Dynamic Correlation Functions for Quantum Spin Chains

New exact results are presented on the long-time asymptotic expansions of the T = 0 autocorrelation functions, and on the leading singularities of their frequency-dependent Fourier transforms, for the one-dimensional S = ½ isotropic XY model and the S = ½ transverse Ising model at the critical field. High-precision numerical calculations of the latter functions are also given, and experiments are proposed to observe the functional behaviors that are found

Wave-Number Dependent Susceptibilities of One-Dimensional Quantum Spin Models

We calculate the zero-temperature q-dependent susceptibilities of the one-dimensional, S=1/2, transverse Ising model at the critical magnetic field and of the isotropic XY model in zero field which have not been previously determined. Our method, which is based on a rigorous method of calculating dynamic correlation functions for these models, provides precise numerical values for the susceptibilities at wave numbers q=kπ/M for integral M and odd integral k, as well as exact analytic results for the dominant singularities at q=0 and q=π

Susceptibilities of One-Dimensional Quantum Spin Models at Zero Temperature

We calculate precise numerical values for the nondivergent direct or staggered zero-temperature susceptibilities of the one-dimensional, S=1/2, transverse Ising model at the critical field and for the isotropic XY model in zero field which have not been previously determined analytically. Our method is based on a rigorous approach to calculate dynamic correlation functions for these models. We also investigate the exact nature of the divergenices in the q-dependent susceptibilities. Our results are compared with existing predictions of approximate analytic approaches and numerical finite-chain calculations. Our result for the XY case is directly relevant for the interpretation of recent susceptibility measurements on the quasi-one-dimensional magnetic compound Cs2CoCl4

Implications of Direct-Product Ground States in the One-Dimensional Quantum XYZ and XY Spin Chains

We state the conditions under which the general spin-s quantum XYZ ferromagnet (H−) and antiferromagnet (H+) with an external magnetic field along one axis, specified by the Hamiltonian H±=± Nl=1 (JxSxlSxl+1+JySylS l+1y+JzSzlSzl+1)-h Nl=1Szl exhibits a fully ordered ground state described by a wave function which is a direct product of single-site wave functions. We present a detailed analysis of the implications for the zero-temperature dynamical properties of this model. In particular, we derive a rigorous relation between the three dynamic structure factors Sμμ(q,ω), μ=x,y,z at T=0. For the special case of the s=(1/2) anisotropic XY model (Jz=0), these relations are used to determine the dynamic structure factors Sxx(q,ω) and Syy(q,ω) at T=0 and h=(JxJy)1/2 in terms of the known dynamic structure factor Szz(q,ω)

Dynamic Correlation Functions for the One-Dimensional XY Z Model: New Exact Results

It is found that there exist special circumstances for which a rigorous relation between the three dynamic structure factors Sμμ(q, ω), μ=x, y, z, at T=0 of the one-dimensional spin-sXYZ model in a uniform magnetic field can be derived. This relation is used to infer new exact results for Sxx(q, ω) of the S= case1/2 anisotropic XY model

Exact T=0 Partition Functions for Potts Antiferromagnets on Sections of the Simple Cubic Lattice

We present exact solutions for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial $P$) on tube sections of the simple cubic lattice of fixed transverse size $L_x \times L_y$ and arbitrarily great length $L_z$, for sizes $L_x \times L_y = 2 \times 3$ and $2 \times 4$ and boundary conditions (a) $(FBC_x,FBC_y,FBC_z)$ and (b) $(PBC_x,FBC_y,FBC_z)$, where $FBC$ ($PBC$) denote free (periodic) boundary conditions. In the limit of infinite-length, $L_z \to \infty$, we calculate the resultant ground state degeneracy per site $W$ (= exponent of the ground-state entropy). Generalizing $q$ from ${\mathbb Z}_+$ to ${\mathbb C}$, we determine the analytic structure of $W$ and the related singular locus ${\cal B}$ which is the continuous accumulation set of zeros of the chromatic polynomial. For the $L_z \to \infty$ limit of a given family of lattice sections, $W$ is analytic for real $q$ down to a value $q_c$. We determine the values of $q_c$ for the lattice sections considered and address the question of the value of $q_c$ for a $d$-dimensional Cartesian lattice. Analogous results are presented for a tube of arbitrarily great length whose transverse cross section is formed from the complete bipartite graph $K_{m,m}$.Comment: 28 pages, latex, six postscript figures, two Mathematica file

Technicolor Models with Color-Singlet Technifermions and their Ultraviolet Extensions

We study technicolor models in which all of the technifermions are color-singlets, focusing on the case in these fermions transform according to the fundamental representation of the technicolor gauge group. Our analysis includes a derivation of restrictions on the weak hypercharge assignments for the technifermions and additional color-singlet, technisinglet fermions arising from the necessity of avoiding stable bound states with exotic electric charges. Precision electroweak constraints on these models are also discussed. We determine some general properties of extended technicolor theories containing these technicolor sectors.Comment: 17 pages, latex, 2 figure

Ground-State Degeneracy of Potts Antiferromagnets on Two-Dimensional Lattices: Approach Using Infinite Cyclic Strip Graphs

The q-state Potts antiferromagnet on a lattice $\Lambda$ exhibits nonzero ground state entropy $S_0=k_B \ln W$ for sufficiently large q and hence is an exception to the third law of thermodynamics. An outstanding challenge has been the calculation of W(sq,q) on the square (sq) lattice. We present here an exact calculation of W on an infinite-length cyclic strip of the square lattice which embodies the expected analytic properties of W(sq,q). Similar results are given for the kagom\'e lattice.Comment: 8 pages, Latex, 2 postscript figure

Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals

We prove a general rigorous lower bound for $W(\Lambda,q)=\exp(S_0(\Lambda,q)/k_B)$, the exponent of the ground state entropy of the $q$-state Potts antiferromagnet, on an arbitrary Archimedean lattice $\Lambda$. We calculate large-$q$ series expansions for the exact $W_r(\Lambda,q)=q^{-1}W(\Lambda,q)$ and compare these with our lower bounds on this function on the various Archimedean lattices. It is shown that the lower bounds coincide with a number of terms in the large-$q$ expansions and hence serve not just as bounds but also as very good approximations to the respective exact functions $W_r(\Lambda,q)$ for large $q$ on the various lattices $\Lambda$. Plots of $W_r(\Lambda,q)$ are given, and the general dependence on lattice coordination number is noted. Lower bounds and series are also presented for the duals of Archimedean lattices. As part of the study, the chromatic number is determined for all Archimedean lattices and their duals. Finally, we report calculations of chromatic zeros for several lattices; these provide further support for our earlier conjecture that a sufficient condition for $W_r(\Lambda,q)$ to be analytic at $1/q=0$ is that $\Lambda$ is a regular lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in Phys. Rev.

Z Boson Propagator Correction in Technicolor Theories with ETC Effects Included

We calculate the Z boson propagator correction, as described by the S parameter, in technicolor theories with extended technicolor interactions included. Our method is to solve the Bethe-Salpeter equation for the requisite current-current correlation functions. Our results suggest that the inclusion of extended technicolor interactions has a relatively small effect on S.Comment: 15pages, 8 figure