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We consider one-dimensional quantum spin chain, which is called XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We study the model on the infinite lattice at zero temperature. We are interested in the entropy of a subsystem [a block of L neighboring spins] it describes entanglement of the block with the rest of the ground state.… (More)
Painlevé analysis of correlation functions of the impenetrable Bose gas1] was based on the determinant representation of these correlation functions obtained by A. Lenard . The impenetrable Bose gas is the free fermionic case of the quantum non-linear Schrödinger equation. In this paper we generalize the Lenard determinant representation for ψ(0, 0)ψ †… (More)
We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.
Riemann zeta function is an important object of number theory. We argue that it is related to Heisenberg spin 1/2 anti-ferromagnet. In the XXX spin chain we study the probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state. We prove that for short strings the probability can be expressed in terms of Riemann zeta function… (More)
We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of formation of a ferromagnetic string P (n) in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the… (More)
We consider correlation functions of the spin-1 2 XXX and XXZ Heisenberg chains in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in terms of determinants of Fredholm integral operators.
We consider a model of strongly correlated electrons that exhibits superconduc-tivity. It diiers from the Hubbard model by nearest neighbour interactions. We nd the ground state wave function (in one, two or three dimensions) and show it to be superconducting for attractive and moderately repulsive on-site interaction. 1 The phenomenon of high-T c… (More)
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… (More)
We consider one-dimensional quantum spin chain, which is called XX model (XX0 model or isotropic XY model) in a transverse magnetic field. We are interested in the case of zero temperature and infinite volume. We study the entanglement of a block of L neighboring spins with the rest of the system. We represent the entanglement in terms of a Toeplitz… (More)