The fully nonlinear dynamics of spin and charge in spin-Calogero model is studied. The latter is an integrable one-dimensional model of quantum spin-1/2 particles interacting through inverse-square interaction and exchange. Classical hydrodynamic equations of motion are written for this model in the regime where gradient corrections to the exact hydrodynamic formulation of the theory may be neglected. In this approximation variables separate in terms of dressed Fermi momenta of the model. Hydrodynamic equations reduce to a set of decoupled Riemann-Hopf (or inviscid Burgers') equations for the dressed Fermi momenta. We study the dynamics of some nonequilibrium spin-charge configurations for times smaller than the time scale of the gradient catastrophe. We find an interesting interplay between spin and charge degrees of freedom. In the limit of large coupling constant the hydrodynamics reduces to the spin hydrodynamics of the Haldane-Shastry model.
The fully nonlinear dynamics of spin and charge in spin-Calogero model is studied. The latter is an integrable one-dimensional model of quantum spin-1/2 particles interacting through inverse-square interaction and exchange. Classical hydrodynamic equations of motion are written for this model in the regime where gradient corrections to the exact hydrodynamic formulation of the theory may be neglected. In this approximation variables separate in terms of dressed Fermi momenta of the model. Hydrodynamic equations reduce to a set of decoupled Riemann-Hopf (or inviscid Burgers') equations for the dressed Fermi momenta. We study the dynamics of some nonequilibrium spin-charge configurations for times smaller than the time scale of the gradient catastrophe. We find an interesting interplay between spin and charge degrees of freedom. In the limit of large coupling constant the hydrodynamics reduces to the spin hydrodynamics of the Haldane-Shastry model.
Recent ground-breaking experiments have realized strongly interacting quantum degenerate Fermi gas in a cold atomic system with tunable interactions. This has provided a table-top system which is extremely hydrodynamic in nature. This experimental realization helps us to investigate several aspects such as the interplay between nonlinearity, dissipation and dispersion. We find, for instance, that the dynamics in such a system shows near perfect agreement with a hydrodynamic theory. In collaboration with the group of John Thomas at Duke we interpreted studies of collision of two strongly interacting Fermi gases that led to shock waves which are a hallmark of nonlinear physics. Due to reasons such as the nature of interactions, higher dimensionality, these cold atomic systems are non-integrable and moreover the underlying field theory construction is mostly phenomenological in nature. On the other hand there are certain one-dimensional systems which are not only integrable but also facilitate more formal and rigorous ways of deriving the corresponding integrable field theories. One such family of models is the family of Calogero models (and their generalizations). They provide an extraordinary insight into the field of strongly correlated systems and hydrodynamics. We study the collective field theory of such models and address aspects of nonlinear physics such as Spin-Charge Interaction, Emptiness Formation Probability, Solitons etc; We derive a two-component nonlinear, nonlocal, integrable field theory. We also show that the Calogero family which is integrable even in an external harmonic trap (usually unavoidable in cold atom setups) is relatively short ranged thereby qualifying as a toy model for cold atom experiments. Transport in certain strongly correlated systems (impurity models) was studied using few low-dimensional techniques such as a 1/N diagrammatic expansion, Slave Boson Mean Field Theory and the Bethe Ansatz. A mesoscopic setup such as parallel quantum dots forms an ideal platform for such an investigation and comparison between different low-dimensional techniques. We studied transport, correlations and nature of the ground state of double quantum dots. We probed several non-perturbative aspects of this double-impurity model. For example, we showed that the RKKY interaction in closely spaced dots can be non-ferromagnetic due to its non-pertubative nature. This study helped us to point some discrepancies between different methods (such as the Numerical Renormalization Group). We give possible reasons for these discrepancies.
Quantum liquids in two dimensions represent interesting dynamical quantum systems for several reasons, among them the possibility of the existence of infinite hidden symmetries, such as conformal symmetry or the symmetry associated with area preserving diffeomorphisms. It is known that when the symmetry algebra is large enough, symmetry may fully prescribe the dynamics. However, the way this is borne out in two-dimensional hydrodynamics, both classical and quantum, is not fully understood. Here we take a step towards clarifying this issue, by focusing on a particular example, namely that of a two-dimensional phase space liquid which emerges when one considers the Calogero model, a many-body one-dimensional system interacting through an inverse square law potential. We demonstrate how the symmetry algebra of conserved quantities of the one-dimensional system is expressed in terms of the incompressible Euler hydrodynamics of point vortices in phase space. Due to a formal relation between quantum hydrodynamics and classical stochastic hydrodynamics, which is inherent in the method of stochastic quantization, the ideas and methods developed here may also have application in the study of stochastic classical hydrodynamics, after suitable modifications.
We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings in the time domain by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provide an exact description, at large space-time scales, for arbitrary temperature T, particle density, and interactions. At T=0 and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low T>0 effects of SCS survive and characterize explicitly the value of T for which the two distinguishable excitations melt.
We consider the known effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles, obtained from the standard procedure in conformal field theory: the Hilbert space is constructed a priori in terms of irreducible representations of the symmetry algebra, and not by diagonalization of the hamiltonian, which is given in terms of fields that carry representations of the W 1 + ∞ algebra (representing the incompressibility of the Fermi sea). Nevertheless, the role of the effective hamiltonian of the theory is to establish a specific dynamics, which deserves further consideration. We show that the time evolution of the (chiral or antichiral) density field is given by the quantum Benjamin-Ono equation, in agreement with previous results obtained from the alternative description of the continuous limit of the model, based on quantum hydrodynamics. In this study, all calculations are performed at the quantum operator level, without making any assumption on the semiclassical limit of the fields and their equations of motion. This result may be considered as a reliable indication of the equivalence between the quantum field theoretic and quantum hydrodynamical formulations of the effective theories of the model. A one-dimensional quantum compressible fluid that includes both chiralities is the physical picture that emerges for the continuous limit of the Calogero-Sutherland model. • The chiral density field of the Calogero-Sutherland EFT satisfies a quantum Benjamin-Ono equation. • Agrees with quantum hydrodynamics results by Abanov and Wiegmann, extending their validity to quantum fields themselves. • Findings could be of interest to the QFT community, with new tools to deal with time non-locality within the realm of CFT. • Equivalence between the EFT and the hydrodynamic formulations of the thermodynamic limit of the Calogero-Sutherland model is supported.
Quasi-particle picture in a magnetic field is pursued for dynamical spin and charge correlation functions of the one-dimensional supersymmetric t-J model with inverse-square interaction. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of relevant excited states are identified which are valid in the thermodynamic limit. The excitation contents are composed of spinons, antispinons, holons and antiholons obeying fractional statistics. Both longitudinal and transverse components of the dynamical spin structure factor are independent of the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. The dynamical charge structure factor does not depend on the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. These features indicate the strong spin-charge separation in dynamics, reflecting the high symmetry of the model.