We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e. the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.A few years ago some key works [1] initiated a new vein of research using concepts borrowed from Quantum Information Theory in the analysis of quantum phase transitions (QPT, i.e. phase transition driven by quantum as opposed to thermal fluctuations). The best known examples are no-doubt the measures of entanglement, which quantifies the strength of quantum correlations between subsystems of a compound system and represents a basic quantumcomputational resource [2]. A more recent proposal is based on the fidelity, a key parameter in the characterization of the performance of logical quantum gates [3]. The main advantage of this tool lies in the fact that, being a purely Hilbert-space geometrical quantity, it does not require any a priori knowledge of the correlations driving the QPT, or of the order parameter thereof [4].While most of the works in this relatively new field focus either on fermionic models [5,6,7,8,9] or on spin models [1,4,10,11,12,13] that can be often effectively posed as free spinless fermionic systems, bosonic models went somewhat unaddressed so far. Two exceptions in this respect are Refs. [14] and [15], which propose the study of the hallmark QPT of the Bose-Hubbard (BH) model using respectively entanglement and Loschmidt Echo, a quantity kindred to fidelity. We note that the latter also provides an experimental scheme to measure fidelity. Also, the crossovers characterizing the ground-state properties of the attractive BH model [16] are investigated in terms of fidelity in Ref. [17]. This substantial lack of attention does not make justice of this paradigmatic bosonic model. Indeed, on the one hand the BH model has a clear experimental relevance, being standardly realized in terms of optically trapped ultracold atoms [18]. On the other hand, it is a genuinely many-body model which in general cannot be reduced to an effective noninteracting model, hence posing a significant computational challenge. These features make the BH model ideal grounds for investigating the effectiveness of Quantum Information tools in the study of QPT. This is the aim of the present work. We focus two specific topologies, i.e. the one dimensional lattice with periodic boundary conditions (ring) and the completely connected graph (CCG), i.e. a model with the same hopping amplitude across any two sites. A twofold reason makes the latter a convenient benchmark [8,9,10,11,14,19]. First, the critical lines of its ...

We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.

We study the ground state properties of the Bose-Hubbard model with attractive interactions on a M -site one-dimensional periodic -necklace-like -lattice, whose experimental realization in terms of ultracold atoms is promised by a recently proposed optical trapping scheme, as well as by the control over the atomic interactions and tunneling amplitudes granted by well-established optical techniques. We compare the properties of the quantum model to a semiclassical picture based on a number-conserving su(M ) coherent state, which results into a set of modified discrete nonlinear Schrödinger equations. We show that, owing to the presence of a correction factor ensuing from number conservation, the ground-state solution to these equations provides a remarkably satisfactory description of its quantum counterpart not only -as expected -in the weak-interaction, superfluid regime, but even in the deeply quantum regime of large interactions and possibly small populations. In particular, we show that in this regime, the delocalized, Schrödinger-cat-like quantum ground state can be seen as a coherent quantum superposition of the localized, symmetry-breaking groundstate of the variational approach. We also show that, depending on the hopping to interaction ratio, three regimes can be recognized both in the semiclassical and quantum picture of the system. PACS numbers: 03.75.Lm 05.30.Jp, 03.65.Sq 31.15.Pf I. OVERVIEWOwing to the impressive progress in experimental techniques, ultracold neutral atoms trapped in optical lattices are nowadays widely recognized as a versatile toolbox bringing into reality ideal models of condensed matter physics [1]. A prominent example in this respect is no doubt the Bose-Hubbard model, originally introduced to sketch the physics of superfluid helium in porous media [2] and subsequently shown to be realizable in terms of optically trapped ultracold Bosonic atoms [3,4]. This model, describing interacting Bosonic particles hopping across the M sites of a discrete structure, is characterized by a Hamiltonian of the forma † m and n m = a † m a m are on-site Bosonic operators, U measures the strength of the (on-site) bosonboson interaction, T is the hopping amplitude across neighboring sites and J is the so-called adjacency matrix, describing the lattice topology. Its generic entry, J mm ′ , equals 1 if the sites m and m ′ are adjacent, and 0 otherwise. Parameters U and T are directly related to well defined experimental quantities, i.e. the scattering length of the Bosonic atoms and the intensity of the laser beams giving rise to the optical lattice, respectively [3]. The possibility of tuning the lattice strength over a wide range of values played a fundamental role in the experimental observation [4] of the superfluid-insulator quantum phase transition predicted for Hamiltonian (1) in the case of repulsive interaction [2]. Further aspects of versatility of optically trapped ultracold atoms lie in the possibil-ity of tuning the atomic scattering length, and hence the boson-boson interaction, via Fe...

The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction. 05.20.Gg, 05.30.Ch PACS numbers