Solution of Some Integrable One-Dimensional Quantum Systems

In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential. We show these systems to be integrable, and exploit this integrability to completely determine the spectrum including degeneracy, and thus the thermodynamics. The periodic inverse square case is worked out explicitly. Next, we show that in the limit of strong interaction the "spin" degrees of freedom decouple. Taking this limit for our example, we obtain a complete solution to a lattice system introduced recently by Shastry, and Haldane; our solution reproduces the numerical results. Finally, we emphasize the simple explanation for the high multiplicities found in this model

Extracting Hidden Symmetry from the Energy Spectrum

In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal vapors. We consider this spin Hamiltonian in detail and use this example to outline a general approach to finding symmetries when eigenvalues and eigenstates of the Hamiltonian are known. We extract all nontrivial symmetries responsible for the degeneracy and show that the symmetry group of the Hamiltonian is SU(2). The symmetry operators have a simple meaning which becomes transparent in the limit of large spin. As an additional example we apply the method to the Hydrogen atom.Comment: 14 pages, 1 figure. A minor typo correcte

Extremely Correlated Fermi Liquids

We present the theory of an extremely correlated Fermi liquid (ECFL) with $U\to \infty$. This liquid has an underlying Fermi liquid (FL) Greens function that is further caparisoned. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct $T$ dependent left skew. An important energy scale $\Delta(\vec{k},x)$ emerges as the average inelasticity of the FL Greens function, and influences the photoemission spectra profoundly. A duality is identified wherein an apparent loss of coherence of the ECFL results from an excessively sharp FL.Comment: Published version, 3 figures; Published July 29, 201

Electron concentration effects on the Shastry-Sutherland phase stability in Ce_{2-x}Pd_{2+y}In_{1-z} solid solutions

The stability of a Shastry-Sutherland ShSu phase as a function of electron concentration is investigated through the field dependence of thermal and magnetic properties of the solid solution Ce_{2-x}Pd_{2+y}In_{1-z} in the antiferromagnetic branch. In these alloys the electronic (holes) variation is realized by increasing $Pd$ concentration. The AF transition T_M decreases from 3.5K to 2.8K as $Pd$ concentration increases from y=0.2 to y=0.4. By applying magnetic field, the ShSu phase is suppressed once the field induced ferromagnetic polarization takes over at a critical field B_{cr} which increases with $Pd$ content. A detailed analysis around the critical point reveals a structure in the maximum of the dM/dB derivative, which is related with incipient steps in the magnetization M(B) as predicted by the theory for the ShSu lattice. The crossing of M(B) isotherms, observed in ShSu prototype compounds, is also analyzed. The effect of $In$ substitution by $Pd$ is interpreted as an increase of the number of 'holes' in the conduction band and results in a unique parameter able to describe the variation of the magnetic properties along the studied range of concentration.Comment: 8 pages, 11 figure

Ising pyrochlore magnets: Low temperature properties, ice rules and beyond

Pyrochlore magnets are candidates for spin-ice behavior. We present theoretical simulations of relevance for the pyrochlore family R2Ti2O7 (R= rare earth) supported by magnetothermal measurements on selected systems. By considering long ranged dipole-dipole as well as short-ranged superexchange interactions we get three distinct behaviours: (i) an ordered doubly degenerate state, (ii) a highly disordered state with a broad transition to paramagnetism, (iii) a partially ordered state with a sharp transition to paramagnetism. Thus these competing interactions can induce behaviour very different from conventional ``spin ice''. Closely corresponding behaviour is seen in the real compounds---in particular Ho2Ti2O7 corresponds to case (iii) which has not been discussed before, rather than (ii) as suggested earlier.Comment: 5 pages revtex, 4 figures; some revisions, additional data, additional co-authors and a changed title. Basic ideas of paper remain the same but those who downloaded the original version are requested to get this more complete versio