Boson core compressibility

Khorramzadeh, Yasamin; Lin, Feng; Scarola, V. W.

doi:10.1103/physreva.85.043610

Cited by 7 publications

(3 citation statements)

References 51 publications

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“…As our first example, we consider a 2-site Bose-Fermi-Hubbard model with varying U b = C, t b = t f = 0.01, and n b = n f ↑ = 1. We find that our results for the potential energies, kinetic energies, condensate fractions, and double occupancies per site [71] agree with ED to within small error bars for U b /t = C/t values up to 13. U b /t = C/t ratios up to 7 are shown in Fig.…”

Section: B Spin-polarized Bose-fermi-hubbard Modelsupporting

confidence: 74%

Finite-temperature auxiliary-field quantum Monte Carlo technique for Bose-Fermi mixtures

2012

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We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi Auxiliary-Field Quantum Monte Carlo (BF-AFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in BF-AFQMC. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand BF-AFQMC's reach. The new algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems.

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Section: B Spin-polarized Bose-fermi-hubbard Modelsupporting

confidence: 74%

Finite-temperature auxiliary-field quantum Monte Carlo technique for Bose-Fermi mixtures

2012

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“…The above edge scaling behaviors are expected to be universal apart from a multiplicative constant and normalizations of the arguments of the scaling functions. They are universal with respect to changes of the chemical potential µ, thus υ, and microscopic short-ranged interactions, for example adding the nearest-neighbor interaction (52), essentially because they are controlled by the dilute fixed point of the field theory (16) in the presence of an external linear field.…”

Section: Interactionsmentioning

confidence: 99%

Universal quantum behavior of interacting fermions in one-dimensional traps: From few particles to the trap thermodynamic limit

2014

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We investigate the ground-state properties of trapped fermion systems described by the Hubbard model with an external confining potential. We discuss the universal behaviors of systems in different regimes: from few particles, i.e. in dilute regime, to the trap thermodynamic limit.The asymptotic trap-size (TS) dependence in the dilute regime (increasing the trap size ℓ keeping the particle number N fixed) is described by a universal TS scaling controlled by the dilute fixed point associated with the metal-to-vacuum quantum transition. This scaling behavior is numerically checked by DMRG simulations of the one-dimensional (1D) Hubbard model. In particular, the particle density and its correlations show crossovers among different regimes: for strongly repulsive interactions they approach those of a spinless Fermi gas, for weak interactions those of a free Fermi gas, and for strongly attractive interactions they match those of a gas of hard-core bosonic molecules.The large-N limit keeping the ratio N/ℓ fixed corresponds to a 1D trap thermodynamic limit. We address issues related to the accuracy of the local density approximation (LDA). We show that the particle density approaches its LDA in the large-ℓ limit. When the trapped system is in the metallic phase, corrections at finite ℓ are O(ℓ −1 ) and oscillating around the center of the trap. They become significantly larger at the boundary of the fermion cloud, where they get suppressed as O(ℓ −1/3 ) only. This anomalous behavior arises from the nontrivial scaling at the metal-to-vacuum transition occurring at the boundaries of the fermion cloud.

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“…Since the Gutzwiller approach maps the 2D Bose-Hubbard model to a string of coefficients the input data is one dimensional and therefore the convolutional neural network is also one dimensional. An arbitrary line of the phase diagram at a fixed z J/U = 0.005 is labelled for all the values of µ with the help of the compressibility κ = ∂ n i /∂µ [45]. Here, z = 4 is the number of nearest neighbours of each site, which is two for the one dimensional case.…”

Section: B Bose-hubbard Modelmentioning

confidence: 99%

Identifying quantum phase transitions with adversarial neural networks

2018

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The identification of phases of matter is a challenging task, especially in quantum mechanics, where the complexity of the ground state appears to grow exponentially with the size of the system. Traditionally, physicists have to identify the relevant order parameters for the classification of the different phases. We here follow a radically different approach: we address this problem with a state-of-the-art deep learning technique, adversarial domain adaptation. We derive the phase diagram of the whole parameter space starting from a fixed and known subspace using unsupervised learning. This method has the advantage that the input of the algorithm can be directly the ground state without any ad-hoc feature engineering. Furthermore, the dimension of the parameter space is unrestricted. More specifically, the input data set contains both labelled and unlabelled data instances. The first kind is a system that admits an accurate analytical or numerical solution, and one can recover its phase diagram. The second type is the physical system with an unknown phase diagram. Adversarial domain adaptation uses both types of data to create invariant feature extracting layers in a deep learning architecture. Once these layers are trained, we can attach an unsupervised learner to the network to find phase transitions. We show the success of this technique by applying it on several paradigmatic models: the Ising model with different temperatures, the Bose-Hubbard model, and the Su-Schrieffer-Heeger model with disorder. The method finds unknown transitions successfully and predicts transition points in close agreement with standard methods. This study opens the door to the classification of physical systems where the phases boundaries are complex such as the many-body localization problem or the Bose glass phase.

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Boson core compressibility

Cited by 7 publications

References 51 publications

Finite-temperature auxiliary-field quantum Monte Carlo technique for Bose-Fermi mixtures

Finite-temperature auxiliary-field quantum Monte Carlo technique for Bose-Fermi mixtures

Universal quantum behavior of interacting fermions in one-dimensional traps: From few particles to the trap thermodynamic limit

Identifying quantum phase transitions with adversarial neural networks

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