Multi-state asymmetric simple exclusion processes

It is known that the Markov matrix of the asymmetric simple exclusion process (ASEP) is invariant under the Uq(sl2) algebra. This is the result of the fact that the Markov matrix of the ASEP coincides with the generator of the Temperley-Lieb (TL) algebra, the dual algebra of the Uq(sl2) algebra. Various types of algebraic extensions have been considered for the ASEP. In this paper, we considered the multi-state extension of the ASEP, by allowing more than two particles to occupy the same box. We constructed the Markov matrix by dimensionally extending the TL generators and derived explicit forms of the particle densities and the currents on the steady states. Then we showed how decay lengths differ from the original two-state ASEP under the closed boundary conditions.Comment: 41pages, 10 figures; explicit forms of the fused Temperley-Lieb generators are added; J. Stat. Phys. (2014

Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach

We discussed subspaces of the N=1 supersymmetric sine-Gordon model with Dirichlet boundaries through light-cone lattice regularization. In this paper, we showed, unlike the periodic boundary case, both of Neveu-Schwarz (NS) and Ramond (R) sectors of a superconformal field theory were obtained. Using a method of nonlinear integral equations for auxiliary functions defined by eigenvalues of transfer matrices, we found that an excitation state with an odd number of particles is allowed for a certain value of a boundary parameter even on a system consisting of an even number of sites. In a small-volume limit where conformal invariance shows up in the theory, we derived conformal dimensions of states constructed through the lattice-regularized theory. The result shows existence of the R sector, which cannot be obtained from the periodic system, while a winding number is restricted to an integer or a half-integer depending on boundary parameters.Comment: Typos were correcte

Construction of the steady state density matrix and quasilocal charges for the spin-1/2 XXZ chain with boundary magnetic fields

We construct the nonequilibrium steady state (NESS) density operator of the spin-1/2 XXZ chain with non-diagonal boundary magnetic fields coupled to boundary dissipators. The Markovian boundary dis- sipation is found with which the NESS density operator is expressed in terms of the product of the Lax operators by relating the dissipation parameters to the boundary parameters of the spin chain. The NESS density operator can be expressed in terms of a non-Hermitian transfer operator (NHTO) which forms a commuting family of quasilocal charges. The optimization of the Mazur bound for the high temperature Drude weight is discussed by using the quasilocal charges and the conventional local charges constructed through the Bethe ansatz.Comment: 15 page

Phase coexistence phenomena in an extreme case of the misanthrope process with open boundaries

The misanthrope process is a class of stochastic interacting particle systems, generalizing the simple exclusion process. It allows each site of the lattice to accommodate more than one particle. We consider a special case of the one dimensional misanthrope process whose probability distribution is completely equivalent to the ordinary simple exclusion process under the periodic boundary condition. By imposing open boundaries, high- and low-density domains can coexist in the system, which we investigate by Monte Carlo simulations. We examine finite-size corrections of density profiles and correlation functions, when the jump rule for particles is symmetric. Moreover, we study properties of delocalized and localized shocks in the case of the totally asymmetric jump rule. The localized shock slowly moves to its stable position in the bulk.Comment: 8 pages, 7 figures. v2: minor changes. v3: changed the structure of the work, added 7 references, replaced some figure

Algebraic aspects of the correlation functions of the integrable higher-spin XXZ spin chains with arbitrary entries

We discuss some fundamental properties of the XXZ spin chain, which are important in the algebraic Bethe-ansatz derivation for the multiple-integral representations of the spin-s XXZ correlation function with an arbitrary product of elementary matrices. For instance, we construct Hermitian conjugate vectors in the massless regime and introduce the spin-s Hermitian elementary matrices.Comment: 24 pages, to appear in the proceedings of "Infinite Analysis 09 - New Trends in Quantum Integrable Systems -", July 27-31, 2009, Kyoto University, Japa

Exactly solvable subspaces of non-integrable spin chains with boundaries and quasiparticle interactions

We propose two new strategies to construct a family of non-integrable spin chains with exactly solvable subspace based on the idea of quasiparticle excitations from the matrix product vacuum state. The first one allows the boundary generalization, while the second one makes it possible to construct the solvable subspace with interacting quasiparticles. Each generalization is realized by removing the assumption made in the conventional method, which is the frustration-free condition or the local orthogonality, respectively. We found that the structure of embedded equally-spaced energy spectrum is not violated by the diagonal boundaries, as log as quasiparticles are non-interacting in the invariant subspace. On the other hand, we show that there exists a one-parameter family of non-integrable Hamiltonians which show perfectly embedded energy spectrum of the integrable spin chain. Surprisingly, the embedded energy spectrum does change by varying the free parameter of the Hamiltonian. The constructed eigenstates in the solvable subspace are the candidates of quantum many-body scar states, as they show up in the middle of the energy spectrum and have entanglement entropies expected to obey the sub-volume law.Comment: 11 page