Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets

TL;DR

This paper introduces a sign-problem-free quantum Monte Carlo method in the trimer basis to study frustrated quantum magnets, revealing first-order quantum phase transitions and thermal critical points with complex thermal behavior.

Contribution

The authors develop a novel quantum Monte Carlo approach in the trimer basis that overcomes the sign problem for frustrated models, enabling detailed study of phase transitions.

Findings

Identification of a first-order quantum phase transition in the frustrated trilayer model.

Discovery of a finite-temperature line of first-order transitions ending at a thermal critical point.

Observation of significant changes in specific heat maxima near the critical point.

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.