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arXiv:cond-mat/0507234 · Physical Review B

Exact spontaneous plaquette ground states for high-spin ladder models

Shu Chen, Congjun Wu, Shoucheng Zhang, Yupeng Wang

Published Dec 15, 2005• 55 citations
arXivHTMLPDF

Abstract

We study the exchange physics in high-spin Mott insulating systems with $S=3∕2$ which is realizable in ultracold atomic systems. The high symmetry of $\mathit{SO}(5)$ or $\mathit{SU}(4)$ therein renders stronger quantum fluctuations than the usual spin-$1∕2$ systems. A spontaneous plaquette ground state without any site and bond spin orders is rigorously proved in a ladder spin-$3∕2$ model, whose topological excitations exhibit fractionalization behavior. The generalization to the $\mathit{SU}(N)$ plaquette state is also investigated.

DOI
10.1103/physrevb.72.214428

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We study the exchange physics in high-spin Mott insulating systems with S=3∕2S=3∕2S=3∕2 which is realizable in ultracold atomic systems. The high symmetry of SO(5)\mathit{SO}(5)SO(5) or SU(4)\mathit{SU}(4)SU(4) therein renders stronger quantum fluctuations than the usual spin-1∕21∕21∕2 systems. A spontaneous plaquette ground state without any site and bond spin orders is rigorously proved in a ladder spin-3∕23∕23∕2 model, whose topological excitations exhibit fractionalization behavior. The generalization to the SU(N)\mathit{SU}(N)SU(N) plaquette state is also investigated.
We study small systems of strongly interacting ultracold atoms under the influence of gauge potentials and spin-orbit couplings. We use second-order perturbation theory in tunneling, derive an effective theory for the strongly correlated insulating states with one atom per site, and solve it exactly. We find dramatic changes in the level structure and in the amount of degeneracies expected. We also demonstrate the dynamical behavior as the barriers between plaquettes are gradually removed and find potentially high overlap with the resonating valence bond (RVB) state of the larger system.
Inspired by our recent works on SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase diagram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases, such as Dirac semimetals, antiferromagnetic Mott insulators, valence bond solids (VBSs), and Dirac spin liquid and phase transitions, including Gross-Neveu chiral transitions with emergent continuous symmetry, deconfined quantum criticality, and the first-order transition between an interaction-driven columnar VBS and a plaquette VBS. These rich phenomena coming from simple-looking lattice models firmly convey the message that the interplay between the SU(N)\mathrm{SU}(N)SU(N) Dirac fermions (with enhanced internal symmetries) and extended plaquette interactions (beyond the on-site Hubbard type) is the new playground to synthesize novel highly entangled quantum matter both at the model level and with experimental feasibilities.
In this thesis, the Hubbard model with hopping amplitude, t, and on-site interaction, U, in the Mott-insulating regime is explored for unconventional magnetic phases at T = 0 K. These phases are captured within effective low-energy descriptions, and are triggered by quantum fluctuations due to finite hopping. We aim for unconventional phases from two mechanisms, an increased symmetry SU(N) with N > 2 compared to the most common SU(2), and highly frustrated interactions. For SU(N)-symmetric fermions in artificial gauge fields, chiral spin liquid phases (CSLs) are investigated. They are determined within effective spin models, which we derive in order six in t/U for the honeycomb lattice for general values of N, and study in detail for the triangular lattice up to order five in t/U for SU(3) and SU(7) by exact diagonalisations and variational Monte Carlo simulations. On the triangular lattice, the third-order effective model is the J -K model with nearest-neighbour coupling, J ∈ R, and ring exchange, K ∈ C. For SU(3) and Im K = 0, the three-sublattice long-range ordered phase is ruled out by a spontaneously time-reversal symmetry breaking π/3-flux CSL through � nite hopping. Further, for Im K = 0, a lattice nematic, a 120◦ long-ranged ordered, and the ferromagnetically ordered phase occur. The CSL is found to be extended to Re K = 0. It is also present in the fourth- and fifth-order model in the most relevant π-flux case, where time-reversal symmetry is spontaneously broken. Together with the estimated metal-insulator transition point at larger hoppings, this CSL is therefore expected to be realised in the SU(3) Hubbard model. The analogous CSL is also predicted for SU(7)-symmetric fermions. Experimental realisations with ultra-cold atoms in optical lattices are described. SrCu2(BO3)2 is a highly frustrated quantum magnet. At ambient pressure it is captured by the spin-1/2 Shastry-Sutherland model, which yields the effective strong-coupling description of the associated SU(2) Hubbard model. To describe SrCu2(BO3)2 under higher pressure, we extend the Shastry-Sutherland model by asymmetric coupling strengths, and find that asymmetries of a few percent are sufficient to replace the empty plaquette singlet phase (EPP) of the Shastry-Sutherland model with the filled plaquette singlet phase (FPP) that is found to be identical to a quasi one-dimensional Haldane phase. These results are achieved by series expansions and infinite projected entangled-pair states. The dispersions and dynamic structure factors of both plaquette phases are derived. The EPP naturally hosts one low-lying triplon, whereas the FPP has two. Therefore, the FPP appears to be the likely candidate for SrCu2(BO3)2 under pressure. The excitations of both phases show some agreement with experimental data if the exchange amplitudes change more than expected. Further measurements are suggested. At last, an orthogonal-plaquette model of spins-1/2 is introduced and proven to host two exact valence bond crystals based on plaquette singlets with an extensive degeneracy at the phase transition. This model exhibits an extensive number of conserved quantities, which is used for further investigations of the phase diagram.
Abstract Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain 1,2 . Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter 3,4 . More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement 5–7 . Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi–Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.
We study various Mott insulating phases of interacting spin-32\frac{3}{2}23​ fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.