We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into 2×2 composite bosons and solve it within a generalized Hartree-Bogoliubov approximation. The resulting Mott insulator-superfluid phase diagram reproduces well quantum Monte Carlo results. The Higgs boson behavior in the superfluid phase along the unit density line is unraveled and in remarkable agreement with experiments. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles.

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Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a nontrivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner-superfluid to vortex-superfluid transition, and a nontrivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a nonchiral and a chiral superfluid, both characterized by nontrivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.

We study the quantum phase diagram of a system of hard-core bosons on the Kagome lattice with nearest-neighbor repulsive interactions, for arbitrary densities, by means of the hierarchical mean field theory and exact diagonalization techniques. This system is isomorphic to the spin S=1/2 XXZ model in presence of an external magnetic field, a paradigmatic example of frustrated quantum magnetism. In the non-frustrated regime, we find two crystal phases at densities 1/3 and 2/3 that melt into a superfluid phase when increasing the hopping amplitude, in semi-quantitative agreement with quantum Monte Carlo computations. In the frustrated regime and away from halffilling, we find a series of plateaux with densities commensurate with powers of 1/3. The broader density plateaux (at densities 1/3 and 2/3) are remnants of the classical degeneracy in the Ising limit. For densities near half-filling, this staircase of crystal phases melts into a superfluid, which displays finite chiral currents when computed with clusters having an odd number of sites. Both the staircase of crystal phases and the superfluid phase prevail in the non-interacting limit, suggesting that the lowest dispersionless single-particle band may be at the root of this phenomenon.

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We present a general method to construct translation-invariant and SU(2) symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBCs). The method is based on a canonical mapping transforming S = 1/2 spin operators into a bilinear form of a new set of dimer fermion operators. We construct parent Hamltonians of the columnar-and the staggered-VBC on the square lattice, for which the VBC is an eigenstate in all regimes and the exact ground state in some region of the phase diagram. We study the depart from the exact VBC regime upon tuning the anisotropy by means of the hierarchical mean field theory and exact diagonalization on finite clusters. In both Hamiltonians, the VBC phase extends over the exact regime and transits to a columnar antiferromagnet (CAFM) through a window of intermediate phases, revealing an intriguing competition of correlation lengths at the VBC-CAFM transition. The method can be readily applied to construct other VBC parent Hamiltonians in different lattices and dimensions.Quantum magnets host a wealth of phases and exotic phenomena. The complex interplay between spin interactions and lattice topology may eventually prevent the stabilization of magnetic order. In particular, frustrated antiferromagnetic spin-1/2 interactions may favor the partition of the system into nearest-neighbor (NN) spin singlets, so-called valence-bonds (VB), covering the lattice in a periodic pattern or VB crystal (VBC) [1]. Eventually, VBs may resonate and recover translational invariance by forming a resonating-VB (RVB) spin liquid, as has been conjectured to occur in high-T c cuprates [2,3]. Particularly interesting is the zero-temperature quantum phase transition from the former state to an ordered AF phase [4], a transition that can be experimentally probed upon tuning external pressure [5] or magnetic field on various materials [6]. Under certain specific conditions, it has been argued that a class of VBC-AF transitions in two-dimensions (2D) are driven by the deconfinement of fractional excitations at a critical point [7], contrary to what is generally expected within Landau theory. To test these ideas, a family of antiferromagnetic Heisenberg Hamiltonians with additional four-and six-spin interactions favoring VBC order and amenable to quantum Monte Carlo (QMC) computations has been introduced during the last decade [8][9][10]. These models, socalled J −Q models, show unusual scaling behavior at the VBC-AF transition point [10][11][12][13][14] and, in some cases, a weak VBC signal [8,11]. In order to furnish this putative new class, it would be desirable to enlarge the number of Hamiltonians hosting VBC-AF transitions. In particular, antiferromagnetic Hamiltonians hosting an exact VBC ground-state (GS) shall provide a convenient test bed where the VBC phase is unambiguously defined. In this Letter, we present a general method to construct SU(2) symmetric and translation-invariant VBC parent Hamiltonians based on a canonical mapping that exactly identifies a VBC state with the vacuum of a new ...

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the 1D and 2D Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost.

We introduce a hybrid quantum-classical variational algorithm to simulate ground-state phase diagrams of frustrated quantum spin models in the thermodynamic limit. The method is based on a cluster-Gutzwiller ansatz where the wave function of the cluster is provided by a parameterized quantum circuit. The key ingredient is a tunable real XY gate allowing to generate valence-bonds on nearest-neighbor qubits. Additional tunable single-qubit Z-and two-qubit ZZ-rotation gates permit the description of magnetically ordered phases while efficiently restricting the variational optimization to the U(1) symmetric subspace. We benchmark the method against the paradigmatic J1-J2 Heisenberg model on the square lattice, for which the present hybrid ansatz is an exact realization of the cluster-Gutzwiller with 4-qubit clusters. In particular, we describe the Néel order and its continuous quantum phase transition onto a valence-bond solid characterized by a periodic pattern of 2×2 strongly-correlated plaquettes, providing a route to synthetically realize valence-bond solids with currently developed superconducting circuit devices.