Excitation spectrum and quantum phase transitions in the one-dimensional ionic Hubbard model
Loading...
Date
2014
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Alternative Title(s)
Continuous unitary transformations approach
Abstract
Strongly correlated electron systems are one of the most fascinating problems in
current physics. The strong electron-electron interaction in these materials leads to
the emergence of nontrivial elementary excitations (quasiparticles, QPs) above the ground state
ranging from fractional spins in quasi-one-dimensional materials to magnetic monopole in
the pyrochlore lattice. The condensation of these quasiparticles upon changing some external
parameters may stabilize new exotic states of matter. Experimental measurements such as
inelastic neutron scattering provide us with valuable information about the excitation
spectrum of such systems which require microscopic models to be described.
This thesis is devoted to a detailed analysis of the excitation spectrum and of the quantum
phase transitions in the one-dimensional (1D) ionic Hubbard model (IHM). The IHM
consists of a nearest-neighbor (n.n.) hopping, onsite Hubbard interaction, and an
ionic (staggered) potential separating the odd and even sites energetically.
The model
exhibits two continuous phase transitions on increasing the Hubbard interaction identified
by a low-energy effective field theory and confirmed by a rigorous density matrix renormalization
group (DMRG) analysis after several attempts. The first transition occurs from band insulator
(BI) phase to the 2-fold degenerate spontaneously dimerized insulator (SDI) phase.
The transition is in the Ising universality class as is plausible from symmetry considerations.
The SDI phase becomes unstable towards a quasi-long-range order Mott insulator (MI) phase at
a second transition point resembling the Kosterlitz-Thouless (KT) transition in the frustrated Heisenberg
chain.
We employ continuous unitary transformations (CUT) to systematically map the IHM to
effective Hamiltonians (almost) conserving the number of QPs in the system. Using
an analysis in the BI regime where electrons and holes define QPs, the low-energy excitation
spectrum of the model is quantitatively determined in the BI phase almost up to the
first transition point. The transition from the BI to the SDI phase is signaled by the vanishing of
an S=0 exciton mode at the total momentum K=\pi. The condensation of these excitons
beyond the first transition point is described by a BCS-type-theory showing the stabilization
of the SDI phase. The mean-field solution indicates no second phase transition to the
quasi-long-range order MI phase. This is interpreted as the effect of strong quantum
fluctuations in one dimension.
We consider the IHM in the dimer limit where the uniform chain is separated into independent dimers.
The different phases of the IHM are studied by increasing the interdimer hopping and reaching
the uniform limit. This dimer limit satisfactorily produces the excitation spectrum of the BI phase
confirming the vanishing of an S=0 exciton mode at the first transition point.
It is found that
the SDI-to-MI transition takes place by softening of a magnetic S=1 excitation, i.e., a triplon.
We report rigorous results for the gapless triplon dispersion in the MI phase and
discuss the binding effects in the 2-triplon sector.
Description
Table of contents
Keywords
Condensed matter physics, Hubbard model, Quantum phase transition, Renormalization, Bound states
Subjects based on RSWK
Hubbard-Modell, Kondensierte Materie, Inelastische Neutronenstreuung, Anregungsspektrum, Phasenumwandlung