Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain

Abstract

We construct a family of integrable vertex model based on the typical four-dimensional representations of the quantum group deformation of the Lie superalgebra $sl(2|1)$. Upon alternation of such a representation with its dual this model gives rise to a mixed superspin Hamiltonian with local interactions depending on the representation parameter $\pm b$ and the deformation parameter $\gamma$. As a subsector this model contains integrable vertex models with ordinary symmetries for twisted boundary conditions. The thermodynamic limit and low energy properties of the mixed superspin chain are studied using a combination of analytical and numerical methods. Based on these results we identify the phases realized in this system as a function of the parameters $b$ and $\gamma$. The different phases are characterized by the operator content of the corresponding critical theory. Only part of the spectrum of this effective theory can be understood in terms of the U(1) symmetries related to the physical degrees of freedom corresponding to spin and charge. The other modes lead to logarithmic finite-size corrections in the spectrum of the theory.

arXiv comment62 pages, 8 figures included

References in corpus (22)

• Quantum Inverse Scattering Method and Correlation Functions
• The antiferromagnetic transition for the square-lattice Potts model
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Algebraic Bethe Ansatz for gl(2,1) Invariant 36-Vertex Models
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• One parameter family of an integrable $spl(2|1)$ vertex model : Algebraic Bethe ansatz approach and ground state structure
• $U_{q}osp(2,2)$ Lattice Models
• Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
• The continuum limit of sl(N/K) integrable super spin chains
• Properties of the chiral spin liquid state in generalized spin ladders
• The $Z_2$ staggered vertex model and its applications
• On Type-I Quantum Affine Superalgebras
• Doping of a spin-1 chain: integrable model
• Doped Heisenberg chains: spin-S generalizations of the supersymmetric t-J model
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• New R-matrices from Representations of Braid-Monoid Algebras based on Superalgebras
• Dilute Birman--Wenzl--Murakami Algebra and $D_{n+1}^{(2)}$ models
• Twisted Boundary Conditions and the Adiabatic Ground State for the Attractive XXZ Luttinger Liquid
• Unified algebraic Bethe ansatz for two-dimensional lattice models
• Exact solution and finite size properties of the $U_q[osp(2|2m)]$ vertex model
• The antiferromagnetic Potts model

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