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

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.Contents arXiv:1809.00746v2 [cond-mat.str-el]

Boundary conformal spectrum and surface critical behavior of classical spin systems: A tensor network renormalization study

“…In this section, we show the conformal spectrum for each boundary fixed point by the tesor network method, which can be the complete numerical evidence of the Affleck's scenario in contrast to the Monte Carlo study which can investigate only the relevant scaling dimensions through the analyses of the order parameters. Though the conformal spectrum for the five of the six Cardy states are computed in the context of the quantum dimer model with a magnetic field [41], the consistency between the BCFT conjecture and the spectrum in the lattice model for the degenerated boundary condition |d is still not confirmed. In addition to the results for every Cardy's fixed point, we show the spectrum for the +&− fixed boundary condition.…”

Kibble-Zurek exponent and chiral transition of the period-4 phase of Rydberg chains

“…In order to fully profit from the restricted Hilbert space we implement the blockade explicitly into the DMRG. Recently it has been shown that the hard-boson model with r = 1 can be rigorously mapped onto a quantum dimer model on a two-leg ladder 39 that provides a simple and intuitive way to encode the constraint into DMRG. Although this mapping is not valid for r > 1, we can rely on the idea of auxiliary quantum numbers that would preserve the block-diagonal structure of the local tensors.…”

Microscopic characterization of Ising conformal field theory in Rydberg chains

“…It was further explored via large-scale numerics in Refs. [14,[26][27][28] (see also Refs. [13,15,24]).…”

“…The broader phase diagram features additional phases (not shown) including a threefold-degenerate charge density wave and incommensurate order; see Refs. [11,14,[26][27][28].…”