Related papers: On finite-temperature Fredholm determinants
The quantum ferromagnetic transition of itinerant electrons is considered. We give a pedagogical review of recent results which show that zero-temperature soft modes that are commonly neglected, invalidate the standard…
The purpose of this paper is to compute the asymptotics of determinants of finite sections of operators that are trace class perturbations of Toeplitz operators. For example, we consider the asymptotics in the case where the matrices are of…
We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in…
Explicit factorized formulas for the matrix elements (form-factors) of the spin operators \sigma^x and \sigma^y between the eigenvectors of the Hamiltonian of the finite quantum periodic XY-chain in a transverse field were derived. The…
We consider a multiple integral representation for the finite temperature density-density correlation functions of the one-dimensional Bose gas with delta function interaction in the limits of infinite and vanishing repulsion. In the former…
We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant,…
We study a system of spinless electrons moving in a two dimensional noncommutative space subject to a perpendicular magnetic field $\vec B$ and confined by a harmonic potential type ${1\over 2}mw_{0}r^2$. We look for the orbital magnetism…
We demonstrate the existence of topological phase transitions in interacting, symmetry-protected quantum matter at finite temperatures. Using a combined numerical and analytical approach, we study a one-dimensional Su-Schrieffer-Heeger…
We study the one-parameter family of Fredholm determinants $\det(I-\rho^2\mathcal{K}_{n,x})$, $\rho\in\mathbb{R}$, where $\mathcal{K}_{n,x}$ stands for the integral operator acting on $L^2(x,+\infty)$ with the higher order Airy kernel. This…
We study finite-temperature phase transitions in a two-dimensional boson Hubbard model with zero-point quantum fluctuations via Monte Carlo simulations of quantum rotor model, and construct the corresponding phase diagram. Compressibility…
This paper studies the asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infinity either within a Weyl chamber of the associated…
Space and time dependent temepreture correlation fucntions in the Hiesenberg XXO chain are evaluated in the magnetic field. The other name of the model is isotropic xy model in the transverse magnetic field. In the thermodynamic limit…
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…
We work out a generalization of the Szeg\"o limit theorems on the determinant of large matrices. We focus on matrices with nonzero leading principal minors and elements that decay to zero exponentially fast with the distance from the main…
Evaluating a lattice path integral in terms of spectral data and matrix elements pertaining to a suitably defined quantum transfer matrix, we derive form-factor series expansions for the dynamical two-point functions of arbitrary local…
Using functional RG, we reexamine the glass phase of the 2D random-field Sine Gordon model. It is described by a line of fixed points (FP) with a super-roughening amplitude $\bar{(u(0)-u(r))^2} \sim A(T) \ln^2 r $ as temperature $T$ is…
In this expository article we describe the asymptotics of certain Fredholm determinants which provide solutions to the cylindrical Toda equations, and we explain how these asymptotics are derived. The connection with Fredholm determinants…
We use the coupled 2d-spin-3d-fermion model proposed by Rosch {\sl et. al.} (Phys. Rev. Lett. {\bf 79}, 159 (1997)) to study the thermoelectric behaviour of a heavy fermion compound when it is close to an antiferromagnetic quantum critical…
Using the determinant representation for the field-field correlation functions of impenetrable anyons at finite temperature obtained in a previous paper, we derive a system of nonlinear partial differential equations completely…
We study the finite-temperature expectation values of exponential fields in the sine-Gordon model. Using finite-volume regularization, we give a low-temperature expansion of such quantities in terms of the connected diagonal matrix…