A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra

Abstract

We define and study a lattice model which we argue is in the universality class of the $OSp(2S+2|2S)$ supercoset sigma model for a large range of values of the coupling constant $g_{\sigma }^2$. In this first paper, we analyze in details the symmetries of this lattice model, in particular the decomposition of the space of the quantum spin chain $V^{\otimes L}$ as a bimodule over $OSp(2S+2|2S)$ and its commutant, the Brauer algebra $B_L(2)$. It turns out that $V^{\otimes L}$ is a nonsemisimple module for both $OSp(2S+2|2S)$ and $B_L(2)$. The results are used in the companion paper to elucidate the structure of the (boundary) conformal field theory.

arXiv comment36 pages, 20 figures

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• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrum
• Cohomological Reduction of Sigma Models
• Global phase diagram of two-dimensional Dirac fermions in random potentials
• Exact exponents for the spin quantum Hall transition in the presence of multiple edge channels
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• The decomposition matrices of the Brauer algebra over the complex field
• On the Spectrum of Superspheres
• Continuum Limit of gl(M/N) Spin Chains
• Superspace Parafermions
• Anomalous Dimensions in Deformed WZW Models on Supergroups
• Edge states and conformal boundary conditions in super spin chains and super sigma models
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Spectra of Coset Sigma Models
• Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups