Spin-ordered ground state and thermodynamic behaviors of the spin-32kagome Heisenberg antiferromagnet

Abstract

Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the √ 3 × √ 3 state (i.e., the state with 120 • spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m s = 1/3, 23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T 2 behavior, and the susceptibility approaches a finite constant as T → 0. Our TN results of thermodynamic properties are compared with those from high temperature series expansion. In addition, we disclose a quantum phase transition between q = 0 state (i.e. the state with 120 • spin configuration within a unit cell containing three sites) and √ 3 × √ 3 state in a spin-3/2 kagome XXZ model at the critical point ∆ c = 0.54. This study provides reliable and useful information for further explorations on high spin kagome physics.

Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin S

“…As briefly discussed in the introduction, more sophisticated GS methods such as the CCM and the DMRG yield evidence that for S = 1 semiclassical magnetic LRO is also lacking [25,[38][39][40][41][42]. On the other hand, recent results obtained by CCM, tensor network approaches, and series expansion indicate weak GS √ 3 × √ 3 LRO for S = 3/2 [25,38,43,45]. Previous experience in applying the RGM on frustrated quantum antiferromagnets, see, e.g., [16,83,86,95,97] and references therein, indicate, however, that the implementation of rotational invariance by setting Ŝ z i = 0 in the equations of motions may overestimate the tendency to melt semiclassical GS magnetic LRO in RGM calculations.…”

“…Meanwhile also for spin quantum number S = 1 there is evidence that the KHAF does not exhibit magnetic LRO [25,[38][39][40][41][42]. Recently it has been argued that there is a route to magnetic GS LRO in the KHAF as increasing the spin quantum number to S ≥ 3/2, see [25,38,43,45].…”

Quantum Monte Carlo study of the spin-1/2 honeycomb Heisenberg model with mixed antiferromagnetic and ferromagnetic interactions in external magnetic fields

“…For instance, by searching for exotic states of matter or studying quantum phase transitions (QPTs), people usually invoke this model with different interactions on various lattices as prototypes. To name but a few, quantum spin liquid is thought to exist in spin-1/2 AF Heisenberg models on lattices with geometrical frustrations, but its nature is still under active debate [1][2][3][4][5][6][7][8]; whether exotic phase transitions beyond the traditional Landau-Ginzburg-Wilson framework [9] exist or not were also discussed by introducing more complex interactions or by tuning the spatial anisotropy in coupling strength; and so on.…”

Emergence of magnetic order in kagomé antiferromagnets

“…(also DMRG) [38]. Results for the s =3 /2K A F Ma r eEg/(NJs 2 )=−1.253022 (series expansions) [34], −1.26798 (CCM) [19,35], and −1.265(2) (tensor network) [39]. CCM calculations [19,35] also indicate that the ground-state energy scales with s (for s ≥ 3/2) via the following equation,…”