sl(N) Onsager's Algebra and Integrability

We define an $sl(N)$ analog of Onsager's Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a fixed point subalgebra of $sl(N)$ Loop Algebra with respect to a certain involution. As the consequence of the generalized Dolan Grady relations a Hamiltonian linear in the generators of $sl(N)$ Onsager's Algebra is shown to posses an infinite number of mutually commuting integrals of motion

Analyticity and Integrabiity in the Chiral Potts Model

We study the perturbation theory for the general non-integrable chiral Potts model depending on two chiral angles and a strength parameter and show how the analyticity of the ground state energy and correlation functions dramatically increases when the angles and the strength parameter satisfy the integrability condition. We further specialize to the superintegrable case and verify that a sum rule is obeyed.Comment: 31 pages in harvmac including 9 tables, several misprints eliminate

Thermodynamics of the 3-State Potts Spin Chain

We demonstrate the relation of the infrared anomaly of conformal field theory with entropy considerations of finite temperature thermodynamics for the 3-state Potts chain. We compute the free energy and compute the low temperature specific heat for both the ferromagnetic and anti-ferromagnetic spin chains, and find the central charges for both.Comment: 18 pages, LaTex. Preprint # ITP-SB-92-60. References added and first section expande

Low-Temperature Expansions and Correlation Functions of the Z_3-Chiral Potts Model

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z_3-chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z_n-spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z_3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.Comment: 17 pages (Plain TeX), BONN-HE-93-1

Impact of positivity and complete positivity on accessibility of Markovian dynamics

We consider a two-dimensional quantum control system evolving under an entropy-increasing irreversible dynamics in the semigroup form. Considering a phenomenological approach to the dynamics, we show that the accessibility property of the system depends on whether its evolution is assumed to be positive or completely positive. In particular, we characterize the family of maps having different accessibility and show the impact of that property on observable quantities by means of a simple physical model.Comment: 11 pages, to appear in J. Phys.

A non-Hermitian critical point and the correlation length of strongly correlated quantum systems

We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In a previous article, we conjectured that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system and we confirmed the conjecture for two exactly solvable systems. In this article, we present more evidence for the conjecture. We also argue the basis of our conjecture by noting the dispersion relation of the elementary excitation.Comment: 25 pages, 18 figure

Asymmetric XXZ chain at the antiferromagnetic transition: Spectra and partition functions

The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero vertical field. The energy gaps scale with size $N$ as $N^{-1/2}$ and its amplitudes are obtained in terms of level-dependent scaling functions. Exactly on the phase boundary, the amplitudes are proportional to a sum of square-root of integers and an anomaly term. By summing over all low-lying levels, the partition functions are obtained explicitly. Similar analysis is performed also at the phase boundary of zero horizontal field in which case the energy gaps scale as $N^{-2}$. The partition functions for this case are found to be that of a nonrelativistic free fermion system. From symmetry of the lattice model under $\pi /2$ rotation, several identities between the partition functions are found. The $N^{-1/2}$ scaling at zero vertical field is interpreted as a feature arising from viewing the Pokrovsky-Talapov transition with the space and time coordinates interchanged.Comment: Minor corrections only. 18 pages in RevTex, 2 PS figure

Nonequilibrium Forces Between Neutral Atoms Mediated by a Quantum Field

We study all known and as yet unknown forces between two neutral atoms, modeled as three dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center of mass motion of the atom, its internal degrees of freedom and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first principle, systematic and unified description including the intrinsic field fluctuations and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces -- London, van der Waals and Casimir-Polder forces -- between neutral atoms in the long-time limit but also discover the existence of two new types of interatomic forces. The first, a `nonequilibrium force', arises when the field and atoms are not in thermal equilibrium, and the second, which we call an `entanglement force', originates from the correlations of the internal degrees of freedom of entangled atoms.Comment: 16 pages, 2 figure

Quantum spin chains of Temperley-Lieb type: periodic boundary conditions, spectral multiplicities and finite temperature

We determine the spectra of a class of quantum spin chains of Temperley-Lieb type by utilizing the concept of Temperley-Lieb equivalence with the S=1/2 XXZ chain as a reference system. We consider open boundary conditions and in particular periodic boundary conditions. For both types of boundaries the identification with XXZ spectra is performed within isomorphic representations of the underlying Temperley-Lieb algebra. For open boundaries the spectra of these models differ from the spectrum of the associated XXZ chain only in the multiplicities of the eigenvalues. The periodic case is rather different. Here we show how the spectrum is obtained sector-wise from the spectra of globally twisted XXZ chains. As a spin-off, we obtain a compact formula for the degeneracy of the momentum operator eigenvalues. Our representation theoretical results allow for the study of the thermodynamics by establishing a TL-equivalence at finite temperature and finite field.Comment: 29 pages, LaTeX, two references added, redundant figures remove