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Register a new userCompeting valence bond and symmetry breaking Mott states of spin-3/2 fermions on a honeycomb lattice
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We investigate magnetic properties of strongly interacting four component spin-3/2 ultracold fermionic atoms in the Mott insulator limit with one particle per site in an optical lattice with honeycomb symmetry. In this limit, atomic tunneling is virtual, and only the atomic spins can exchange. We find a competition between symmetry breaking and liquid like disordered phases. Particularly interesting are valence bond states with bond centered magnetizations, situated between the ferromagnetic and conventional valence bond phases. In the framework of a mean-field theory, we calculate the phase diagram and identify an experimentally relevant parameter region where a homogeneous SU(4) symmetric Affleck-Kennedy-Lieb-Tasaki-like valence bond state is present.
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We propose an experimentally feasible setup with ultracold alkaline earth atoms to simulate the dynamics of U(1) lattice gauge theories in 2+1 dimensions with a Chern-Simons term. To this end we consider the ground state properties of spin-5/2 alkaline earth fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin liquid state with $2pi/3$ flux per plaquette, which spontaneously violates time reversal invariance. We demonstrate that due to the breaking of time reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge field dynamics. We discuss also properties of the lowest energy competing orders.
We study the possible ground state configurations of two strongly coupled chains of charge neutral spin-3/2 fermionic atoms interacting via short range van der Waals interaction. The coupling between the two chains is realized by relatively large hopping amplitude. Exploiting that such a ladder configuration can be mapped to an effective one-band model we analyze the emerging ground states of the system. We show that various spatially inhomogeneous states, valence bond states, plaquette states compete depending on the filling and the ratio of the interaction strengths in the singlet and quintet scattering channel. We find that a Luttinger liquid state is the ground state of the strongly coupled ladder in an extended region of the parameter space, and we also show that a topologically nontrivial charge Haldane state can emerge in the strongly coupled ladder at quarter and three-quarter fillings.
The honeycomb lattice material Li2RuO3 undergoes a dimerization of Ru4+ cations on cooling below 270C, where the magnetic susceptibility vanishes. We use density functional theory calculations to show that this reflects the formation of a valence bond crystal, with a strong bond disproportionation. On warming, x-ray diffraction shows that discrete three-fold symmetry is regained on average, and the dimerization apparently disappears. In contrast, local structural measurements using high-energy x-rays, show that disordered dimers survive at the nanoscale up to at least 650C. The high temperature phase of Li2RuO3 is thus an example of a valence bond liquid, where thermal fluctuations drive resonance between different dimer coverages, a classic analogue of the resonating valence bond state often discussed in connection with high T$_c$ cuprates.
Conflicting predictions have been made for the ground state of the SU(3) Heisenberg model on the honeycomb lattice: Tensor network simulations found a plaquette order [Zhao et al, Phys. Rev. B 85, 134416 (2012)], where singlets are formed on hexagons, while linear flavor-wave theory (LFWT) suggested a dimerized, color ordered state [Lee and Yang, Phys. Rev. B 85, 100402 (2012)]. In this work we show that the former state is the true ground state by a systematic study with infinite projected-entangled pair states (iPEPS), for which the accuracy can be systematically controlled by the so-called bond dimension $D$. Both competing states can be reproduced with iPEPS by using different unit cell sizes. For small $D$ the dimer state has a lower variational energy than the plaquette state, however, for large $D$ it is the latter which becomes energetically favorable. The plaquette formation is also confirmed by exact diagonalizations and variational Monte Carlo studies, according to which both the dimerized and plaquette states are non-chiral flux states.
The concept of valence bond resonance plays a fundamental role in the theory of the chemical bond and is believed to lie at the heart of many-body quantum physical phenomena. Here we show direct experimental evidence of a time-resolved valence bond quantum resonance with ultracold bosonic atoms in an optical lattice. By means of a superlattice structure we create a three-dimensional array of independent four-site plaquettes, which we can fully control and manipulate in parallel. Moreover, we show how small-scale plaquette resonating valence bond states with s- and d-wave symmetry can be created and characterized. We anticipate our findings to open the path towards the creation and analysis of many-body RVB states in ultracold atomic gases.
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