Boundary conformal spectrum and surface critical behaviors of the classical spin systems: a tensor network renormalization study

Abstract

We numerically obtain the conformal spectrum of several classical spin models on a two-dimensional lattice with open boundaries, for every boundary fixed point obtained by the Cardy's derivation [J. L. Cardy, Nucl. Phys. B 324, 581 (1989)]. In order to extract accurate conformal data, we implement the tensor network renormalization algorithm [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] extended so as to be applicable to a square lattice with open boundaries. We successfully compute the boundary conformal spectrum consistent with the underlying boundary conformal field theories (BCFTs) for the Ising, tri-critical Ising, and 3-state Potts models on the lattice, which allows us to confirm the validity of the BCFT analyses for the surface critical behaviors of those lattice models.

arXiv comment12 pages, 12 figures

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Cited by in corpus (10)

• Critical properties of quantum three- and four-state Potts models with boundaries polarized along the transverse field
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Calculation of critical exponents on fractal lattice Ising model by higher-order tensor renormalization group method
• Measurements of magnetization on the Sierpiński carpet
• Transfer Matrix and Lattice Dilatation Operator for High-Quality Fixed Points in Tensor Network Renormalization Group
• Boundary CFT and tensor network approach to surface critical phenomena of the tricritical 3-state Potts model
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
• Boundary Criticality of Complex Conformal Field Theory: A Case Study in the Non-Hermitian 5-State Potts Model
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method