We study the BCS-BEC crossover phenomenon of triplet exciton condensation using a half-filled bilayer Hubbard model.We calculate the dynamical spin structure factor and the exciton wave function on the phase boundary between the antiferromagnetically ordered and disordered phases.In the BCS regime, the formation and condensation of particle-hole bound states, namely excitons, occur simultaneously at the phase transition point, and the exciton wave function is extended in real space.In the BEC regime, on the other hand, bound states are well defined over the whole Brillouin zone also in the disordered phase, and the size of particle-hole pairs is smaller than a lattice space.Quantum criticality of charge-spin-orbital entangled states can emerge from intermediate coupling materials in the crossover regime.
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q=\ensuremath{\pi}$ in
t2g4 spin-orbit coupled three-orbital Hubbard models at electronic density
n=4. In parallel, experiments involving iridates with noninteger valence states for the Ir ions are starting to attract considerable attention. In this publication, using the density matrix renormalization group technique we present evidence for the existence of an excitonic condensate at
n=3.5 in a one-dimensional Hubbard model with a degenerate
t2g sector, when in the presence of spin-orbit coupling. At intermediate Hubbard
U and spin-orbit $\ensuremath{\lambda}$ couplings, we found an excitonic condensate at the unexpected momentum $q=\ensuremath{\pi}/2$ involving ${j}_{\mathrm{eff}}=3/2,m=\ifmmode\pm\else\textpm\fi{}1/2$, and ${j}_{\mathrm{eff}}=1/2,m=\ifmmode\pm\else\textpm\fi{}1/2$ bands in the triplet channel, coexisting with an also unexpected block magnetic order. We also present the entire $\ensuremath{\lambda}$ vs
U phase diagram, at a fixed and robust Hund coupling. Interestingly, this new ``block excitonic phase'' is present even at large values of $\ensuremath{\lambda}$, unlike the
n=4 excitonic phase discussed before. Our computational study helps to understand and predict the possible magnetic phases of materials with
d3.5 valence and robust spin-orbit coupling.
The condensation of spin-orbit-induced excitons in
t2g4 electronic systems is attracting considerable attention. At large Hubbard
U, antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons (
Jeff=1). Here, we show that even at intermediate
U regimes, the spin-orbit exciton condensation is possible leading also to staggered magnetic order. The canonical electron-hole excitations (excitons) transform into local triplon excitations at large
U, and this BEC strong coupling regime is smoothly connected to the intermediate
U excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling ($\ensuremath{\lambda}$) in one dimension using the density matrix renormalization group, while in two dimensions we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full $\ensuremath{\lambda}$ versus
U phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard
U, increasing $\ensuremath{\lambda}$ at fixed
U the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length
rcoh of
O(a) and
O(10a) in
1d and
2d, respectively, with
a being the lattice spacing. Further increasing $\ensuremath{\lambda}$, the system eventually crosses over to the BEC limit (with ${r}_{\mathrm{coh}}\ensuremath{\ll}a$).
We investigate the emergence of an exciton condensate and associated collective modes in a bilayer configuration of
MnBi2Te4, an antiferromagnetic topological insulator and van der Waals material, recognized for hosting axion physics. Utilizing a minimal low-energy Hamiltonian for the two layer system which is gapped by the intrinsic Néel order, we first employ mean-field theory to establish the conditions for exciton condensation. Our analysis identifies a nonzero, spin-singlet exciton order parameter which is tuned by external displacement field, temperature, and Coulomb attraction. Beyond the mean-field, we explore collective mode fluctuations in the uncondensed phase via many-body perturbation theory and the random phase approximation. From this, we derive the exciton spectral function which allows for a direct comparison between theoretical prediction and experimental observation. We detail how the softening of the collective mode peak is a function of the competition between interlayer detuning and thermal fluctuations. This work elucidates how the unique topological and magnetic environment of
MnBi2Te4 offers a tunable platform for the realization and manipulation of exciton condensates and the corresponding collective excitations. Our findings contribute to understanding the interplay of topology and bosonic condensates, which could inspire application in optically accessing topological properties, dissipationless transport, and gate-tunable optoelectronics.
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.
We studied the possibility of exciton condensation in Mott insulating bilayers. In these strongly correlated systems, an exciton is the bound state of a double occupied and empty site. In the strong coupling limit, the exciton acts as a hard-core boson. Its physics is captured by the exciton
t-
J model, containing an effective
XXZ model describing the exciton dynamics only. Using numerical simulations and analytical mean-field theory, we constructed the ground-state phase diagram. Three homogeneous phases can be distinguished: the antiferromagnet, the exciton checkerboard crystal, and the exciton superfluid. For most model parameters, however, we predict macroscopic phase separation between these phases. The exciton superfluid exists only for large exciton hopping energy. Additionally, we studied the collective modes and susceptibilities of the three phases. In the superfluid phase, we find the striking feature that the bandwidth of the spin-triplet excitations, potentially detectable by resonant inelastic x-ray scattering (RIXS), is proportional to the superfluid density. The superfluid phase mode is visible in the charge susceptibility, measurable by RIXS or electron energy loss spectroscopy (EELS).