10 research outputs found
Confinement in the q-state Potts model: an RG-TCSA study
In the ferromagnetic phase of the q-state Potts model, switching on an
external magnetic field induces confinement of the domain wall excitations. For
the Ising model (q = 2) the spectrum consists of kink-antikink states which are
the analogues of mesonic states in QCD, while for q = 3, depending on the sign
of the field, the spectrum may also contain three-kink bound states which are
the analogues of the baryons. In recent years the resulting "hadron" spectrum
was described using several different approaches, such as quantum mechanics in
the confining linear potential, WKB methods and also the Bethe-Salpeter
equation. Here we compare the available predictions to numerical results from
renormalization group improved truncated conformal space approach (RG-TCSA).
While mesonic states in the Ising model have already been considered in a
different truncated Hamiltonian approach, this is the first time that a
precision numerical study is performed for the 3-state Potts model. We find
that the semiclassical approach provides a very accurate description for the
mesonic spectrum in all the parameter regime for weak magnetic field, while the
low-energy expansion from the Bethe-Salpeter equation is only valid for very
weak fields where it gives a slight improvement over the semiclassical results.
In addition, we confirm the validity of the recent predictions for the baryon
spectrum obtained from solving the quantum mechanical three-body problem.Comment: 22 pages, pdflatex source with pdf figures. Version 2: references
added, introduction change
Excited state TBA and renormalized TCSA in the scaling Potts model
We consider the field theory describing the scaling limit of the Potts
quantum spin chain using a combination of two approaches. The first is the
renormalized truncated conformal space approach (TCSA), while the second one is
a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in
finite volume. For the TCSA we investigate and clarify several aspects of the
renormalization procedure and counter term construction. The TBA system is
first verified by comparing its ultraviolet limit to conformal field theory and
the infrared limit to exact S-matrix predictions. We then show that the TBA and
the renormalized TCSA match each other to a very high precision for a large
range of the volume parameter, providing both a further verification of the TBA
system and a demonstration of the efficiency of the TCSA renormalization
procedure. We also discuss the lessons learned from our results concerning
recent developments regarding the low-energy scattering of quasi-particles in
the quantum Potts spin chain.Comment: 39 pages, 5 eps figures. v2: reference added. v3: several misprints
corrected, and an important step in the derivation of counter terms (in
section 3.4.1) is explained in more detai
Breather boundary form factors in sine-Gordon theory
A previously conjectured set of exact form factors of boundary exponential operators in the sinh-Gordon model is tested against numerical results from boundary truncated conformal space approach in boundary sine-Gordon theory, related by analytic continuation to sinh-Gordon model. We find that the numerical data strongly support the validity of the form factors themselves: however, we also report a discrepancy in the case of diagonal matrix elements, which remains unresolved for the time being. (C) 2011 Elsevier B.V. All rights reserved
Relaxation and entropy generation after quenching quantum spin chains
This work considers entropy generation and relaxation in quantum quenches in the Ising and 3-state Potts spin chains. In the absence of explicit symmetry breaking we find universal ratios involving R\ue9nyi entropy growth rates and magnetisation relaxation for small quenches. We also demonstrate that the magnetisation relaxation rate provides an observable signature for the "dynamical Gibbs effect" which is a recently discovered characteristic non-monotonous behaviour of entropy growth linked to changes in the quasi-particle spectrum
Phenotyping under extreme weather conditions and microsatellite based genotyping of some Hungarian grape cultivars
Bound States of Majorana Fermions in Semi-classical Approximation
We derive a semi-classical formula for computing the spectrum of bound states made of Majorana fermions in a generic non-integrable 2d quantum field theory with a set of degenerate vacua. We illustrate the application of the formula in a series of cases, including an asymmetric well potential where the spectra of bosons and fermions may have some curious features. We also discuss the merging of fermionic and bosonic spectra in the presence of supersymmetry. Finally, we use the semi-classical formula to analyse the evolution of the particle spectra in a class of non-integrable supersymmetry models