A. G. Pronko

Boundary correlation functions of the six-vertex model

We consider the six-vertex model on an N × N square lattice with the domain wall boundary conditions. Boundary one-point correlation functions of the model are expressed as determinants of N × N matrices, generalizing the known result for the partition function. In the free fermion case explicit answers are obtained. The introduced correlation functions are closely related to the problem of enumeration of alternating sign matrices and domino tilings.

TEMPERATURE CORRELATORS IN THE TWO-COMPONENT ONE-DIMENSIONAL GAS

Abstract The quantum non-relativistic two-component Bose and Fermi gases with infinitely strong point-like coupling between particles in one space dimension are considered. Time- and temperature-dependent correlation functions are represented in the thermodynamic limit as Fredholm determinants of integrable linear integral operators.

Thermodynamics of the Six-Vertex Model in an L-Shaped Domain

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions. For free-fermion vertex weights the partition function can be expressed in terms of some Hankel determinant, or equivalently as a Coulomb gas with discrete measure and a non-polynomial potential with two hard walls. We use Coulomb gas methods to study the partition function in the thermodynamic limit. We obtain the free energy of the six-vertex model as a function of the parameters describing the geometry of the scaled L-shaped domain. Under variations of these parameters the system undergoes a third-order phase transition. The result can also be considered in the context of dimer models, for the perfect matchings of the Aztec diamond graph with a cut-off corner.

Impurity Green's function of a one-dimensional Fermi gas

Abstract We consider a one-dimensional gas of spin-1/2 fermions interacting through δ -function repulsive potential of an arbitrary strength. For the case of all fermions but one having spin up, we calculate time-dependent two-point correlation function of the spin-down fermion. This impurity Greens function is represented in the thermodynamic limit as an integral of Fredholm determinants of integrable linear integral operators.

Generalized emptiness formation probability in the six-vertex model

In the six-vertex model with domain wall boundary conditions, the emptiness formation probability is the probability that a rectangular region in the top left corner of the lattice is frozen. We generalize this notion to the case where the frozen region has the shape of a generic Young diagram. We derive here a multiple integral representation for this correlation function.

Time and temperature-dependent correlation function of an impurity in one-dimensional Fermi and Tonks-Girardeau gases as a Fredholm determinant.

We investigate a free one-dimensional spinless Fermi gas, and the Tonks–Girardeau gas interacting with a single impurity particle of equal mass. We obtain a Fredholm determinant representation for the time-dependent correlation function of the impurity particle. This representation is valid for an arbitrary temperature and an arbitrary repulsive or attractive impurity-gas δ-function interaction potential. It includes, as particular cases, the representations obtained for zero temperature and arbitrary repulsion in (Gamayun et al 2015 Nucl. Phys. B 892 83–104), and for arbitrary temperature and infinite repulsion in (Izergin and Pronko 1998 Nucl. Phys. B 520 594–632).

Arctic Curve of the Free-Fermion Six-Vertex Model in an L-Shaped Domain

We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions, in the case of free-fermion vertex weights. We describe how the recently developed ‘Tangent method’ can be used to determine the form of the arctic curve. The obtained result is in agreement with numerics.

Emptiness Formation Probability of the Six-Vertex Model and the Sixth Painlevé Equation

We show that the emptiness formation probability of the six-vertex model with domain wall boundary conditions at its free-fermion point is a

On the partition function of the six-vertex model with domain wall boundary conditions

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