Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuench Dynamics of the Gaudin-Yang Model
168
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the quench dynamics of one dimensional bosons or fermion quantum gases with either attractive or repulsive contact interactions. Such systems are well described by the Gaudin-Yang model which turns out to be quantum integrable. We use a contour integral approach, the Yudson approach, to expand initial states in terms of Bethe Ansatz eigenstates of the Hamiltonian. Making use of the contour, we obtain a complete set of eigenstates, including both free states and bound states. These states constitute a larger Hilbert space than described by the standard String hypothesis. We calculate the density and noise correlations of several quenched systems such as a static or kinetic impurity evolving in an array of particles.
rate research
Read More
The dynamic spin structure factor $mathcal{S}(k,omega)$ of a system of spin-1/2 bosons is investigated at arbitrary strength of interparticle repulsion. As a function of $omega$ it is shown to exhibit a power-law singularity at the threshold frequency defined by the energy of a magnon at given $k.$ The power-law exponent is found exactly using a combination of the Bethe Ansatz solution and an effective field theory approach.
We study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang-Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at $2k_F$ and a finite-momentum roton minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as $1/L$ for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the $2k_F$ gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang-Gaudin Bose gas is also host to multi-spinon bound states, known as $Lambda$-strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length $n$ $Lambda$-string dressed energies $epsilon_n(lambda)$ and the dressed energy $epsilon(k)$. We solve the Yang-Yang-Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length $n$ $Lambda$-string dressed energy is Lorentzian over a wide range of real string centers $lambda$ in the vicinity of $lambda = 0$. We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.
Using the Bethe ansatz solution, we analytically study expansionary, magnetic and interacting Gruneisen parameters (GPs) for one-dimensional (1D) Lieb-Liniger and Yang-Gaudin models. These different GPs elegantly quantify the dependences of characteristic energy scales of these quantum gases on the volume, the magnetic field and the interaction strength, revealing the caloric effects resulted from the variations of these potentials. The obtained GPs further confirm an identity which is incurred by the symmetry of the thermal potential. We also present universal scaling behavior of these GPs in the vicinities of the quantum critical points driven by different potentials. The divergence of the GPs not only provides an experimental identification of non-Fermi liquid nature at quantum criticality but also elegantly determine low temperature phases of the quantum gases. Moreover, the pairing and depairing features in the 1D attractive Fermi gases can be captured by the magnetic and interacting GPs, facilitating experimental observation of quantum phase transitions. Our results open to further study the interaction- and magnetic-field-driven quantum refrigeration and quantum heat engine in quantum gases of ultracold atoms.
Pseudogap is a ubiquitous phenomenon in strongly correlated systems such as high-$T_{rm c}$ superconductors, ultracold atoms and nuclear physics. While pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental 1D models, that is, Gaudin-Yang model. In this work, we show that the pseudogap effect can be visible in the single-particle excitation in this system using a diagrammatic approach. Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to pseudogap state with increasing the attractive interaction and the number density at finite temperature. Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, even in the region where the pseudogap appears.
Hopf insulators are exotic topological states of matter outside the standard ten-fold way classification based on discrete symmetries. Its topology is captured by an integer invariant that describes the linking structures of the Hamiltonian in the three-dimensional momentum space. In this paper, we investigate the quantum dynamics of Hopf insulators across a sudden quench and show that the quench dynamics is characterized by a $mathbb{Z}_2$ invariant $ u$ which reveals a rich interplay between quantum quench and static band topology. We construct the $mathbb{Z}_2$ topological invariant using the loop unitary operator, and prove that $ u$ relates the pre- and post-quench Hopf invariants through $ u=(mathcal{L}-mathcal{L}_0)bmod 2$. The $mathbb{Z}_2$ nature of the dynamical invariant is in sharp contrast to the $mathbb{Z}$ invariant for the quench dynamics of Chern insulators in two dimensions. The non-trivial dynamical topology is further attributed to the emergence of $pi$-defects in the phase band of the loop unitary. These $pi$-defects are generally closed curves in the momentum-time space, for example, as nodal rings carrying Hopf charge.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
