DMRG investigation of constrained models: from quantum dimer and quantum loop ladders to hard-boson and Fibonacci anyon chains

TL;DR

This paper uses DMRG to analyze constrained quantum ladder models, mapping them to hard-boson models, and characterizes their phase transitions, including Ising and tricritical Ising points, with implications for Fibonacci anyon chains.

Contribution

Develops a DMRG algorithm exploiting small Hilbert spaces for quantum dimer and loop models, maps them onto a hard-boson model, and characterizes their phase transitions including Ising and tricritical points.

Findings

Full phase diagram of the models is discussed.

Ising transition and tricritical Ising point are characterized.

Fibonacci anyon chain corresponds to critical points of these models.

Abstract

Motivated by the presence of Ising transitions that take place entirely in the singlet sector of frustrated spin-1/2 ladders and spin-1 chains, we study two types of effective dimer models on ladders, a quantum dimer model and a quantum loop model. Building on the constraints imposed on the dimers, we develop a Density Matrix Renormalization Group algorithm that takes full advantage of the relatively small Hilbert space that only grows as Fibonacci number. We further show that both models can be mapped rigorously onto a hard-boson model first studied by Fendley, Sengupta and Sachdev [Phys. Rev. B 69, 075106 (2004)], and combining early results with recent results obtained with the present algorithm on this hard-boson model, we discuss the full phase diagram of these quantum dimer and quantum loop models, with special emphasis on the phase transitions. In particular, using conformal field theory, we fully characterize the Ising transition and the tricritical Ising end point, with a complete analysis of the boundary-field correspondence for the tricritical Ising point including partially polarized edges. Finally, we show that the Fibonacci anyon chain is exactly equivalent to special critical points of these models.