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arXiv:1606.09528 · The European Physical Journal D

Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

F. F. Bellotti, Amin S. Dehkharghani, Nikolaj Thomas Zinner

Published Feb 1, 2017• 20 citations
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Abstract

We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (density matrix renormalization group (DMRG) and exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.

DOI
10.1140/epjd/e2017-70650-8

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We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (density matrix renormalization group (DMRG) and exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.
We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi and Bose-Fermi mixtures. Energies, density profiles and correlation functions are obtained both numerically (DMRG and Exact diagonalization) and analytically. In order to facilitate a direct comparison with DMRG, we introduce a mapping of the energies calculated from a discrete lattice Hamiltonian to that of a continuous Hamiltonian, and show that our DMRG calculations can match the ground state energy for the two-component fermion systems even in the strongly interacting limit. The same is not true for the other features of the ground state and the DMRG method we employ produces unrealistic results when the interaction strength becomes large. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where the strongly interacting limit is reached numerically in which reasonable agreement between DMRG and analytical results can be obtained. In the case of Bose-Fermi mixtures, we find that the ground state of balanced mixtures of four or six particles tends to separate bosons and fermions, while in imbalanced Bose-Fermi mixtures we find pronounced odd-even effects in systems of four or five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition.
We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [I. Brouzos and P. Schmelcher, Phys. Rev. Lett. 108, 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [G. Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012)].
Abstract In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose–Bose and the Fermi–Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose–Fermi mixtures we find pronounced odd–even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.
A one-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties of a multicomponent repulsive Fermi gas trapped in a harmonic trap by a fixed-node diffusion Monte Carlo method. The interaction between all components is considered to be the same. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expressions are derived in the limit of weak interactions within the local density approximation for an arbitrary number of components and for one plus one particle using an exact solution.
We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.
We investigate the properties of fermions trapped in a one-dimensional (1D) optical lattice by using the density-matrix renormalization (DMRG) group method. Owing to a harmonic confinement potential inherent in real experiments, system becomes inhomogeneous structure. Under certain conditions for weak-repulsive interaction, we find that the single-particle excitation spectrum structure changes to band branching and discrete bound-state states as increasing the trap strength. Additionally, we consider the case of strong-repulsive interacting regimes which local density profile show coexist with central Mott-plateau phase with surrounded by metallic regions. As increasing the trap strength, we find the breakdown of 1D Tomonaga-Luttinger (TL) liquid which is alternative to an effective doping into the Mott phase. We will present the various kinds of striking spectra, show the comparison of repulsive interaction case with attractive interaction one.