97 research outputs found
Dynamics in the Ising field theory after a quantum quench
We study the real-time dynamics of the order parameter . Our main result is the development of
a method for treating divergences associated with working directly in the field
theory limit. We recover the scaling limit of the corresponding result by
Calabrese et al. [Phys. Rev. Lett. \textbf{106}, 227203 (2011)], which was
obtained for the lattice model. Our formalism generalizes to integrable quantum
quenches in other integrable models
Threshold Singularities in the One Dimensional Hubbard Model
We consider excitations with the quantum numbers of a hole in the one
dimensional Hubbard model below half-filling. We calculate the finite-size
corrections to the energy. The results are then used to determine threshold
singularities in the single-particle Green's function for commensurate
fillings. We present the analogous results for the Yang-Gaudin model (electron
gas with delta-function interactions).Comment: 26 pages, 12 figures version to appear in Phys Rev
Dynamical Magnetic Susceptibilities in Cu Benzoate
Recent experiments on the quasi 1-D antiferromagnet Cu Benzoate revealed a
magentic field induced gap coexisting with (ferro)magnetic order. A theory
explaining these findings has been proposed by Oshikawa and Affleck. In the
present work we discuss consequences of this theory for inelastic neutron
scattering experiments by calculating the dynamical magnetic susceptibilities
close to the antiferromagnetic wave vector by the formfactor method.Comment: 6 pages of revtex, 9 figures, extended comparison with experimen
Spectrum of Low-Lying Excitations in a Supersymmetric Extended Hubbard Model
We continue the study of the -supersymmetric extension of the Hubbard
model in one dimension. We determine the excitation spectrum at zero
temperature even in the sectors where the ground states are
-descendants of Bethe states. The excitations include spinons, holons,
electrons, localons (local electrons pairs, moving coherently through the
lattice) and their bound states. The spectra are found to be very different for
repulsive and attractive on-site interaction. We also study the thermodynamics
of the model.Comment: 37 pages, uuencoded compressed postscript fil
Applications of Massive Integrable Quantum Field Theories to Problems in Condensed Matter Physics
We review applications of the sine-Gordon model, the O(3) non-linear sigma
model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi
one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We
focus upon the determination of dynamical response functions for these
problems. These quantities are computed by means of form factor expansions of
quantum correlation functions in integrable quantum field theories. This
approach is reviewed here in some detail.Comment: 150 pages, 35 figures, published in the I. Kogan Memorial Volume by
World Scientifi
Time evolution of local observables after quenching to an integrable model
We consider quantum quenches in integrable models. We argue that the
behaviour of local observables at late times after the quench is given by their
expectation values with respect to a single representative Hamiltonian
eigenstate. This can be viewed as a generalization of the eigenstate
thermalization hypothesis to quantum integrable models. We present a method for
constructing this representative state by means of a generalized Thermodynamic
Bethe Ansatz (GTBA). Going further, we introduce a framework for calculating
the time dependence of local observables as they evolve towards their
stationary values. As an explicit example we consider quantum quenches in the
transverse-field Ising chain and show that previously derived results are
recovered efficiently within our framework.Comment: 7 page
A short introduction to Generalized Hydrodynamics
These are notes based on lectures given at the 2021 summer school on
Fundamental Problems in Statistical Physics XV. Their purpose is to give a very
brief introduction to Generalized Hydrodynamics, which provides a description
of the large scale structure of the dynamics in quantum integrable models. The
notes are not meant to be comprehensive or provide an overview of all relevant
literature, but rather give an exposition of the key ideas for non-experts,
using a simple fermionic tight-binding model as the main example.Comment: 24 pages, 6 figure
Dynamical Correlations after a Quantum Quench
In many integrable models static (equal time) correlation functions of local
observables after a quantum quench relax to stationary values, which are
described by a generalized Gibbs ensemble (GGE). Here we establish that the
same holds true for dynamic (non equal time) correlation functions. More
generally we show that in the absence of long-range interactions in the final
Hamiltonian, the dynamics is determined by the same ensemble that describes
static correlations. When the latter is a GGE the basic form of the fluctuation
dissipation theorem holds, although the absorption and emission spectra are not
simply related as in the thermal case. For quenches in the transverse field
Ising chain (TFIC) we derive explicit expressions for the time evolution of
dynamic order parameter correlators after a quench.Comment: 6 pages, 3 figure
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