2,249 research outputs found
Universal Properties of Fermi Gases in One-dimension
In this Rapid Communication, we investigate the universal properties of a
spin-polarized two-component Fermi gas in one dimension (1D) using Bethe
ansatz. We discuss the quantum phases and phase transitions by obtaining exact
results for the equation of state, the contact, the magnetic susceptibility and
the contact susceptibility, giving a precise understanding of the 1D analogue
of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in
three dimension (3D) and the associated universal magnetic properties. In
particular, we obtain the exact form of the magnetic susceptibility at low temperatures, where is the
energy gap and is the temperature. Moreover, we establish exact upper and
lower bounds for the relation between polarization and the contact for
both repulsive and attractive Fermi gases. Our findings emphasize the role of
the pair fluctuations in strongly interacting 1D fermion systems that can shed
light on higher dimensions.Comment: 4 figures, the main pape
Dimensionless ratios: characteristics of quantum liquids and their phase transitions
Dimensionless ratios of physical properties can characterize low-temperature
phases in a wide variety of materials. As such, the Wilson ratio (WR), the
Kadowaki-Woods ratio and the Wiedemann\--Franz law capture essential features
of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases
of many-body interacting multi-component quantum liquids in one dimension (1D)
can be described by WRs based on the compressibility, susceptibility and
specific heat associated with each component. These WRs arise due to additivity
rules within subsystems reminiscent of the rules for multi-resistor networks in
series and parallel --- a novel and useful characteristic of multi-component
Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the
systems. Using experimentally realised multi-species cold atomic gases as
examples, we prove that the Wilson ratios uniquely identify phases of TLL,
while providing universal scaling relations at the boundaries between phases.
Their values within a phase are solely determined by the stiffnesses and sound
velocities of subsystems and identify the internal degrees of freedom of said
phase such as its spin-degeneracy. This finding can be directly applied to a
wide range of 1D many-body systems and reveals deep physical insights into
recent experimental measurements of the universal thermodynamics in ultracold
atoms and spins.Comment: 12 pages (main paper), (6 figures
Exact Spectral Function of One-Dimensional Bose Gases
Strong correlation in one-dimensional (1D) quantum systems drastically
changes their dynamic and transport properties in the presence of the
interaction. In this letter, combining quantum integrable theory with numerics,
we exactly compute the spectral function of 1D Lieb-Liniger gas at a many-body
level of large scales. It turns out that a full capture of the power-law
singularities in the vicinities of thresholds requires system size as large as
thousands of particles. Our research essentially confirms the validity of the
nonlinear Tomonaga-Luttinger liquid and provides a reliable technique for
studying critical behaviour emerged only in thermodynamic limit.Comment: 6 pages, 3 figures, Supplementary Materia
Exact results of dynamical structure factor of Lieb-Liniger model
The dynamical structure factor (DSF) represents a measure of dynamical
density-density correlations in a quantum many-body system. Due to the
complexity of many-body correlations and quantum fluctuations in a system of an
infinitely large Hilbert space, such kind of dynamical correlations often
impose a big theoretical challenge. For one dimensional (1D) quantum many-body
systems, qualitative predictions of dynamical response functions are usually
carried out by using the Tomonaga-Luttinger liquid (TLL) theory. In this
scenario, a precise evaluation of the DSF for a 1D quantum system with
arbitrary interaction strength remains a formidable task. In this paper, we use
the form factor approach based on algebraic Bethe ansatz theory to calculate
precisely the DSF of Lieb-Liniger model with an arbitrary interaction strength
at a large scale of particle number. We find that the DSF for a system as large
as 2000 particles enables us to depict precisely its line-shape from which the
power-law singularity with corresponding exponents in the vicinities of
spectral thresholds naturally emerge. It should be noted that, the advantage of
our algorithm promises an access to the threshold behavior of dynamical
correlation functions, further confirming the validity of nonlinear TLL theory
besides Kitanine et. al. 2012 J. Stat. Mech. P09001. Finally we discuss a
comparison of results with the results from the ABACUS method by J.-S. Caux
2009 J. Math. Phys. 50 095214 as well as from the strongly coupling expansion
by Brand and Cherny 2005 Phys. Rev. A 72 033619.Comment: 20 pages, 5 figure
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