A quantum magnetic analogue to the critical point of water

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

“…In particular, we are able to identify a first-order transition line emerging from a first-order quantum phase transition, which in the FFTL separates two distinct AFM ground states. Similar to the physics of the FFB and SSL [28,34], we show that the firstorder line of the FFTL is also terminated by a critical point, which we identify as belonging to the 2D Ising universality class. This phenomenology shares several similarities to the well known phase diagram of water, in which the line of first-order transitions in the pressuretemperature plane is terminated by a critical point belonging to the 3D Ising universality class.…”

“…In place of the dimers forming the basic components of the FFB, the FFTL is composed of trimer unit cells, whose internal frustration can be varied from zero at J 2 = 0 to maximal at J 1 = J 2 = J 3 , and we will demonstrate that rich physics emerges from this internal degree of freedom. Finding this physics in a real material is likely to be a two-step process: although the geometry of the FFB has to date been realized only in a system with non-Heisenberg spin interactions [39], almost exactly the same physics is found in the compound SrCu 2 (BO 3 ) 2 [34]. Similarly, while it is unlikely that a real material would possess the precise inter-trimer bonding of Fig.…”

“…In the example of the FFB, the spin dimers shape the ground-state phase diagram, which is divided into a dimer-singlet quantum disordered and a dimer-triplet antiferromagnetic (AFM) phase, separated by a first-order quantum phase transition [33]. At finite temperature, it was observed that this transition persists, forming a first-order line, which terminates at a critical point [28], a scenario that has immediate parallels [34] to the liquid-gas [35], ferromagnetic [36], and Mott transitions [37].…”

“…Our observations thus establish the FFTL as a generic quantum spin model in which to explore the full complexity of the thermal physics uncovered in Refs. [28,34], by the unbiased numerical technique of sign-free QMC simulations. Taken together, these provide us with the basis on which to understand the differences between the superficially distinct forms of thermodynamic behavior in certain quantum magnets and in water.…”

Automatic differentiation applied to excitations with projected entangled pair states

“…While the iPEPS ansatz is best known for its use in ground-state simulations, also recently new extensions have emerged that target low-lying excited states [12] as well as thermal states [13][14][15][16][17][18][19]. The excitation ansatz for iPEPS, based on its one-dimensional MPS equivalent [20][21][22][23], offers the possibility to accurately simulate quasiparticle excitations on top of a strongly correlated ground state.…”