of some simple function. The root of these results is the derivation of
a compact formula for the multiple action on a general quantum state of the
chain of transfer matrix operators for arbitrary values of their spectral
parameters.Comment: 34 page

### Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain

Using its multiple integral representation, we compute the large distance
asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2
Heisenberg chain in the massless regime.Comment: LPENSL-TH-10, 8 page

### Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV

We solve the longstanding problem to define a functional characterization of
the spectrum of the transfer matrix associated to the most general spin-1/2
representations of the 6-vertex reflection algebra for general inhomogeneous
chains. The corresponding homogeneous limit reproduces the spectrum of the
Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most
general integrable boundaries. The spectrum is characterized by a second order
finite difference functional equation of Baxter type with an inhomogeneous term
which vanishes only for some special but yet interesting non-diagonal boundary
conditions. This functional equation is shown to be equivalent to the known
separation of variable (SOV) representation hence proving that it defines a
complete characterization of the transfer matrix spectrum. The polynomial
character of the Q-function allows us then to show that a finite system of
equations of generalized Bethe type can be similarly used to describe the
complete transfer matrix spectrum.Comment: 28 page

### Correlation functions of the XXZ spin-1/2 Heisenberg chain at the free fermion point from their multiple integral representations

Using multiple integral representations, we derive exact expressions for the
correlation functions of the spin-1/2 Heisenberg chain at the free fermion
point.Comment: 24 pages, LaTe

### Dynamical correlation functions of the XXZ spin-1/2 chain

We derive a master equation for the dynamical spin-spin correlation functions
of the XXZ spin-1/2 Heisenberg finite chain in an external magnetic field. In
the thermodynamic limit, we obtain their multiple integral representation.Comment: 25 page

### The open XXX spin chain in the SoV framework: scalar product of separate states

We consider the XXX open spin-1/2 chain with the most general non-diagonal
boundary terms, that we solve by means of the quantum separation of variables
(SoV) approach. We compute the scalar products of separate states, a class of
states which notably contains all the eigenstates of the model. As usual for
models solved by SoV, these scalar products can be expressed as some
determinants with a non-trivial dependance in terms of the inhomogeneity
parameters that have to be introduced for the method to be applicable. We show
that these determinants can be transformed into alternative ones in which the
homogeneous limit can easily be taken. These new representations can be
considered as generalizations of the well-known determinant representation for
the scalar products of the Bethe states of the periodic chain. In the
particular case where a constraint is applied on the boundary parameters, such
that the transfer matrix spectrum and eigenstates can be characterized in terms
of polynomial solutions of a usual T-Q equation, the scalar product that we
compute here corresponds to the scalar product between two off-shell Bethe-type
states. If in addition one of the states is an eigenstate, the determinant
representation can be simplified, hence leading in this boundary case to direct
analogues of algebraic Bethe ansatz determinant representations of the scalar
products for the periodic chain.Comment: 39 page

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