1,569 research outputs found
Scaling Relation for Excitation Energy Under Hyperbolic Deformation
We introduce a one-parameter deformation for one-dimensional (1D) quantum
lattice models, the hyperbolic deformation, where the scale of the local energy
is proportional to cosh lambda j at the j-th site. Corresponding to a 2D
classical system, the deformation does not strongly modify the ground state. In
this situation, the effective Hamiltonian of the quantum system shows that the
quasi particle is weakly bounded around the center of the system. By analyzing
this binding effect, we derive scaling relations for the mean-square width
of confinement, the energy correction with respect to the excitation gap
\Delta, and the deformation parameter . This finite-size scaling
allows us to investigate excitation gap of 1D non-deformed bulk quantum
systems.Comment: 9 pages, 5 figure
Private school choice among Muslim parents: the public–private school decision in Delhi, India
This article examines Muslim parents’ private school choice, their understanding of public–private schooling and how they navigate the choice between fee-free public schools and fee-charging private schools. This article draws on qualitative data from open-ended, semi-structured interviews with 38 parents from Muslim-majority areas in Delhi, India. The findings show that parents choose private schools for several reasons, such as their proximity, discipline, emphasis on Islamic teachings and values, safety and caring teachers. The analysis suggests that structural and social factors influence and construct parents’ choice of a particular school. The neighbourhood where they reside, their minority status, their socio-economic and demographic profile, and the type of schools that are available to them influence their decision making
Theorems on ground-state phase transitions in Kohn-Sham models given by the Coulomb density functional
Some theorems on derivatives of the Coulomb density functional with respect
to the coupling constant are given. Consider an electron density
given by a ground state. A model Fermion system with the
reduced coupling constant, , is defined to reproduce and the ground state energy. Fixing the charge density, possible phase
transitions as level crossings detected in a value of the reduced density
functional happen only at discrete points along the axis. If the
density is -representable also for , accumulation of phase
transition points is forbidden when . Relevance of the
theorems for the multi-reference density functional theory is discussed.Comment: 19 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
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