Abstract
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.
Highlights
(inset) are coupled by intra-trimer interactions J1, J2, and J3 and to all spins in the nearest-neighbor unit cells by the same inter-trimer interaction, J
In place of the dimers forming the basic components of the FFB, the fully frustrated inter-trimer couplings (FFTL) is composed of trimer unit cells, whose internal frustration can be varied from zero at J2 = 0 to maximal at J1 = J2 = J3, and we will demonstrate that rich physics emerges from this internal degree of freedom
We have applied our algorithm to the S = 1/2 Heisenberg antiferromagnet on the FFTL, where it performs efficient and sign-problem-free simulations up to large system sizes, allowing us to investigate the full finite-temperature physics of this model
Summary
The SSE QMC method offers a highly efficient means of simulating quantum spin systems It is based on expressing the quantum Boltzmann operator as an infinite-order high-temperature expansion with evaluated, positive coefficients [18]. While formulating the SSE in an alternative basis is straightforward, finding a directed-loop Monte Carlo update scheme that works efficiently in a given basis often is not. To date such update schemes have typically been implemented by hand-crafting loop processes describing the physics of the model to the chosen basis; this situation makes the exploration of new bases, for any of the three reasons listed above, a somewhat tedious task.
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