Quantum criticality on a chiral ladder: An SU(2) infinite density matrix renormalization group study

Abstract

In this paper we study the ground-state properties of a ladder Hamiltonian with chiral $\text{SU}(2)$-invariant spin interactions, a possible first step toward the construction of truly two-dimensional nontrivial systems with chiral properties starting from quasi-one-dimensional ones. Our analysis uses a recent implementation by us of $\text{SU}(2)$ symmetry in tensor network algorithms, specifically for infinite density matrix renormalization group. After a preliminary analysis with Kadanoff coarse graining and exact diagonalization for a small-size system, we discuss its bosonization and recap the continuum limit of the model to show that it corresponds to a conformal field theory, in agreement with our numerical findings. In particular, the scaling of the entanglement entropy as well as finite-entanglement scaling data show that the ground-state properties match those of the universality class of a $c=1$ conformal field theory (CFT) in $(1+1)$ dimensions. We also study the algebraic decay of spin-spin and dimer-dimer correlation functions, as well as the algebraic convergence of the ground-state energy with the bond dimension, and the entanglement spectrum of half an infinite chain. Our results for the entanglement spectrum are remarkably similar to those of the spin-$\frac{1}{2}$ Heisenberg chain, which we take as a strong indication that both systems are described by the same CFT at low energies, i.e., an $\text{SU}{(2)}_{1}$ Wess-Zumino-Witten theory. Moreover, we explain in detail how to construct matrix product operators for $\text{SU}(2)$-invariant three-spin interactions, something that had not been addressed with sufficient depth in the literature.