We define an infinite class of frustration-free'' interacting lattice quantum Hamiltonians for bosons, constructed such that their exact ground states have a density distribution specified by the Boltzmann weight of a corresponding classical lattice gas problem. By appropriately choosing the classical weights, we obtain boson representations of various known solvable models, including quantum dimer and vertex models, toric code, and certain Levin-Wen string-net models. We also systematically construct solvable models with other interesting ground states, including quantum spin liquids, supersolids, Bose-Einstein insulators,'' Bose liquids with ``Bose surfaces,'' and Bose-Einstein condensates that permit adiabatic evolution from a noninteracting limit to a Gutzwiller-projected limit.
In a conventional boson system, the ground state can either be an insulator or a superfluid (SF) due to the duality between particle number and phase. This paper reveals that the long-sought Bose metal (BM) state can be realized in an exactly solvable interacting bosonic model, i.e. the Bose-Hatsugai-Kohmoto (BHK) model, which acts as the nontrivial extension of Bose-Hubbard (BH) model. By tuning the parameters such as bandwidth
W, chemical potential
μ, and interaction strength
U, a BM state without any symmetry-breaking can be accessed for a generic
W/U ratio, while a Mott insulator (MI) with integer boson density is observed at small
W/U. The quantum phase transition between the MI and BM states belongs to the universality class of the Lifshitz transition, which is further confirmed by analyzing the momentum-distribution function, the Drude weight, and the superfluid density. Additionally, our investigation at finite temperature reveals similarities between the BM state and the Fermi liquid, such as a linear-
T dependent heat capacity (
Cv∼γT) and a saturated charge susceptibility ($χ_{c} \sim $ constant) as
T approaches zero. Comparing the BM state with the SF state in the standard BH model, we find that the key feature of the BM state is a compressible total wavefunction accompanied by an incompressible zero-momentum component. Given that the BM state prevails over the SF state at any finite
U in the BHK model, our work suggests the possibility of realizing the BM state with on-site repulsion interactions in momentum space.
In a conventional boson system, the ground state can either be an insulator or a superfluid (SF) due to the duality between particle number and phase. This paper reveals that the long-sought Bose metal (BM) state can be realized in an exactly solvable interacting bosonic model, i.e., the Bose-Hatsugai-Kohmoto (BHK) model, which acts as the nontrivial extension of Bose-Hubbard (BH) model. By tuning the parameters such as bandwidth
W, chemical potential $\ensuremath{\mu}$, and interaction strength
U, a BM state without any symmetry breaking can be accessed for a generic
W/U ratio, while a Mott insulator (MI) with integer boson density is observed at small
W/U. The quantum phase transition between the MI and BM states belongs to the universality class of the Lifshitz transition, which is further confirmed by analyzing the momentum-distribution function, the Drude weight, and the SF weight. Additionally, our investigation at finite temperature reveals similarities between the BM state and the Fermi liquid, such as a linear-
T dependent heat capacity ($Cv\ensuremath{\sim}\ensuremath{\gamma}T$) and a saturated charge susceptibility (${\ensuremath{\chi}}_{c}\ensuremath{\sim}$ constant) as
T approaches zero. Comparing the BM state with the SF state in the standard BH model, we find that the key feature of the BM state is a compressible total wavefunction accompanied by an incompressible zero-momentum component. Given that the BM state prevails over the SF state at any finite
U in the BHK model, our paper suggests the possibility of realizing the BM state with on-site repulsion interactions in momentum space.
Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix γ as a variable but still recovers quantum correlations in an exact way it is particularly well suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying v-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals F[γ] for this N-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. For Bose-Einstein condensates with N_{BEC}≈N condensed bosons, the respective gradient forces are found to diverge, ∇_{γ}F∝1/sqrt[1-N_{BEC}/N], providing a comprehensive explanation for the absence of complete condensation in nature.
We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low-energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multidimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground-state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self-dual under Wegner's duality, with the self-dual point corresponding to the RK point of the original multidimer model. We argue that the self-dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is nonbipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host
Z2 topologically ordered phases.
We discuss a class of lattice S = 1 2 quantum Hamiltonians with bond-dependent Ising couplings and a mutually “anticommuting” algebra of extensively many local Z 2 conserved charges that was explicated by Pujari []. This mutual algebra is reminiscent of the spin- 1 2 Pauli matrix algebra but encoded in the structure of . These models have finite residual entropy density in the ground state with a simple but nontrivial degeneracy counting and concomitant quantum spin liquidity as proved by Pujari []. The spin liquidity relies on a geometrically site-interlinked character of the local conserved Z 2 charges that is rather natural in the presence of an anticommuting structure. One may contrast this with, for example, the bond-interlinked character of the local conserved Z 2 charges on the hexagonal plaquettes of the Kitaev honeycomb spin- 1 2 model, which leads to a mutually commuting local algebra. In this work, we make several exact statements on the kinds of many-body orders that can be present within the class of anticommuting quantum spin liquids coexisting with extensive residual ground state entropy. We elucidate the differences between the many-body order in these models and that found in some gapped quantum spin liquids whose canonical example is the Kitaev toric code. The toric code belongs to the more general class of Levin-Wen or string net constructions that possess mutually commuting algebras for the local conserved charges. We also point out a mutually commuting algebra with local support that is naturally expressed as multilinear Majorana forms in the Kitaev representation of these quantum spin liquids. They capture quantum resonances spread across the lattice in anticommuting Z 2 quantum spin liquids.