SciPost Phys. 6, 033 (2019) ·
published 14 March 2019

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Motivated by the presence of Ising transitions that take place entirely in
the singlet sector of frustrated spin1/2 ladders and spin1 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
hardboson 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 hardboson 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 boundaryfield 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.
SciPost Phys. 5, 030 (2018) ·
published 28 September 2018

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We study the triangularlattice Ising model with dipolar interactions, inspired by its realisation in artificial arrays of nanomagnets. We show that a classical spinliquid forms at intermediate temperatures, and that its behaviour can be tuned by temperature and/or a small lattice distortion between a string Luttinger liquid and a domainwallnetwork state. At low temperature there is a transition into a magnetically ordered phase, which can be firstorder or continous with a crossover in the critical behaviour between PokrovskyTalapov and 2DIsing universality. When the PokrovskyTalapov criticality dominates, the transition is essentially of the Kasteleyn type.
Stefan Wessel, B. Normand, Frédéric Mila, Andreas Honecker
SciPost Phys. 3, 005 (2017) ·
published 18 July 2017

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Quantum Monte Carlo simulations provide one of the more powerful and
versatile numerical approaches to condensed matter systems. However, their
application to frustrated quantum spin models, in all relevant temperature
regimes, is hamstrung by the infamous "sign problem." Here we exploit the fact
that the sign problem is basisdependent. Recent studies have shown that
passing to a dimer (twosite) basis eliminates the sign problem completely for
a fully frustrated spin model on the twoleg ladder. We generalize this result
to all partially frustrated twoleg spin1/2 ladders, meaning those where the
diagonal and leg couplings take any antiferromagnetic values. We find that,
although the sign problem does reappear, it remains remarkably mild throughout
the entire phase diagram. We explain this result and apply it to perform
efficient quantum Monte Carlo simulations of frustrated ladders, obtaining
accurate results for thermodynamic quantities such as the magnetic specific
heat and susceptibility of ladders up to L=200 rungs (400 spins 1/2) and down
to very low temperatures.