Lukas Weber, Andreas Honecker, Bruce Normand, Philippe Corboz, Frédéric Mila, Stefan Wessel
SciPost Phys. 12, 054 (2022) ·
published 8 February 2022
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The phase diagrams of highly frustrated quantum spin systems can exhibit
first-order quantum phase transitions and thermal critical points even in the
absence of any long-ranged magnetic order. However, all unbiased numerical
techniques for investigating frustrated quantum magnets face significant
challenges, and for generic quantum Monte Carlo methods the challenge is the
sign problem. Here we report on a general quantum Monte Carlo approach with a
loop-update scheme that operates in any basis, and we show that, with an
appropriate choice of basis, it allows us to study a frustrated model of
coupled spin-1/2 trimers: simulations of the trilayer Heisenberg
antiferromagnet in the spin-trimer basis are sign-problem-free when the
intertrimer couplings are fully frustrated. This model features a first-order
quantum phase transition, from which a line of first-order transitions emerges
at finite temperatures and terminates in a thermal critical point. The trimer
unit cell hosts an internal degree of freedom that can be controlled to induce
an extensive entropy jump at the quantum transition, which alters the shape of
the first-order line. We explore the consequences for the thermal properties in
the vicinity of the critical point, which include profound changes in the lines
of maxima defined by the specific heat. Our findings reveal trimer quantum
magnets as fundamental systems capturing in full the complex thermal physics of
the strongly frustrated regime.
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 basis-dependent. Recent studies have shown that
passing to a dimer (two-site) basis eliminates the sign problem completely for
a fully frustrated spin model on the two-leg ladder. We generalize this result
to all partially frustrated two-leg spin-1/2 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.
