19 research outputs found
Excited state g-functions from the Truncated Conformal Space
In this paper we consider excited state g-functions, that is, overlaps
between boundary states and excited states in boundary conformal field theory.
We find a new method to calculate these overlaps numerically using a variation
of the truncated conformal space approach. We apply this method to the Lee-Yang
model for which the unique boundary perturbation is integrable and for which
the TBA system describing the boundary overlaps is known. Using the truncated
conformal space approach we obtain numerical results for the ground state and
the first three excited states which are in excellent agreement with the TBA
results. As a special case we can calculate the standard g-function which is
the overlap with the ground state and find that our new method is considerably
more accurate than the original method employed by Dorey et al.Comment: 21 pages, 6 figure
Quantum Sine(h)-Gordon Model and Classical Integrable Equations
We study a family of classical solutions of modified sinh-Gordon equation,
$\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\
\re^{-2\eta}=0p(z)=z^{2\alpha}-s^{2\alpha}Q(\alpha>0)(\alpha<-1)$ models.Comment: 35 pages, 3 figure
BPS States in Omega Background and Integrability
We reconsider string and domain wall central charges in N=2 supersymmetric
gauge theories in four dimensions in presence of the Omega background in the
Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of
the corresponding topological defects in the theory - vortices and domain
walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy
effective theory living on the BPS vortex in N=2 Supersymmetric Quantum
Chromodynamics (SQCD). We discuss some aspects of the brane realization of the
dualities between various quantum integrable models. A chain of such dualities
enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos
correcte
Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
We review recent theoretical work on two closely related issues: excitation
of an isolated quantum condensed matter system driven adiabatically across a
continuous quantum phase transition or a gapless phase, and apparent relaxation
of an excited system after a sudden quench of a parameter in its Hamiltonian.
Accordingly the review is divided into two parts. The first part revolves
around a quantum version of the Kibble-Zurek mechanism including also phenomena
that go beyond this simple paradigm. What they have in common is that
excitation of a gapless many-body system scales with a power of the driving
rate. The second part attempts a systematic presentation of recent results and
conjectures on apparent relaxation of a pure state of an isolated quantum
many-body system after its excitation by a sudden quench. This research is
motivated in part by recent experimental developments in the physics of
ultracold atoms with potential applications in the adiabatic quantum state
preparation and quantum computation.Comment: 117 pages; review accepted in Advances in Physic