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

Angelone, Adriano; Campostrini, Massimo; Vicari, Ettore

doi:10.1103/physreva.89.023635

Cited by 23 publications

(57 citation statements)

References 103 publications

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“…Perhaps the simplest conceivable setting is a system of fermions confined by optical laser traps into a limited region of space [2][3][4][5][6][7][8]. In this experimentally rather common setup, there is a well-known connection between the ground state (T = 0) many-body wavefunction and the statistics of eigenvalues of a certain class of random matrices.…”

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confidence: 99%

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Spectral order statistics of Gaussian random matrices: Large deviations for trapped fermions and associated phase transitions

Castillo

2014

Phys. Rev. E

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We compute the full order statistics of a one-dimensional gas of fermions in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to computing the probability distribution of the kth smallest eigenvalue λ (k) of a large dimensional Gaussian random matrix. We find that this probability behaves for large N as, where β is the Dyson index of the ensemble. The rate function ψ(c, x), computed explicitly as a function of x in terms of the intensive label c = k/N , has a quadratic behavior modulated by a weak logarithmic singularity at its minimum. This is shown to be related to phase transitions in the associated Coulomb gas problem. The connection with statistics of extreme eigenvalues of random matrices is also elucidated.Introduction -Recent spectacular progresses in the fabrication of devices for the manipulation of cold atoms [1,2] have given a formidable impulse towards the theoretical understanding of the behavior of quantum many-body systems using tools and techniques borrowed from classical statistical physics. Perhaps the simplest conceivable setting is a system of fermions confined by optical laser traps into a limited region of space [2][3][4][5][6][7][8]. In this experimentally rather common setup, there is a well-known connection between the ground state (T = 0) many-body wavefunction and the statistics of eigenvalues of a certain class of random matrices. More precisely, in presence of a harmonic potential U (x) =

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“…This tiny separation in the (c, x) plane between the double support phases is ultimately responsible for the weak non-analytic behavior of the rate function close to its minimum in both the c and x directions (see (8)). Once the saddle-point density is known, we precisely find the law (6) …”

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Spectral order statistics of Gaussian random matrices: Large deviations for trapped fermions and associated phase transitions

Castillo

2014

Phys. Rev. E

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“…The properties of a balanced two-component Fermi gas in a harmonic trap were studied by means of the coupled-cluster method [24]. The lattice Hubbard model and its continuum limit for trapped two component gas was studied by the DMRG method [25]. The limit of strong interactions is special and allows different approaches.…”

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One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study

Matveeva¹,

Astrakharchik²

2016

New J. Phys.

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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.fermions with a single atom in each component should have similar energetic properties as a single component Bose gas consisting of N c atoms [15]. Recently a six-component mixture of one-dimensional fermions was realized in LENS group [16]. The measured frequency of the breathing mode approaches that of a Bose system as N c is increased from 1 to 6. It was observed that the momentum distribution increases its width as the number of components is increased, keeping the number of atoms in each spin component fixed.The Bethe ansatz theory is well suited for finding the energetic properties in a homogeneous geometry, predicting the equation of state for the case of N c = 2 components [17,18] and an arbitrary N c [19,20]. Unfortunately the Bethe ansatz method is not applicable in the presence of an external potential. The use of LDA is generally good for energy but misses two-body correlations. Instead, quantum Monte Carlo methods can be efficiently used to tackle the problem. Recently, lattice and path integral Monte Carlo algorithms were successfully used to study the properties of trapped bosons [21], trapped fermions with attraction [22] and fermions in a box with periodic boundary [23]. The properties of a balanced two-component Fermi gas in a harmonic trap were studied by means of the coupled-cluster method [24]. The lattice Hubbard model and its continuum limit for trapped two component gas was studied by the DMRG method [25]. The limit of strong interactions is special and allows different approaches. The three-particle system can be studied analytically in this regime [26]. Multicomponent gases were analyzed in the same regime using a spin-chain model in Ref. [27], resulting in an effective Hamiltonian description for that regime. The spin-chain model permitted the study of the effect of population imbalance on the momentum distribution in a two-component trapped system [28]. For bosonic systems the regime of strong repulsion corresponds to the vicinity of the Tonks-Girardeau limit and the system can be mappe...

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“…where ℓ should be considered as the trap size [7,16]. The potential with power law p = 2 gives rise to harmonic traps, where ω = v is the corresponding frequency.…”

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Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps

Vicari

2019

Phys. Rev. A

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We investigate the particle-number dependence of some features of the out-of-equilibrium dynamics of d-dimensional Fermi gases in the dilute regime. We consider protocols entailing the variation of the external potential which confines the particles within a limited spatial region, in particular sudden changes of the trap size. In order to characterize the dynamic behavior of the Fermi gas, we consider various global quantities such as the ground-state fidelity for different trap sizes, the quantum work statistics associated with the protocol considered, and the Loschmidt echo measuring the overlap of the out-of-equilibrium quantum states with the initial ground state. Their asymptotic particle-number dependences show power laws for noninteracting Fermi gases. We also discuss the effects of short-ranged interactions to the power laws of the average work and its square fluctuations, within the Hubbard model and its continuum limit, arguing that they do not generally change the particle-number power laws of the free Fermi gases, in any spatial dimensions.

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

Cited by 23 publications

References 103 publications

Spectral order statistics of Gaussian random matrices: Large deviations for trapped fermions and associated phase transitions

Spectral order statistics of Gaussian random matrices: Large deviations for trapped fermions and associated phase transitions

One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study

Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps

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