Exact ground states of generalized Hubbard models

We present a simple method for the construction of exact ground states of generalized Hubbard models in arbitrary dimensions. This method is used to derive rigorous criteria for the stability of various ground state types, like the $\eta$-pairing state, or N\'eel and ferromagnetic states. Although the approach presented here is much simpler than the ones commonly used, it yields better bounds for the region of stability.Comment: Revtex, 8 page

Yang-Mills theory for non-semisimple groups

For semisimple groups, possibly multiplied by U(1)'s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for non-semisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical consequences worth studying. The non-semisimple group with only two generators that do not commute is studied in detail.Comment: 16 pages, no figures, prepared with ReVTeX

Dynamical Structure Factor in Cu Benzoate and other spin-1/2 antiferromagnetic chains

Recent experiments of the quasi-one-dimensional spin-1/2 antiferromagnet Copper Benzoate established the existence of a magnetic field induced gap. The observed neutron scattering intensity exhibits resolution limited peaks at both the antiferromagnetic wave number and at incommensurate wave numbers related to the applied magnetic field. We determine the ratio of spectral weights of these peaks within the framework of a low-energy effective field theory description of the problem.Comment: 5 pages, 3figure

A direct calculation of critical exponents of two-dimensional anisotropic Ising model

Using an exact solution of the one-dimensional (1D) quantum transverse-field Ising model (TFIM), we calculate the critical exponents of the two-dimensional (2D) anisotropic classical Ising model (IM). We verify that the exponents are the same as those of isotropic classical IM. Our approach provides an alternative means of obtaining and verifying these well-known results.Comment: 3 pages, no figures, accepted by Commun. Theor. Phys.(IPCAS

Domain wall dynamics of the Ising chains in a transverse field

We show that the dynamics of an Ising spin chain in a transverse field conserves the number of domains (strings of down spins in an up-spin background) at discrete times. This enables the determination of the eigenfunctions of the time-evolution operator, and the dynamics of initial states with domains. The transverse magnetization is shown to be identically zero in all sectors with a fixed number of domains. For an initial state with a single string of down spins, the local magnetization, the equal-time and double-time spin-spin correlation functions, are calculated analytically as functions of time and the initial string size. The domain size distribution function can be expressed as a simple integral involving Bessel functions.Comment: 4 pages with three figure

Quantum renormalization group of XYZ model in a transverse magnetic field

We have studied the zero temperature phase diagram of XYZ model in the presence of transverse magnetic field. We show that small anisotropy (0 =< Delta <1) is not relevant to change the universality class. The phase diagram consists of two antiferromagnetic ordering and a paramagnetic phases. We have obtained the critical exponents, fixed points and running of coupling constants by implementing the standard quantum renormalization group. The continuous phase transition from antiferromagnetic (spin-flop) phase to a paramagnetic one is in the universality class of Ising model in transverse field. Numerical exact diagonalization has been done to justify our results. We have also addressed on the application of our findings to the recent experiments on Cs_2CoCl_4.Comment: 5 pages, 5 figures, new references added to the present versio

A Note on Pseudo-Hermitian Systems with Point Interactions and Quantum Separability

We study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail.Comment: 6 page

Rigorous results on superconducting ground states for attractive extended Hubbard models

We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang "eta-paired" state for any non-vanishing value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping.Comment: 12 page

Dynamical correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions $\langle \psi(x_1,0)\psi^\dagger(x_2,t)\rangle _{\pm,T}$. We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case $x_1=0$, we express correlation functions with Neumann boundary conditions $\langle\psi(0,0)\psi^\dagger(x_2,t)\rangle _{+,T}$, in terms of solutions of nonlinear partial differential equations which were introduced in \cite{kojima:Sl} as a generalization of the nonlinear Schr\"odinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functions $\langle\psi(x_1)\psi^\dagger(x_2)\rangle _{\pm,0}$ in \cite{kojima:K}, to the Fredholm determinant formulae for the time and temperature dependent correlation functions $\langle\psi(x_1,0)\psi^\dagger(x_2,t)\rangle _{\pm,T}$, $t \in {\bf R}$, $T \geq 0$

Quantum Field Kinetics

Using the general framework of quantum field theory, we derive basic equations of quantum field kinetics. The main goal of this approach is to compute the observables associated with a quark-gluon plasma at different stages of its evolution. We start by rewriting the integral equations for the field correlators in different forms, depending on the relevant dynamical features at each different stage. Next, two versions of perturbation expansion are considered. The first is best suited for the calculation of electromagnetic emission from chaotic, but not equilibrated, strongly interacting matter. The second version allows one to derive evolution equations, which are generalizations of the familiar QCD evolution equations, and provide a basis for the calculation of the initial quark and gluon distributions after the first hard interaction of the heavy ions.Comment: 13 pages, REVTeX, 2 postscript figures appende