819 research outputs found

### Phase separation in a polarized Fermi gas at zero temperature

We investigate the phase diagram of asymmetric two-component Fermi gases at
zero temperature as a function of polarization and interaction strength. The
equations of state of the uniform superfluid and normal phase are determined
using quantum Monte Carlo simulations. We find three different mixed states,
where the superfluid and the normal phase coexist in equilibrium, corresponding
to phase separation between: (a) the polarized superfluid and the fully
polarized normal gas, (b) the polarized superfluid and the partially polarized
normal gas and (c) the unpolarized superfluid and the partially polarized
normal gas.Comment: 4 pages, 4 figures, revised, accepted for publication in Phys. Rev.
Let

### Ferromagnetism of a Repulsive Atomic Fermi Gas in an Optical Lattice: a Quantum Monte Carlo Study

Using continuous-space quantum Monte Carlo methods we investigate the
zero-temperature ferromagnetic behavior of a two-component repulsive Fermi gas
under the influence of periodic potentials that describe the effect of a
simple-cubic optical lattice. Simulations are performed with balanced and with
imbalanced components, including the case of a single impurity immersed in a
polarized Fermi sea (repulsive polaron). For an intermediate density below half
filling, we locate the transitions between the paramagnetic, and the partially
and the fully ferromagnetic phases. As the intensity of the optical lattice
increases, the ferromagnetic instability takes place at weaker interactions,
indicating a possible route to observe ferromagnetism in experiments performed
with ultracold atoms. We compare our findings with previous predictions based
on the standard computational method used in material science, namely density
functional theory, and with results based on tight-binding models.Comment: Published version with Supplemental Material. Added comparison with
Hubbard model result

### Quantum Monte Carlo simulation of a two-dimensional Bose gas

The equation of state of a homogeneous two-dimensional Bose gas is calculated
using quantum Monte Carlo methods. The low-density universal behavior is
investigated using different interatomic model potentials, both finite-ranged
and strictly repulsive and zero-ranged supporting a bound state. The condensate
fraction and the pair distribution function are calculated as a function of the
gas parameter, ranging from the dilute to the strongly correlated regime. In
the case of the zero-range pseudopotential we discuss the stability of the
gas-like state for large values of the two-dimensional scattering length, and
we calculate the critical density where the system becomes unstable against
cluster formation.Comment: 6 pages, 5 figures, 1 tabl

### Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks

The autoregressive neural networks are emerging as a powerful computational
tool to solve relevant problems in classical and quantum mechanics. One of
their appealing functionalities is that, after they have learned a probability
distribution from a dataset, they allow exact and efficient sampling of typical
system configurations. Here we employ a neural autoregressive distribution
estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a
paradigmatic classical model of spin-glass theory, namely the two-dimensional
Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately
mimic the Boltzmann distribution using unsupervised learning from system
configurations generated using standard MCMC algorithms. The trained NADE is
then employed as smart proposal distribution for the Metropolis-Hastings
algorithm. This allows us to perform efficient MCMC simulations, which provide
unbiased results even if the expectation value corresponding to the probability
distribution learned by the NADE is not exact. Notably, we implement a
sequential tempering procedure, whereby a NADE trained at a higher temperature
is iteratively employed as proposal distribution in a MCMC simulation run at a
slightly lower temperature. This allows one to efficiently simulate the
spin-glass model even in the low-temperature regime, avoiding the divergent
correlation times that plague MCMC simulations driven by local-update
algorithms. Furthermore, we show that the NADE-driven simulations quickly
sample ground-state configurations, paving the way to their future utilization
to tackle binary optimization problems.Comment: 13 pages, 14 figure

### Simulating disordered quantum systems via dense and sparse restricted Boltzmann machines

In recent years, generative artificial neural networks based on restricted
Boltzmann machines (RBMs) have been successfully employed as accurate and
flexible variational wave functions for clean quantum many-body systems. In
this article we explore their use in simulations of disordered quantum spin
models. The standard dense RBM with all-to-all inter-layer connectivity is not
particularly appropriate for large disordered systems, since in such systems
one cannot exploit translational invariance to reduce the amount of parameters
to be optimized. To circumvent this problem, we implement sparse RBMs, whereby
the visible spins are connected only to a subset of local hidden neurons, thus
reducing the amount of parameters. We assess the performance of sparse RBMs as
a function of the range of the allowed connections, and compare it with the one
of dense RBMs. Benchmark results are provided for two sign-problem free
Hamiltonians, namely pure and random quantum Ising chains. The RBM ansatzes are
trained using the unsupervised learning scheme based on projective quantum
Monte Carlo (PQMC) algorithms. We find that the sparse connectivity facilitates
the training process and allows sparse RBMs to outperform the dense
counterparts. Furthermore, the use of sparse RBMs as guiding functions for PQMC
simulations allows us to perform PQMC simulations at a reduced computational
cost, avoiding possible biases due to finite random-walker populations. We
obtain unbiased predictions for the ground-state energies and the magnetization
profiles with fixed boundary conditions, at the ferromagnetic quantum critical
point. The magnetization profiles agree with the Fisher-de Gennes scaling
relation for conformally invariant systems, including the scaling dimension
predicted by the renormalization-group analysis.Comment: 11 pages, 5 figure

### Path-integral Monte Carlo worm algorithm for Bose systems with periodic boundary conditions

We provide a detailed description of the path-integral Monte Carlo worm
algorithm used to exactly calculate the thermodynamics of Bose systems in the
canonical ensemble. The algorithm is fully consistent with periodic boundary
conditions, that are applied to simulate homogeneous phases of bulk systems,
and it does not require any limitation in the length of the Monte Carlo moves
realizing the sampling of the probability distribution function in the space of
path configurations. The result is achieved adopting a representation of the
path coordinates where only the initial point of each path is inside the
simulation box, the remaining ones being free to span the entire space.
Detailed balance can thereby be ensured for any update of the path
configurations without the ambiguity of the selection of the periodic image of
the particles involved. We benchmark the algorithm using the non-interacting
Bose gas model for which exact results for the partition function at finite
number of particles can be derived. Convergence issues and the approach to the
thermodynamic limit are also addressed for interacting systems of hard spheres
in the regime of high density.Comment: v1: 18 pages, 6 figures. v2: Fixed typo in eq.(30) and (31), minor
changes, matches published versio

### Superfluid transition in a Bose gas with correlated disorder

The superfluid transition of a three-dimensional gas of hard-sphere bosons in
a disordered medium is studied using quantum Monte Carlo methods. Simulations
are performed in continuous space both in the canonical and in the
grand-canonical ensemble. At fixed density we calculate the shift of the
transition temperature as a function of the disorder strength, while at fixed
temperature we determine both the critical chemical potential and the critical
density separating normal and superfluid phases. In the regime of strong
disorder the normal phase extends up to large values of the degeneracy
parameter and the critical chemical potential exhibits a linear dependence in
the intensity of the random potential. The role of interactions and disorder
correlations is also discussed.Comment: 4 pages, 4 figure

### Quantum Monte Carlo simulations of two-dimensional repulsive Fermi gases with population imbalance

The ground-state properties of two-component repulsive Fermi gases in two
dimensions are investigated by means of fixed-node diffusion Monte Carlo
simulations. The energy per particle is determined as a function of the
intercomponent interaction strength and of the population imbalance. The regime
of universality in terms of the s-wave scattering length is identified by
comparing results for hard-disk and for soft-disk potentials. In the large
imbalance regime, the equation of state turns out to be well described by a
Landau-Pomeranchuk functional for two-dimensional polarons. To fully
characterize this expansion, we determine the polarons' effective mass and
their coupling parameter, complementing previous studies on their chemical
potential. Furthermore, we extract the magnetic susceptibility from
low-imbalance data, finding only small deviations from the mean-field
prediction. While the mean-field theory predicts a direct transition from a
paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results
suggest that the partially ferromagnetic phase is stable in a narrow interval
of the interaction parameter. This finding calls for further analyses on the
effects due to the fixed-node constraint.Comment: 10 pages, 5 figure

### Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials

The one-body density matrix of weakly interacting, condensed bosons in
external potentials is calculated using inhomogeneous Bogoliubov theory. We
determine the condensate deformation caused by weak external potentials on the
mean-field level. The momentum distribution of quantum fluctuations around the
deformed ground state is obtained analytically, and finally the resulting
quantum depletion is calculated. The depletion due to the external potential,
or potential depletion for short, is a small correction to the homogeneous
depletion, validating our inhomogeneous Bogoliubov theory. Analytical results
are derived for weak lattices and spatially correlated random potentials, with
simple, universal results in the Thomas-Fermi limit of very smooth potentials.Comment: 17 pages, 4 figures. v2: published version, minor change

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