400 research outputs found
Exactly Solvable Models of Strongly Correlated Electrons
This is a reprint volume devoted to exact solutions of models of strongly
correlated electrons in one spatial dimension by means of the Bethe Ansatz.Comment: Editors 490 pages, World Scientific, 1994, ISBN 981-02-1534-
Threshold singularities in the dynamic response of gapless integrable models
We develop a method of an asymptotically exact treatment of threshold
singularities in dynamic response functions of gapless integrable models. The
method utilizes the integrability to recast the original problem in terms of
the low-energy properties of a certain deformed Hamiltonian. The deformed
Hamiltonian is local, hence it can be analysed using the conventional field
theory methods. We apply the technique to spinless fermions on a lattice with
nearest-neighbors repulsion, and evaluate the exponent characterizing the
threshold singularity in the dynamic structure factor
Dynamical response functions in the quantum Ising chain with a boundary
We determine dynamical response functions in the scaling limit of the quantum Ising chain on the half line in
the presence of a boundary magnetic field. Using a spectral representation in
terms of infinite volume form factors and a boundary state, we derive an
expansion for the correlator that is found to be rapidly convergent as long as
|\frac{x_1+x_2}{\xi}|\agt 0.2 where is the correlation length. At
sufficiently late times we observe oscillatory behaviour of the correlations
arbitrarily far away from the boundary. We investigate the effects of the
boundary bound state that is present for a range of boundary magnetic fields.Comment: 32 page
Thermodynamics and excitations of the one-dimensional Hubbard model
We review fundamental issues arising in the exact solution of the
one-dimensional Hubbard model. We perform a careful analysis of the Lieb-Wu
equations, paying particular attention to so-called `string solutions'. Two
kinds of string solutions occur: strings, related to spin degrees of
freedom and strings, describing spinless bound states of electrons.
Whereas strings were thoroughly studied in the literature, less is
known about strings. We carry out a thorough analytical and
numerical analysis of strings. We further review two different
approaches to the thermodynamics of the Hubbard model, the Yang-Yang approach
and the quantum transfer matrix approach, respectively. The Yang-Yang approach
is based on strings, the quantum transfer matrix approach is not. We compare
the results of both methods and show that they agree. Finally, we obtain the
dispersion curves of all elementary excitations at zero magnetic field for the
less than half-filled band by considering the zero temperature limit of the
Yang-Yang approach.Comment: 72 pages, 11 figures, revte
Different types of integrability and their relation to decoherence in central spin models
We investigate the relation between integrability and decoherence in central
spin models with more than one central spin. We show that there is a transition
between integrability ensured by the Bethe ansatz and integrability ensured by
complete sets of commuting operators. This has a significant impact on the
decoherence properties of the system, suggesting that it is not necessarily
integrability or nonintegrability which is related to decoherence, but rather
its type or a change from integrability to nonintegrability.Comment: 4 pages, 3 figure
Painlev\'e Transcendent Describes Quantum Correlation Function of the XXZ Antiferromagnet away from the free-fermion point
We consider quantum correlation functions of the antiferromagnetic
spin- Heisenberg XXZ spin chain in a magnetic field. We show that
for a magnetic field close to the critical field (for the critical
magnetic field the ground state is ferromagnetic) certain correlation functions
can be expressed in terms of the solution of the Painlev\'e V transcendent.
This establishes a relation between solutions of Painlev\'e differential
equations and quantum correlation functions in models of {\sl interacting}
fermions. Painlev\'e transcendents were known to describe correlation functions
in models with free fermionic spectra.Comment: 10 pages, LaTeX2
Entanglement entropy and entanglement witnesses in models of strongly interacting low-dimensional fermions
We calculate the entanglement entropy of strongly correlated low-dimensional
fermions in metallic, superfluid and antiferromagnetic insulating phases. The
entanglement entropy reflects the degrees of freedom available in each phase
for storing and processing information, but is found not to be a state function
in the thermodynamic sense. The role of critical points, smooth crossovers and
Hilbert space restrictions in shaping the dependence of the entanglement
entropy on the system parameters is illustrated for metallic, insulating and
superfluid systems. The dependence of the spin susceptibility on entanglement
in antiferromagnetic insulators is obtained quantitatively. The opening of spin
gaps in antiferromagnetic insulators is associated with enhanced entanglement
near quantum critical points.Comment: 5 pages, 5 figures, accepted by PR
Correlation functions of the one-dimensional attractive Bose gas
The zero-temperature correlation functions of the one-dimensional attractive
Bose gas with delta-function interaction are calculated analytically for any
value of the interaction parameter and number of particles, directly from the
integrability of the model. We point out a number of interesting features,
including zero recoil energy for large number of particles, analogous to a
M\"ossbauer effect.Comment: 4 pages, 2 figure
Classical realization of two-site Fermi-Hubbard systems
A classical wave optics realization of the two-site Hubbard model, describing
the dynamics of interacting fermions in a double-well potential, is proposed
based on light transport in evanescently-coupled optical waveguides.Comment: 4 page
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