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

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

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

Spin-Hall effect with quantum group symmetry

We construct a model of spin-Hall effect on a noncommutative 4 sphere with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum orthogonal group. The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on higher dimensional noncommutative spheres and noncommutative projective spaces.Comment: v2: 14 pages, latex. Several changes and additional material; two extra sections added. To appear in LMP. Dedicated to Rafael Sorkin with friendship and respec

Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box

The wave mechanics of two impenetrable hard core particles in 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a {\it macro-orbital} (a kind of pair waveform). While the expectation value of their interaction, $$, vanishes for every state of two particles, the expectation value of their relative separation,$$, satisfies $\ge \lambda/2$ (or $q \ge \pi/d$, with $2d = L$ being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with $= \lambda/2$, phase position separation $\Delta\phi = 2\pi$ and momentum $|q_o| = \pi/d$) and experience a mutual repulsive force ({\it zero point repulsion}) $f_o = h^2/2md^3$ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining the correct microscopic understanding of widely different many body systems.Comment: 12 pages, no figur

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

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 $\langle\psi(x_1,0)\psi^\dagger(x_2,t)\rangle _{\pm,T}$, $t \in {\bf R}$, $T \geq 0$