Pseudospin S = 1 formalism and skyrmion-like excitations in the three-body constrained extended Bose–Hubbard model

Abstract

We have focused in the paper on the most prominent and intensively studied S=1 pseudospin formalism for extended bosonic Hubbard model (EHBM) with truncation of the on-site Hilbert space to the three lowest occupation states n = 0, 1, 2. The EHBM Hamiltonian is a paradigmatic model for the highly topical field of ultracold gases in optical lattices. Generalized non-Heisenberg effective pseudospin Hamiltonian does provide a deep link with boson system and physically clear description of "the myriad of phases" from uniform Mott insulating phases and density waves to two types of superfluids and supersolids. We argue that the 2D pseudospin system is prone to a topological phase separation and focus on several types of unconventional skyrmion-like topological structures in 2D boson systems, which have not been analysed till now. The structures are characterized by a complicated interplay of insulating and the two superfluid phases with a single boson and two-boson condensation, respectively.

Competition of Spin and Charge Orders in a Model Cuprate

“…Effective S = 1 pseudo-spin Hamiltonian which does commute with the z-component of the total pseudo-spin i S iz can be written to be a sum of the three terms [3]:…”

Model of charge triplets for high-T$_c$ cuprates

“…The S = 1 spin algebra includes the eight independent nontrivial pseudospin operators, the three dipole and five quadrupole operators [17,18,19,6] with irreducible form as follows…”

Asymptotics of quasi-classical localized states in 2D system of charged hard-core bosons

“…The S = 1 pseudospin formalism [1,2] developed for the copper oxides implies that the on-site Hilbert space described by three effective valence states of the copper ions, Cu 1+,2+,3+ , or, strictly speaking, of the copper-oxygen clusters CuO 7−,6−,5− 4 in the CuO 2 plane. These states correspond to the hole occupation numbers n h = 0, 1, 2 and can be considered as components of the pseudospin S = 1 triplet with projections M S = −1, 0, +1, respectively.…”

“…Last years the interest to these models was boosted by finding of a coexistence of charge ordering and superconductivity in high temperature superconductors. The charge degree of freedom in high-T c cuprates such as La 2−x Sr x CuO 4 can be described in terms of a pseudospin S = 1 model [1,2]. Here in the paper we consider the limiting case of the model, reduced to the 2D system of charged hard-core (hc) bosons on a square lattice.…”