Symmetry Properties on Magnetization in the Hubbard Model at Finite Temperatures

By making use of some symmetry properties of the relevant Hamiltonian, two fundamental relations between the ferromagnetic magnetization and a spin correlation function are derived for the $d (=1,2,3)$-dimensional Hubbard model at finite temperatures. These can be viewed as a kind of Ward-Takahashi identities. The properties of the magnetization as a function of the applied field are discussed. The results thus obtained hold true for both repulsive and attractive on-site Coulomb interactions, and for arbitrary electron fillings.Comment: Latex file, no figur

On Blowup for time-dependent generalized Hartree-Fock equations

We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.Comment: 24 page

Sign Rules for Anisotropic Quantum Spin Systems

We present new and exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive-definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the effects of sign rules in variational calculations and quantum Monte Carlo calculations are considered. They are illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.Comment: 4 pages, 1 ps-figur

One Dimensional Chain with Long Range Hopping

The one-dimensional (1D) tight binding model with random nearest neighbor hopping is known to have a singularity of the density of states and of the localization length at the band center. We study numerically the effects of random long range (power-law) hopping with an ensemble averaged magnitude \expectation{|t_{ij}|} \propto |i-j|^{-\sigma} in the 1D chain, while maintaining the particle-hole symmetry present in the nearest neighbor model. We find, in agreement with results of position space renormalization group techniques applied to the random XY spin chain with power-law interactions, that there is a change of behavior when the power-law exponent $\sigma$ becomes smaller than 2

Chiral Spin Liquids and Quantum Error Correcting Codes

The possibility of using the two-fold topological degeneracy of spin-1/2 chiral spin liquid states on the torus to construct quantum error correcting codes is investigated. It is shown that codes constructed using these states on finite periodic lattices do not meet the necessary and sufficient conditions for correcting even a single qubit error with perfect fidelity. However, for large enough lattice sizes these conditions are approximately satisfied, and the resulting codes may therefore be viewed as approximate quantum error correcting codes.Comment: 9 pages, 3 figure

Equilibrium and dynamical properties of the ANNNI chain at the multiphase point

We study the equilibrium and dynamical properties of the ANNNI (axial next-nearest-neighbor Ising) chain at the multiphase point. An interesting property of the system is the macroscopic degeneracy of the ground state leading to finite zero-temperature entropy. In our equilibrium study we consider the effect of softening the spins. We show that the degeneracy of the ground state is lifted and there is a qualitative change in the low temperature behaviour of the system with a well defined low temperature peak of the specific heat that carries the thermodynamic ``weight'' of the ground state entropy. In our study of the dynamical properties, the stochastic Kawasaki dynamics is considered. The Fokker-Planck operator for the process corresponds to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with constraints on allowed states. This leads to a number of differences in its properties which are obtained through exact numerical diagonalization, simulations and by obtaining various analytic bounds.Comment: 9 pages, RevTex, 6 figures (To appear in Phys. Rev. E

The Aharonov-Bohm effect for an exciton

We study theoretically the exciton absorption on a ring shreded by a magnetic flux. For the case when the attraction between electron and hole is short-ranged we get an exact solution of the problem. We demonstrate that, despite the electrical neutrality of the exciton, both the spectral position of the exciton peak in the absorption, and the corresponding oscillator strength oscillate with magnetic flux with a period $\Phi_0$---the universal flux quantum. The origin of the effect is the finite probability for electron and hole, created by a photon at the same point, to tunnel in the opposite directions and meet each other on the opposite side of the ring.Comment: 13 RevTeX 3.0 pages plus 4 EPS-figures, changes include updated references and an improved chapter on possible experimental realization

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio

Finite temperature mobility of a particle coupled to a fermion environment

We study numerically the finite temperature and frequency mobility of a particle coupled by a local interaction to a system of spinless fermions in one dimension. We find that when the model is integrable (particle mass equal to the mass of fermions) the static mobility diverges. Further, an enhanced mobility is observed over a finite parameter range away from the integrable point. We present a novel analysis of the finite temperature static mobility based on a random matrix theory description of the many-body Hamiltonian.Comment: 11 pages (RevTeX), 5 Postscript files, compressed using uufile

Dynamics of trapped bright solitons in the presence of localized inhomogeneities

We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized ``impurity'' in Bose-Einstein condensates (BECs). We study the generation and stability of a pair of steady states in the vicinity of the impurity as the impurity strength is varied. These two new steady states, one stable and one unstable, disappear through a saddle-node bifurcation as the strength of the impurity is decreased. The dynamics of the soliton is also examined in all the cases (including cases where the soliton is offset from one of the relevant fixed points). The numerical results are corroborated by theoretical calculations which are in very good agreement with the numerical findings.Comment: 8 pages, 5 composite figures with low res (for high res pics please go to http://www.rohan.sdsu.edu/~rcarrete/ [Publications] [Publication#41