73 research outputs found
Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations
We calculate exactly matrix elements between states that are not eigenstates
of the quantum XY model for general anisotropy. Such quantities therefore
describe non equilibrium properties of the system; the Hamiltonian does not
contain any time dependence. These matrix elements are expressed as a sum of
Pfaffians. For single particle excitations on the ground state the Pfaffians in
the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of
refs. modifie
Electrostatic analogy for integrable pairing force Hamiltonians
For the exactly solved reduced BCS model an electrostatic analogy exists; in
particular it served to obtain the exact thermodynamic limit of the model from
the Richardson Bethe ansatz equations. We present an electrostatic analogy for
a wider class of integrable Hamiltonians with pairing force interactions. We
apply it to obtain the exact thermodynamic limit of this class of models. To
verify the analytical results, we compare them with numerical solutions of the
Bethe ansatz equations for finite systems at half-filling for the ground state.Comment: 14 pages, 6 figures, revtex4. Minor change
Bethe Ansatz solution of a new class of Hubbard-type models
We define one-dimensional particles with generalized exchange statistics. The
exact solution of a Hubbard-type Hamiltonian constructed with such particles is
achieved using the Coordinate Bethe Ansatz. The chosen deformation of the
statistics is equivalent to the presence of a magnetic field produced by the
particles themselves, which is present also in a ``free gas'' of these
particles.Comment: 4 pages, revtex. Essentially modified versio
Mesoscopic BCS pairing in the repulsive 1d-Hubbard model
We study mesoscopic pairing in the one dimensional repulsive Hubbard model
and its interplay with the BCS model in the canonical ensemble. The key tool is
comparing the Bethe ansatz equations of the two models in the limit of small
Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations
with infinite pairing coupling are recovered; a finite pairing is obtained by
considering a further density-dependent phase-correlation in the hopping
amplitude of the Hubbard model. We find that spin degrees of freedom in the
Hubbard ground state are arranged in a state of the BCS type, where the
Cooper-pairs form an un-condensed liquid on a ``lattice'' of single particle
energies provided by the Hubbard charge degrees of freedom; the condensation in
the BCS ground state corresponds to Hubbard excitations constituted by a sea of
spin singlets.Comment: 15 pages, 6 figures. To be published on Physical Review
Integrable spin-boson models descending from rational six-vertex models
We construct commuting transfer matrices for models describing the
interaction between a single quantum spin and a single bosonic mode using the
quantum inverse scattering framework. The transfer matrices are obtained from
certain inhomogeneous rational vertex models combining bosonic and spin
representations of SU(2), subject to non-diagonal toroidal and open boundary
conditions. Only open boundary conditions are found to lead to integrable
Hamiltonians combining both rotating and counter-rotating terms in the
interaction. If the boundary matrices can be brought to triangular form
simultaneously, the spectrum of the model can be obtained by means of the
algebraic Bethe ansatz after a suitable gauge transformation; the corresponding
Hamiltonians are found to be non-hermitian. Alternatively, a certain
quasi-classical limit of the transfer matrix is considered where hermitian
Hamiltonians are obtained as members of a family of commuting operators; their
diagonalization, however, remains an unsolved problem.Comment: 16 pages, 2 eps figure
Three-tangle for mixtures of generalized GHZ and generalized W states
We give a complete solution for the three-tangle of mixed three-qubit states
composed of a generalized GHZ state, a|000>+b|111>, and a generalized W state,
c|001>+d|010>+f|100>. Using the methods introduced by Lohmayer et al. we
provide explicit expressions for the mixed-state three-tangle and the
corresponding optimal decompositions for this more general case. Moreover, as a
special case we obtain a general solution for a family of states consisting of
a generalized GHZ state and an orthogonal product state
Exact relationship between the entanglement entropies of XY and quantum Ising chains
We consider two prototypical quantum models, the spin-1/2 XY chain and the
quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of
l spins in homogeneous or inhomogeneous systems of length L. By using two
different approaches, free-fermion techniques and perturbational expansion, an
exact relationship between the entropies is revealed. Using this relation we
translate known results between the two models and obtain, among others, the
additive constant of the entropy of the critical homogeneous quantum Ising
chain and the effective central charge of the random XY chain.Comment: 6 page
Entanglement evolution after connecting finite to infinite quantum chains
We study zero-temperature XX chains and transverse Ising chains and join an
initially separate finite piece on one or on both sides to an infinite
remainder. In both critical and non-critical systems we find a typical increase
of the entanglement entropy after the quench, followed by a slow decay towards
the value of the homogeneous chain. In the critical case, the predictions of
conformal field theory are verified for the first phase of the evolution, while
at late times a step structure can be observed.Comment: 15 pages, 11 figure
Entanglement study of the 1D Ising model with Added Dzyaloshinsky-Moriya interaction
We have studied occurrence of quantum phase transition in the one-dimensional
spin-1/2 Ising model with added Dzyaloshinsky-Moriya (DM) interaction from bi-
partite and multi-partite entanglement point of view. Using exact numerical
solutions, we are able to study such systems up to 24 qubits. The minimum of
the entanglement ratio R \tau 2/\tau 1 < 1, as a novel estimator of
QPT, has been used to detect QPT and our calculations have shown that its
minimum took place at the critical point. We have also shown both the
global-entanglement (GE) and multipartite entanglement (ME) are maximal at the
critical point for the Ising chain with added DM interaction. Using matrix
product state approach, we have calculated the tangle and concurrence of the
model and it is able to capture and confirm our numerical experiment result.
Lack of inversion symmetry in the presence of DM interaction stimulated us to
study entanglement of three qubits in symmetric and antisymmetric way which
brings some surprising results.Comment: 18 pages, 9 figures, submitte
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