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Register a new userGround state of weakly repulsive soft-core bosons on a sphere
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We study a system of penetrable bosons embedded in a spherical surface. Under the assumption of weak interaction between the particles, the ground state of the system is, to a good approximation, a pure condensate. We employ thermodynamic arguments to investigate, within a variational ansatz for the single-particle state, the crossover between distinct finite-size phases in the parameter space spanned by the sphere radius and the chemical potential. In particular, for radii up to a few interaction ranges we examine the stability of the fluid phase with respect to a number of crystal-like arrangements having the symmetry of a regular or semi-regular polyhedron. We find that, while quantum fluctuations keep the system fluid at low density, upon compression it eventually becomes inhomogeneous, i.e., particles gather together in clusters. As the radius increases, the nature of the high-density aggregate varies and we observe a sequence of transitions between different cluster phases (solids), whose underlying rationale is to maximize the coordination number of clusters, while ensuring at the same time the proper distance between each neighboring pair. We argue that, at least within our mean-field description, every cluster phase is supersolid.
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The properties of a macroscopic assembly of weakly-repulsive bosons at zero temperature are well described by Gross-Pitaevskii mean-field theory. According to this formalism the system exhibits a quantum transition from superfluid to cluster supersolid as a function of pressure. We develop a thermodynamically rigorous treatment of the different phases of the system by adopting a variational formulation of the condensate wave function --- represented as a sum of Gaussians --- that is amenable to exact manipulations. Not only is this description quantitatively accurate, but it is also capable to predict the order (and sometimes even the location) of the transition. We consider a number of crystal structures in two and three dimensions and determine the phase diagram. Depending on the lattice, the transition from fluid to solid can be first-order or continuous, a lower coordination entailing a milder transition. In two dimensions, crystallization would occur at the same pressure on three distinct lattices (square, honeycomb, and stripes), all providing metastable phases with respect to the triangular crystal. A similar scenario holds in three dimensions, where the simple-cubic and diamond crystals also share a common melting point; however, the stable crystal at low pressure is typically fcc. Upon compression and depending on the shape of the potential, the fcc crystal may transform into hcp. We conclude by sketching a theory of the solid-fluid interface and of quantum nucleation of the solid from the fluid.
We study hard core bosons on a two leg ladder lattice under the orbital effect of a uniform magnetic field. At densities which are incommensurate with flux, the ground state is a Meissner state, or a vortex state, depending on the strength of the flux. When the density is commensurate with the flux, analytical arguments predict the existence of a ground state of central charge $c = 1$, which displays signatures compatible with the expected Laughlin state at $ u=1/2$. This differs from the coupled wire construction of the Laughlin state in that there exists a nonzero backscattering term in the edge Hamiltonian. We construct a phase diagram versus density and flux in order to delimit the region where this precursor to the Laughlin state is the ground state, by using a combination of bosonization and numerics based on the density matrix renormalization group (DMRG) and exact diagonalization. We obtain the phase diagram from local observables and central charge. We use bipartite charge fluctuations to deduce the Luttinger parameter for the edge Luttinger liquid corresponding to the Laughlin state. The properties studied with local observables are confirmed by the long distance behavior of correlation functions. Our findings are consistent with a calculation of the many body ground state transverse conductivity in a thin torus geometry for parameters corresponding to the Laughlin state. The model considered is simple enough such that the precursor to the Laughlin state could be realized in current ultracold atom, Josephson junction array, and quantum circuit experiments.
We calculate analytically the entanglement and Renyi entropies, the negativity and the mutual information together with all the density and many-particle correlation functions for free bosons on a lattice in the ground state. We show that those quantities can be derived from a multinomial form of the reduced density matrix in the configuration space whose diagonal elements dictate the statistics of the particle distribution, while the off-diagonal coherence terms control the quantum fluctuations. We clarify by this analysis how to reconcile the logarithmic behavior of the entanglement entropy with the volume law of the particle number fluctuations.
We study a system of penetrable bosons on a line, focusing on the high-density/weak-interaction regime, where the ground state is, to a good approximation, a condensate. Under compression, the system clusterizes at zero temperature, i.e., particles gather together in separate, equally populated bunches. We compare predictions from the Gross-Pitaevskii (GP) equation with those of two distinct variational approximations of the single-particle state, written as either a sum of Gaussians or the square root of it. Not only the wave functions in the three theories are similar, but also the phase-transition density is the same for all. In particular, clusterization occurs together with the softening of roton excitations in GP theory. Compared to the latter theory, Gaussian variational theory has the advantage that the mean-field energy functional is written in (almost) closed form, which enables us to extract the phase-transition and high-density behaviors in fully analytic terms. We also compute the superfluid fraction of the clustered system, uncovering its exact behavior close, as well as very far away from, the transition.
Using anyon-fermion mapping method, we investigate the ground state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix are obtained. Basing on the formula, we evaluated the momentum distribution, the natural orbitals and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground state properties of anyons interplay between Bosons and Fermions continuously. We can expect that the hard-core anyons of larger statistical parameter exhibit the similar properties to the hard-core Bosons although anyon system satisfy specific fractional statistics.
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