Variational cluster perturbation theory for Bose–Hubbard models

Koller, Winfried; Dupuis, N.

doi:10.1088/0953-8984/18/41/019

Cited by 40 publications

(80 citation statements)

References 43 publications

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“…Menotti and Trivedi 23 argued that the appearance of gapped modes and the redistribution of spectral weight from coherent phonon modes to incoherent gapped modes indicate the strongly correlated nature of the SF state near the transition. Let us point out that particle and hole dispersions in the MI have been calculated by several authors before, 12,13,17,18,19,22,23,63,64,65 whereas the full spectral function of the MI (which also reveals the spectral weight and the width of the excitations) was only shown in [18,23].…”

Section: Single-particle Spectrummentioning

confidence: 96%

“…However, the dynamical properties and excitations in particular of the SF phase in the vicinity of the quantum phase transition, are still not completely understood. A number of authors have addressed the dynamics of the Bose-Hubbard model in different dimensions, 12,13,14,15,16,17,18,19,20,21,22,23 with results providing valuable information about the underlying physics, while corresponding work on coupled cavity models has just begun. 24,25 The two most important dynamic observables are the dynamic structure factor and the single-particle spectral function, which are also at the heart of theoretical and experimental works on Bose fluids.…”

Section: Introductionmentioning

confidence: 99%

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Excitation spectra of strongly correlated lattice bosons and polaritons

2009

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Spectral properties of the Bose-Hubbard model and a recently proposed coupled-cavity model are studied by means of quantum Monte Carlo simulations in one dimension. Both models exhibit a quantum phase transition from a Mott insulator to a superfluid phase. The dynamic structure factor S(k, ω) and the single-particle spectrum A(k, ω) are calculated, focusing on the parameter region around the phase transition from the Mott insulator with density one to the superfluid phase, where correlations are important. The strongly interacting nature of the superfluid phase manifests itself in terms of additional gapped modes in the spectra. Comparison is made to recent analytical work on the Bose-Hubbard model. Despite some subtle differences due to the polaritonic particles in the cavity model, the gross features are found to be very similar to the Bose-Hubbard case. For the polariton model, emergent particle-hole symmetry near the Mott lobe tip is demonstrated, and temperature and detuning effects are analyzed. A scaling analysis for the generic transition suggests mean field exponents, in accordance with field theory results.

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Section: Single-particle Spectrummentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Excitation spectra of strongly correlated lattice bosons and polaritons

2009

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“…In particular, quantum fluctuations on a finite length scale are included. We discuss Mott lobes (also at experimentally relevant finite temperatures), the effect of detuning and for the first time in such systems calculate single-particle spectra, a necessary connection to experiment and also a key metric in early proof of concept calculations of CAOL systems.The Variational Cluster Approach (VCA)-introduced first for strongly correlated electrons [13]-has previously been applied to the BHM [14]. The main idea is to approximate the self-energy Σ of the infinite system by that of a finite reference system.…”

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confidence: 99%

“…The stationary solution is given by ∂Ω/∂ξ c = 0. Traces can be evaluated exactly using only the poles of the Green's function but not their weights [13,14]. The poles ω m of G 0 −1 − Σ are obtained from a bosonic formulation of the Q-matrix method [15].…”

