The "topological" charge for the finite XX quantum chain

It is shown that an operator (in general non-local) commutes with the Hamiltonian describing the finite XX quantum chain with certain non-diagonal boundary terms. In the infinite volume limit this operator gives the "topological" charge.Comment: 5 page

The XX--model with boundaries. Part I: Diagonalization of the finite chain

This is the first of three papers dealing with the XX finite quantum chain with arbitrary, not necessarily hermitian, boundary terms. This extends previous work where the periodic or diagonal boundary terms were considered. In order to find the spectrum and wave-functions an auxiliary quantum chain is examined which is quadratic in fermionic creation and annihilation operators and hence diagonalizable. The secular equation is in general complicated but several cases were found when it can be solved analytically. For these cases the ground-state energies are given. The appearance of boundary states is also discussed and in view to the applications considered in the next papers, the one and two-point functions are expressed in terms of Pfaffians.Comment: 56 pages, LaTeX, some minor correction

PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields

The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construction of a new inner product employing a "quasi-fermion" algebra in momentum space where creation and annihilation operators are not related via Hermitian conjugation. For a special example, when the boundary fields lie on the imaginary axis, we show the spectral equivalence of the quasi-Hermitian XX spin-chain with a non-local fermion model, where long range hopping of the particles occurs as the non-Hermitian boundary fields increase in strength. The corresponding Hamiltonian interpolates between the open XX and the quantum group invariant XXZ model at the free fermion point. For an even number of sites the former is known to be related to a CFT with central charge c=1, while the latter has been connected to a logarithmic CFT with central charge c=-2. We discuss the underlying algebraic structures and show that for an odd number of sites the superalgebra symmetry U(gl(1|1)) can be extended from the unit circle along the imaginary axis. We relate the vanishing of one of its central elements to the appearance of Jordan blocks in the Hamiltonian.Comment: 37 pages, 5 figure

Exact solution of the open XXZ chain with general integrable boundary terms at roots of unity

We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are arbitrary, and need not satisfy any constraint. The solution is in terms of generalized T - Q equations, having more than one Q function. We find numerical evidence that this solution gives the complete set of 2^N transfer matrix eigenvalues, where N is the number of spins.Comment: 22 page

Hidden symmetries in the asymmetric exclusion process

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However, we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies become generic in the limit of very large systems. This behaviour can be explained by the Bethe Ansatz and suggests the presence of hidden symmetries in the model. Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe Ansatz.Comment: 16 page

Structure of the two-boundary XXZ model with non-diagonal boundary terms

We study the integrable XXZ model with general non-diagonal boundary terms at both ends. The Hamiltonian is considered in terms of a two boundary extension of the Temperley-Lieb algebra. We use a basis that diagonalizes a conserved charge in the one-boundary case. The action of the second boundary generator on this space is computed. For the L-site chain and generic values of the parameters we have an irreducible space of dimension 2^L. However at certain critical points there exists a smaller irreducible subspace that is invariant under the action of all the bulk and boundary generators. These are precisely the points at which Bethe Ansatz equations have been formulated. We compute the dimension of the invariant subspace at each critical point and show that it agrees with the splitting of eigenvalues, found numerically, between the two Bethe Ansatz equations.Comment: 9 pages Latex. Minor correction

Dynamics of an exclusion process with creation and annihilation

We examine the dynamical properties of an exclusion process with creation and annihilation of particles in the framework of a phenomenological domain-wall theory, by scaling arguments and by numerical simulation. We find that the length- and time scale are finite in the maximum current phase for finite creation- and annihilation rates as opposed to the algebraically decaying correlations of the totally asymmetric simple exclusion process (TASEP). Critical exponents of the transition to the TASEP are determined. The case where bulk creation- and annihilation rates vanish faster than the inverse of the system size N is also analyzed. We point out that shock localization is possible even for rates proportional to 1/N^a, 1<a<2.Comment: 16 pages, 8 figures, typos corrected, references added, section 4 revise

On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with complex electric(magnetic) field, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of Physics A(v3

Spectra of non-hermitian quantum spin chains describing boundary induced phase transitions

The spectrum of the non-hermitian asymmetric XXZ-chain with additional non-diagonal boundary terms is studied. The lowest lying eigenvalues are determined numerically. For the ferromagnetic and completely asymmetric chain that corresponds to a reaction-diffusion model with input and outflow of particles the smallest energy gap which corresponds directly to the inverse of the temporal correlation length shows the same properties as the spatial correlation length of the stationary state. For the antiferromagnetic chain with both boundary terms, we find a conformal invariant spectrum where the partition function corresponds to the one of a Coulomb gas with only magnetic charges shifted by a purely imaginary and a lattice-length dependent constant. Similar results are obtained by studying a toy model that can be diagonalized analytically in terms of free fermions.Comment: LaTeX, 26 pages, 1 figure, uses ioplppt.st

The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics

The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by Bethe ansatz. Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and J. Feinberg editor