Lukas Weber, Andreas Honecker, Bruce Normand, Philippe Corboz, Frédéric Mila, Stefan Wessel
SciPost Phys. 12, 054 (2022) ·
published 8 February 2022
|
· pdf
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
|
· pdf
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.
