Mykola Maksymenko

STRONGLY CORRELATED FLAT-BAND SYSTEMS: THE ROUTE FROM HEISENBERG SPINS TO HUBBARD ELECTRONS

In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

Flat-band ferromagnetism as a Pauli-correlated percolation problem.

We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the one-dimensional case and develop a numerical algorithm for the two-dimensional case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.

Classical dipoles on the kagome lattice

Motivated by recent developments in magnetic materials, frustrated nanoarrays and cold atomic systems, we investigate the behaviour of dipolar spins on the frustrated two-dimensional kagome lattice. By combining the Luttinger-Tisza approach, numerical energy minimization, spin-wave analysis and parallel tempering Monte-Carlo, we study long-range ordering and finite-temperature phase transitions for a Hamiltonian containing both dipolar and nearest-neighbor interactions. For both weak and moderate dipolar interactions, the system enters a three-sublattice long-range ordered state, with each triangle having vanishing dipole and quadrupole moments; while for dominating dipolar interactions we uncover ferrimagnetic three-sublattice order. These are also the ground states for XY spins. We discuss excitations of, as well as phase transitions into, these states. We find behaviour consistent with Ising criticality for the 120-degree state, while the ferrimagnetic state appears to be associated with drifting exponents. The celebrated flat band of zero-energy excitations of the kagome nearest-neighbour Heisenberg model is lifted to finite energies but acquires only minimal dispersion as dipolar interactions are added.

Reversible first-order transition in Pauli percolation

Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical physics. We analyze a new percolation problem in which the first-order nature of an equilibrium percolation transition can be established analytically and verified numerically. The rules for this site percolation model are physical and very simple, requiring only the introduction of a weight W(n)=n+1 for a cluster of size n. This establishes that a discontinuous percolation transition can occur with qualitatively more local interactions than in all currently considered examples of explosive percolation; and that, unlike these, it can be reversible. This greatly extends both the applicability of such percolation models in principle and their reach in practice.

Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N)2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Persistence of the flat band in a kagome magnet with dipolar interactions

The weathervane modes of the classical Heisenberg antiferromagnet on the kagome lattice constitute possibly the earliest and certainly the most celebrated example of a flat band of zero-energy excitations. Such modes arise from the underconstraint that has since become a defining criterion of strong geometrical frustration. We investigate the fate of this flat band when dipolar interactions are added. These change the nearest-neighbour model fundamentally as they remove the Heisenberg spin-rotational symmetry while also introducing a long- range component to the interaction. We explain how the modes continue to remain approximately dispersionless, while being lifted to finite energy as well as being squeezed: they change their ellipticity described by the ratio of the amplitudes of the canonically conjugate variables comprising them. This phenomenon provides interesting connections between concepts such as constraint counting and self-screening underpinning the field of frustrated magnetism. We discuss variants of these phenomena for different interactions, lattices and dimension.