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confidence: 99%

Quantum Fluctuations, Temperature, and Detuning Effects in Solid-Light Systems

et al. 2008

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The superfluid to Mott insulator transition in cavity polariton arrays is analyzed using the variational cluster approach, taking into account quantum fluctuations exactly on finite length scales. Phase diagrams in one and two dimensions exhibit important non-mean-field features. Single-particle excitation spectra in the Mott phase are dominated by particle and hole bands separated by a Mott gap. In contrast to Bose-Hubbard models, detuning allows for changing the nature of the bosonic particles from quasilocalized excitons to polaritons to weakly interacting photons. The Mott state with density one exists up to temperatures T /g 0.03, implying experimentally accessible temperatures for realistic cavity couplings g. PACS numbers: 71.36.+c, 73.43.Nq, 78.20.Bh, 42.50.Ct The prospect of realizing a tunable, strongly correlated system of photons is exciting, both as a testbed for quantum many-body dynamics and for the potential of quantum simulators and other advanced quantum devices. Three proposals based on cavity-QED arrays have recently shown how this might be accomplished [1,2,3], followed by further work [4,5,6,7,8]. Engineered strong photon-photon interactions and hopping between cavities allow photons (as a component of cavity polaritons) to behave much like electrons or atoms in a many-body context. It is clear that a particular signature of quantum many-body physics, the superfluid (SF) to Mott insulator (MI) transition, should be reproducible in such systems and be similar to the widely studied Bose-Hubbard model (BHM). Yet, the BH analogy is not complete. The mixed matter-light nature of the system brings new physics yet to be fully explored."Solid-light" systems-so-named for the intriguing MI state of photons they exhibit-are reminiscent of cold atom optical lattices (CAOL) [9], but have some advantages concerning direct addressing of individual sites and device integration, and the potential for asymmetry construction by individual tuning, local variation, and far from equilibrium devices [4]. Photons as part of the system serve as excellent experimental probes, and have excellent "flying" potential so that they can be transported over long distances. Temporal and spatial correlation functions are accessible, and nonequilibrium quantum dynamics may be studied using coherent laser pumping to create initial states. Here ω 0 is the cavity photon energy, and ∆ = ω 0 − ǫ defines the detuning. Each cavity is described by the well-known Jaynes-Cummings (JC) HamiltonianĤ JC . The atom-photon coupling g (a † i , a i are photon creation and annihilation operators) gives rise to formation of polaritons (combined atomphoton excitations) whose numberN p = i (a † i a i +|↑ i ↑ i |) is conserved and couples to the chemical potential µ [7]. We consider nearest-neighbor photon hopping with amplitude t, define the polariton density n = N p /L, use g as the unit of energy and set ω 0 /g [23], k B and the lattice constant to one.Hamiltonian (1) represents a generic model of strongly correlated photons amenable to numer...

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“…We employ the variational cluster approach [24,25] (VCA) as a numerical tool to study the quantum phase transition, spectral properties and polariton quasiparticles of the two-dimensional JCL model. In particular, VCA provides the single-particle Green's function G(k, ω) of the physical systemĤ JCL and is based on the self-energy functional approach [26,27] and the cluster perturbation theory [28,29].…”

Section: Variational Cluster Approachmentioning

confidence: 99%

Polaritonic properties of the Jaynes–Cummings lattice model in two dimensions

Knap¹,

Arrigoni²,

Linden³

2011

Computer Physics Communications

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Light-matter systems allow to realize a strongly correlated phase where photons are present. In these systems strong correlations are achieved by optical nonlinearities, which appear due to the coupling of photons to atomic-like structures. This leads to intriguing effects, such as the quantum phase transition from the Mott to the superfluid phase. Here, we address the two-dimensional Jaynes-Cummings lattice model. We evaluate the boundary of the quantum phase transition and study polaritonic properties. In order to be able to characterize polaritons, we investigate the spectral properties of both photons as well as two-level excitations. Based on this information we introduce polariton quasiparticles as appropriate wavevector, band index, and filling dependent superpositions of photons and two-level excitations. Finally, we analyze the contributions of the individual constituents to the polariton quasiparticles.

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Variational cluster perturbation theory for Bose–Hubbard models

Cited by 40 publications

References 43 publications

Excitation spectra of strongly correlated lattice bosons and polaritons

Excitation spectra of strongly correlated lattice bosons and polaritons

Quantum Fluctuations, Temperature, and Detuning Effects in Solid-Light Systems

Polaritonic properties of the Jaynes–Cummings lattice model in two dimensions

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