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physica status solidi (b)

Feature Article: Understanding strongly correlated many‐body systems with quantum Monte Carlo simulations

C. Lavalle, Marcos Rigol, Alejandro Muramatsu

Published Jul 29, 2005• 0 citations
Publisher

Abstract

Abstract The cover picture of the current issue, taken from the Feature Article [1], depicts the evolution of local density (a) and its quantum fluctuations (b) in trapped fermions on one‐dimensional optical lattices. As the number of fermions in the trap is increased, figure (a) shows the formation of a Mott‐insulating plateau (local density equal to one) whereas the quantum fluctuations – see figure (b) – are strongly suppressed, but nonzero. For a larger number of fermions new insulating plateaus appear (this time with local density equal to two), but no density fluctuations. Regions with non‐constant density are metallic and exhibit large quantum fluctuations of the density. The first author Catia Lavalle is a Postdoc at the University of Stuttgart. She works in the field of strongly correlated quantum systems by means of Quantum Monte Carlo methods (QMC). While working on her PhD thesis at the University of Stuttgart, she developed a new QMC technique that allows to study dynamical properties of the t–J model.

DOI
10.1002/pssb.200590017

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Bulletin of the American Physical Society•Mar 22, 2013•0 citations
Abstract The cover picture of the current issue, taken from the Feature Article [1], depicts the evolution of local density (a) and its quantum fluctuations (b) in trapped fermions on one‐dimensional optical lattices. As the number of fermions in the trap is increased, figure (a) shows the formation of a Mott‐insulating plateau (local density equal to one) whereas the quantum fluctuations – see figure (b) – are strongly suppressed, but nonzero. For a larger number of fermions new insulating plateaus appear (this time with local density equal to two), but no density fluctuations. Regions with non‐constant density are metallic and exhibit large quantum fluctuations of the density. The first author Catia Lavalle is a Postdoc at the University of Stuttgart. She works in the field of strongly correlated quantum systems by means of Quantum Monte Carlo methods (QMC). While working on her PhD thesis at the University of Stuttgart, she developed a new QMC technique that allows to study dynamical properties of the t–J model.
Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulating transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.
The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated quantum systems. Much attention has now turned to mixtures of bosonic and fermionic atoms. A central puzzle is the disagreement between the experimental observation of a reduced bosonic visibility Vb{\mathcal{V}}_{b}Vb​, and quantum Monte Carlo (QMC) calculations which show Vb{\mathcal{V}}_{b}Vb​ increasing. In this paper, we present QMC simulations which evaluate the density profiles and Vb{\mathcal{V}}_{b}Vb​ of mixtures of bosons and fermions in one-dimensional optical lattices. We resolve the discrepancy between theory and experiment by identifying parameter regimes where Vb{\mathcal{V}}_{b}Vb​ is reduced, and where it is increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that Vb{\mathcal{V}}_{b}Vb​ exhibits kinks which are tied to the domain evolution present in the pure case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments.
The Bose-Hubbard model describes the physics of a system of bosonic ultracold atoms in an optical lattice, in which a phase transition is present between a superfluid phase and a Mott insulator one. \nThe exact solution of this Hamiltonian is only feasible to find the ground-state of small systems, while other techniques (as mean-field schemes or quantum Monte Carlo) are necessary to study systems of larger size. \n \nAs a first application, we study the trapped model - relevant for the comparison with current experiments - through an inhomogeneous mean-field scheme. We describe some signatures of the phase crossover between superfluid and Mott insulator. In particular, the visibility of the quasimomentum distribution shows some kinks as a function of the lattice depth; we describe these features and we link them with the ones observed in other works in the literature. \n \nAs a second application, we use quantum Monte Carlo techniques to study the one-dimensional Bose-Hubbard model with long-range interactions and we focus on the appearance of the Haldane insulating phase, distinguishable from the Mott one through the presence of non-local hidden order. \nNon-local correlation functions are also used to describe the difference between the superfluid phase and the Mott insulator one.
We perform large-scale quantum Monte Carlo (QMC) simulations for strongly interacting bosons in a two-dimensional optical lattice trap and confirm an excellent agreement with the benchmarking in situ density measurements by the Chicago group [N. Gemelke et al., Nature (London) 460, 995 (2009)]. We further present a general finite-temperature phase diagram for both the uniform and the trapped systems, demonstrating how the universal scaling properties near the superfluid-to-Mott insulator transition can be observed from the in situ density profile. The characteristic temperature to find such quantum criticality is estimated to be of the order of the single-particle bandwidth, which should be achievable in the present experiments. Finally, we examine the validity regime of the local fluctuation-dissipation theorem, which can be a used as a thermometry in the strongly interacting regime.
Boson-Fermion mixture confined on an optical lattice is numerically studied. Mott-plateau like behavior is observed under certain conditions in the density profile of the bosons and fermions as one sees in bosonic atoms in a trap potential. In the Mott plateau area, the total number of the bosons and fermions at each site is kept to an integer value but both local density of the bosons and that of the fermions take some intermediate values. Unlike bosonic or fermionic Mott insulators, the bosons and fermions can move even in the Mott plateau area by exchanging their positions. With Monte Carlo simulations we demonstrate the formation of the Mott plateau, examine the property of the bosons and fermions by measuring the densities and local density fluctuations, and give discussion on this rather new state.
The ability to cool fermions in optical lattices to ultra cold temperatures has led to an interdisciplinary area of research, that has attracted a lot of attention in recent years. An interesting development in this area is the possibility to realize models for strongly correlated fermions in the laboratory, such as the fermionic Hubbard Model. Determinantal Quantum Monte Carlo simulations have proven to be an important tool in the study of fermionic atoms. Nonetheless, it is important to compare the results and efficiency of different methods. Here comparisons with Numerical Linked Cluster Expansion and Dynamical Mean Field Theory data for double occupation and short range correlations, both relevant to current optical lattice experiments, will be presented and discussed. Another topic relevant in the context of optical lattice experiments is the study of metal insulator transitions. Indeed, the Mott insulating phase has been realized and observed in two-flavor mixtures of fermionic atoms loaded on optical lattices, being characterized both by the double occupation and the compressibility. An interesting point that has been addressed in the literature over the years is whether the same fermion-fermion interaction, responsible for the Mott insulating state, could drive an insulating system metallic. Here we show that, when fermions are loaded in optical lattices with spatially varying interactions a correlation induced Mott insulator to metal transition can take place. The spatial modulation of the interactions was recently demonstrated and opens the possibility for the experimental realization of such exotic phases.