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arXiv:cond-mat/9701059

Enlarged Symmetry and Coherence in Arrays of Quantum Dots

Alexey V. Onufriev, Brad Marston

Published Jan 9, 1997• 0 citations
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Abstract

Enlarged symmetry characterized by the group SU(4) can be realized in isolated semiconducting quantum dots. A Hubbard model then describes a pillar array of coupled dots and at half-filling the system can be mapped onto an SU(4) spin chain. The physics of these new structures is rich as novel phases are attainable. The spins spontaneously dimerize and, by using the Density Matrix Renormalization Group (DMRG), we show that the dimer state is robust to perturbations which break SU(4) symmetry. We propose ways to experimentally verify the existence of the dimerized phase.

DOI
10.48550/arxiv.cond-mat/9701059

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Enlarged symmetry characterized by the group SU(4) can be realized in isolated semiconducting quantum dots. A Hubbard model then describes a pillar array of coupled dots and at half-filling the system can be mapped onto an SU(4) spin chain. The physics of these new structures is rich as novel phases are attainable. The spins spontaneously dimerize and, by using the Density Matrix Renormalization Group (DMRG), we show that the dimer state is robust to perturbations which break SU(4) symmetry. We propose ways to experimentally verify the existence of the dimerized phase.
The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization-group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of coherent spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become incoherent. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.
Abstract Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi–Hubbard model. We show how the topological phases at half-filling can be characterized by a reduced Zak phase defined based on the reduced density matrix of each spin subsystem. Signatures of bulk–boundary correspondence are observed in the triplon excitation of the bulk and the edge states of uncoupled spins at the boundaries. At quarter-filling, we show that owing to the presence of the Hubbard interaction the system can undergo a transition to the topological ground state of the non-interacting Su–Schrieffer–Heeger model with the application of a moderate-strength external magnetic field. We propose a robust experimental realization with a chain of dopant atoms in silicon or gate-defined quantum dots in GaAs where the transition can be probed by measuring the tunneling current through the many-body state of the chain.
We investigate the phase diagram of a dimerized Bose-Hubbard model, using a density matrix renormalization group technique. We find a new phase, which is the coexistence of superfluid and bond-wave phases, due to the effect of dimerization. Experimentally dimerization in optical lattice can be realized by using two counterpropagating laser beams of different wavelengths. Apart from the conventional superfluid–to–Mott-insulator transition, we find a new quantum phase transition: from superfluid-bond-wave to Mott-insulator-bond wave phase. Our study suggests a rich phase diagram which can be easily probed.
We investigate dynamical symmetry enlargement in the half-filled SU(4) Hubbard chain using nonperturbative renormalization-group and quantum Monte Carlo techniques. A spectral gap is shown to open for arbitrary Coulombic repulsion UUU. At weak coupling, $U\ensuremath{\lesssim}3t$, a SO(8) symmetry between charge and spin-orbital excitations is found to be dynamically enlarged at low energy whereas at strong coupling, $U\ensuremath{\gtrsim}6t$, the charge degrees of freedom dynamically decouple. The crossover between these regimes is discussed.
We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate 6\mathbf{6}6 representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimerlike phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauth\'e, S. Capponi, and D. Poilblanc, Phys. Rev. B 99, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric projected entangled pair states (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations.