One-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branch

We show the renormalization of contact interaction for odd-wave scattering in one-dimension(1D). Based on the renormalized interaction, we exactly solve the two-body problem in a harmonic trap, and further explore the universal properties of spin-polarized fermions near odd-wave resonance using the operator product expansion method. It is found that the high-momentum distribution behaves as C/k 2 , with C the odd-wave contact. Various universal relations are derived. Our work suggests a new universal system emergent in 1D with large odd-wave scattering length.

Section: Introductionmentioning

confidence: 99%

Universal one-dimensional atomic gases near odd-wave resonance

Cui

2016

“…Remarkably, also in the latter case strong correlations occur (again, consistent with quasi long-range order) for interaction strengths γ ≫ 1, where multiband effects are important. While previous theoretical studies on confined onedimensional fermions addressed the case of (typically small) harmonic traps [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65], in this Rapid Communication we considered a commensurate periodic potential, using sufficiently large system sizes to inspect the thermodynamic limit. On the one hand, this study provides new unbiased predictions for a paradigmatic model of strongly-correlated Fermi systems, which interpolates between Yang theory of the homogeneous Fermi gas and Lieb-Wu theory of the Hubbard model; on the other hand, it serves as a guide for possible new cold-atoms experiments aiming at observing antiferromagnetism beyond the tight-binding regime [30,66].…”

mentioning

confidence: 99%

One-dimensional repulsive Fermi gas in a tunable periodic potential

Pilati

Barbiero²,

Fazio

et al. 2017

By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the TonksGirardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.Making unbiased predictions for the properties of strongly correlated Fermi systems is one of the major challenges in quantum physics research. One dimensional systems play a central role in this context since, on the one hand, correlations effects are more pronounced in low dimensions and, on the other hand, exact results have been derived in a few relevant cases [1]. Two such cases are the homogeneous Fermi gas, whose exact ground-state energy was first determined by Yang [2] via the Bethe Anstatz technique, and the single-band Hubbard model, whose solution was provided by Lieb and Wu [3]. These two paradigmatic models describe two opposite limits of realistic physical systems, which in general are neither perfectly homogeneous nor devoid of interband couplings. In the absence of exact analytical theories for the more realistic intermediate regime, developing unbiased computational techniques is of outmost importance. The experiments performed with ultracold atoms trapped in optical lattices (OLs) have emerged as the ideal playground to investigate quantum many-body phenomena in periodic potentials [4]. The intensity of the external periodic field can be easily varied by tuning a laser power, and also the interaction strength can by tuned exploiting Feshbach resonances [5]. This has recently allowed the remarkable observation of antiferromagnetic correlations in a controlled experimental setup, both in two and in one dimension [6][7][8][9][10][11][12]. The bulk of early research activity on OL systems focussed on deep OLs and weak interactions, where single-band tight-binding models are adequate [13]. Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the in...

“…As a consequence, the first order perturbed state and second order perturbed energy require renormalization [39,58,59]. Note that a similar difficulty would also exist when using perturbation theory to extrapolate from the solutions of H ∞ γ (which is solvable for certain traps shapes) to H τ γ .…”

Section: Split Well Hamiltonianmentioning

confidence: 99%

Infinite barriers and symmetries for a few trapped particles in one dimension

Harshman

2017

This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are dependent on the specific shapes of the traps and the interactions, this article applies symmetry analysis to identify generic features in the spectrum of stationary states of few-particle, few-well systems. Extended attention is given to a simple but flexible threeparameter model of two particles in two wells in one dimension. A key insight is that two limiting cases, hard-core repulsion and no inter-well tunneling, can both be treated as emergent symmetries of the few-particle Hamiltonian. These symmetries are the mathematical consequences of infinite barriers in configuration space. They are necessary to explain the pattern of degeneracies in the energy spectrum, to understand how degeneracies are broken for models away from limiting cases, and to explain separability and integrability. These symmetry methods are extendable to more complicated models and the results have practical consequences for stable state control in fewparticle, few-well systems with ultracold atoms in optical traps.