Unified description of pairing, trionic and quarteting states for one-dimensional SU(4) attractive fermions

Paired states, trions and quarteting states in one-dimensional SU(4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground state energy, chemical potentials and complete phase diagrams for isospin $S=1/2, 1, 3/2$ attractive fermions with external fields are presented. Also identified are the magnetization plateaux of $m^z=M_s/3$ and $m^z=2M_s/3$, where $M_s$ is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low energy effective field theory.Comment: 13 pages, 4 figure

Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Magnetic Phase Transitions in One-dimensional Strongly Attractive Three-Component Ultracold Fermions

We investigate the nature of trions, pairing and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the groundstate energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.Comment: 4 pages, 3 figures, minor revisions to text, replacement figure, refs added and update

Shallow soil moisture – ground thaw interactions and controls – Part 2: Influences of water and energy fluxes

The companion paper (Guan et al., 2010) demonstrated variable interactions and correlations between shallow soil moisture and ground thaw in soil filled areas along a wetness spectrum in a subarctic Canadian Precambrian Shield landscape. From wetter to drier, these included a wetland, peatland and soil filled valley. Herein, water and energy fluxes were examined for these same subarctic study sites to discern the key controlling processes on the found patterns. Results showed the presence of surface water was the key control in variable soil moisture and frost table interactions among sites. At the peatland and wetland sites, accumulated water in depressions and flow paths maintained soil moisture for a longer duration than at the hummock tops. These wet areas were often locations of deepest thaw depth due to the transfer of latent heat accompanying lateral surface runoff. Although the peatland and wetland sites had large inundation extent, modified Péclet numbers indicated the relative influence of external and internal hydrological and energy processes at each site were different. Continuous inflow from an upstream lake into the wetland site caused advective and conductive thermal energies to be of equal importance to ground thaw. The absence of continuous surface flow at the peatland and valley sites led to dominance of conductive thermal energy over advective energy for ground thaw. The results suggest that the modified Péclet number could be a very useful parameter to differentiate landscape components in modeling frost table heterogeneity. The calculated water and energy fluxes, and the modified Péclet number provide quantitative explanations for the shallow soil moisture-ground thaw patterns by linking them with hydrological processes and hillslope storage capacity

Shallow soil moisture – ground thaw interactions and controls – Part 1: Spatiotemporal patterns and correlations over a subarctic landscape

Soil moisture and ground thaw state are both indicative of a hillslope's ability to transfer water. In cold regions, in particular, it is widely known that the depth of the active layer and wetness of surface soils are important for runoff generation, but the diversity of interactions between ground thaw and surface soil moisture themselves has not been studied. To fill this knowledge gap, detailed shallow soil moisture and thaw depth surveys were conducted along systematic grids at the Baker Creek Basin, Northwest Territories. Multiple hillslopes were studied to determine how the interactions differed along a spectrum of topological, typological and topographic situations across the landscape. Overall results did not show a simple link between soil moisture and ground thaw as was expected. Instead, correlation was a function of wetness. The interaction between soil moisture and ground thaw was more dependent at wetter sites. This indicates that interactive soil moisture and thaw depth behaviour on hillslopes in cold regions changes with location and cannot necessarily be lumped together in hydrological models. To explore further why these differences arise, a companion paper (Guan et al., 2010) will examine how the hydrological and energy fluxes influenced the patterns of moisture and thaw among the study sites

Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

Universality class of quantum criticality for strongly repulsive spin-1 bosons with antiferromagnetic spin-exchange interaction

Using the thermodynamic Bethe ansatz equations we study the quantum phase diagram, thermodynamics and criticality of one-dimensional spin-1 bosons with strongly repulsive density-density and antiferromagnetic spin-exchange interactions. We analytically derive a high precision equation of state from which the Tomonaga-Luttinger liquid physics and quantum critical behavior of the system are computed. We obtain explicit forms for the scaling functions near the critical points yielding the dynamical exponent $z=2$ and correlation length exponent $\nu=1/2$ for the quantum phase transitions driven by either the chemical potential or the magnetic field. Consequently, we further demonstrate that quantum criticality of the system can be mapped out from the finite temperature density and magnetization profiles of the 1D trapped gas. Our results provide the physical origin of quantum criticality in a 1D many-body system beyond the Tomonaga-Luttinger liquid description.Comment: 12 pages, 11 figure