Numerical investigation on the strongly-frustrated quantum spin systems

Kenn Kubo, Tota Nakamura

Sanzo Miyazawa, M. S. Makivić, T. Horiki +1 more

Cynthia J. Olson, Gergely Zaránd, Gergely T. Zimányi

Lukas Weber, A. Honecker, Bruce Normand +3 more

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.

Dillon Liu

In this thesis, the physics of two systems is investigated, both of which support unconventional phases of matter. We investigate a frustrated system which has a classical spin liquid regime in the paramagnetic phase. We also consider a periodically-driven, disordered system and explore nonequilibrium regimes. Both systems exhibit macroscopic behaviour which differs strongly from the behaviour in standard scenarios. First, the properties of frustrated magnets and related systems are discussed. We introduce three-dimensional generalisations of a well-studied two-dimensional frustrated system. These generalisations consist of coupled layers of two-dimensional triangular lattice Ising antiferromagnets. We study three stackings that have nearest-neighbour interactions: two frustrated stackings (abc and abab) and the unfrustrated stacking (aaa). We use a combination of methods, including numerics and analytics, to show that these generalisations exhibit a strongly correlated, highly fluctuating regime known as a classical spin liquid. We show this by investigating the structure factor and correlations directly and by describing a mapping to a continuum field theory that gives further clarity about the classical spin liquid regime using a renormalisation group analysis and consideration of low-lying excitations in these systems. Second, we study the response of a disordered system to a time-periodic driving potential. We start in the context of Mott's work on a.c. conductivity in Anderson insulators and move beyond this to study the Floquet (long-time) regimes beyond linear response. Using Landau-Zener physics, we construct a description of the various regimes which are possible. We also present the results of thorough numerical studies of these systems.

Makoto Kaburagi, Takashi Tonegawa, T. Nishino