Finite-size effects in the spectrum of the $OSp(3|2)$ superspin chain

Abstract

The low energy spectrum of a spin chain with $OSp(3|2)$ supergroup symmetry is studied based on the Bethe ansatz solution of the related vertex model. This model is a lattice realization of intersecting loops in two dimensions with loop fugacity $z=1$ which provides a framework to study the critical properties of the unusual low temperature Goldstone phase of the $O(N)$ sigma model for $N=1$ in the context of an integrable model. Our finite-size analysis provides strong evidence for the existence of continua of scaling dimensions, the lowest of them starting at the ground state. Based on our data we conjecture that the so-called watermelon correlation functions decay logarithmically with exponents related to the quadratic Casimir operator of $OSp(3|2)$. The presence of a continuous spectrum is not affected by a change to the boundary conditions although the density of states in the continua appears to be modified.

arXiv comment26 pages, 10 figures

References in corpus (14)

• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• The algebraic Bethe ansatz for rational braid-monoid lattice models
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Continuum Limit of the Integrable sl(2/1) 3-\bar{3} Superspin Chain
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Loop models with crossings
• The exact solution and the finite size behaviour of the $Osp(1|2)$ invariant spin chain
• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• The Staggered Six-Vertex Model: Conformal Invariance and Corrections to Scaling
• Phase Diagram of an Integrable Alternating $U_q[sl(2|1)]$ Superspin Chain
• Non-Linear Integral Equations for the SL(2,R)/U(1) black hole sigma model
• Finite size properties of staggered $U_q[sl(2|1)]$ superspin chains
• Monte Carlo study of the hull distribution for the q=1 Brauer model

Cited by in corpus (8)

• Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions
• Integrable boundary conditions for staggered vertex models
• Spectral flow for an integrable staggered superspin chain
• The fine structure of the finite-size effects for the spectrum of the $OSp(n|2m)$ spin chain
• On the critical behaviour of the integrable $q$-deformed $OSp(3|2)$ superspin chain
• $OSp(n|2m)$ quantum chains with free boundaries
• Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups
• $U_q[OSp(3|2)]$ quantum chains with quantum group invariant boundaries