Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet

Abstract

We consider the finite-temperature phase diagram of the S = 1/2 frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of firstorder transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer and the dimer-singlet state terminates on the first-order line, giving a quantum critical end point, and we use tensor-network calculations to follow the first-order discontinuities in its vicinity. possible at T = 0, on top of which thermal fluctuations may cause qualitatively different physics to set in. The model we investigate is represented schematically in the insets of Fig. 1. In addition to the interaction, J ⊥ , defining the dimer unit and the intralayer interaction, J , defining the two planes of the system, we include a symmetrical, diagonal, and frustrating interlayer coupling, J × . Only antiferromagnetic couplings are considered. The Hamiltonian for any quantum spin S iswhere i is the dimer bond index, j denotes the nearestneighbor dimers in the bilayer, m = 1 and 2 denote the two layers, and m is the layer opposite to m.Our initial focus is the fully frustrated bilayer (FFB), J × = J . In this situation, Eq. (1) can be reexpressed as

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

“…For small and intermediate coupling ratios, J/J D , the ground state is an exact product of singlets formed on the dimer bonds [7]. This is a property that the Shastry-Sutherland model shares with the fully frustrated S = 1/2 bilayer square lattice [33][34][35][36][37][38]. Because the sign problem is completely absent in the fully frustrated bilayer [30,31,33], we consider an extended model [27,39] defined by the Hamiltonian…”

“…(1)], and in (2)]. The ground state is clearly a dimer-singlet phase at small inter-dimer couplings and a square-lattice antiferromagnetic phase at large J; this latter phase becomes an effective S = 1 square-lattice antiferromagnet in the bilayer limit (J 2 /J = 1) [33]. Only near the opposite (Shastry-Sutherland) limit does a small regime of a third phase appear, the intermediate "plaquette" phase (inset, Fig.…”

A quantum magnetic analogue to the critical point of water

“…We note that the phonon contribution (Cp(T )/T ∝ T 2 ) to the measured specific heat becomes appreciable at higher temperatures; while this can be subtracted for accurate fitting [16], our focus here is on the peak positions at and below 6 K. e, Convergence of the critical coupling ratio obtained in finite-temperature iPEPS calculations as a function of 1/D; the extrapolated value of 0.67(1) agrees well with the zero-temperature value [14]. The finite-temperature critical point has been discussed theoretically in a two-dimensional (2D) Heisenberg spin model, the "fully frustrated bilayer" [27]. In this geometry, which has no known materials analogue, spin pairs (with coupling J ⊥ ) are arranged vertically on a square lattice with equal couplings (J ) to both spins of all four dimer neighbours, and the ground state jumps discontinuously from exact dimer singlets to exact triplets at J ⊥ /J = 2.315.…”

“…In this geometry, which has no known materials analogue, spin pairs (with coupling J ⊥ ) are arranged vertically on a square lattice with equal couplings (J ) to both spins of all four dimer neighbours, and the ground state jumps discontinuously from exact dimer singlets to exact triplets at J ⊥ /J = 2.315. With increasing temperature, the discontinuity in triplet density reduces until the line of first-order transitions terminates at a critical point, in the 2D Ising universality class, when k B T c 0.52J [27]. The connection [28] between the two fully frustrated geometries (bilayer and Shastry-Sutherland) suggests that they may share similar critical-point physics.…”

Frustrated spin- 12 Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the J1−J2−J

“…The resulting spin- 1 2 J 1 -J 2 -J ⊥ 1 model on a squarelattice bilayer has received much less attention [103,104] than either of the limiting cases δ = 0 or κ = 0 [86][87][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102] discussed above. We note, however, that a very recent paper [105] studied the case where frustration is introduced instead via an interlayer NNN AFM J ⊥ 2 bond, resulting in a J 1 -J ⊥ 1 -J ⊥ 2 model, with very different properties and behavior (and see also Ref. [106]).…”