Magnetic susceptibility of quantum spin systems calculated by sine square deformation: One-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets

Abstract

We develop a simple and unbiased numerical method to obtain the uniform susceptibility of quantum many body systems. When a Hamiltonian is spatially deformed by multiplying it with a sine square function that smoothly decreases from the system center toward the edges, the sizescaling law of the excitation energy is drastically transformed to a rapidly converging one. Then, the local magnetization at the system center becomes nearly size independent; the one obtained for the deformed Hamiltonian of a system length as small as L ∼ 10 provides the value obtained for the original uniform Hamiltonian of L ∼ 100. This allows us to evaluate a bulk magnetic susceptibility by using the magnetization at the center by existing numerical solvers without any approximation, parameter tuning, or the size-scaling analysis. We demonstrate that the susceptibilities of the spin-1/2 antiferromagnetic Heisenberg chain and square lattice obtained by our scheme at L ∼ 10 agree within 10 −3 with exact analytical and numerical solutions for L = ∞ down to temperature of 0.1 times the coupling constant. We apply this method to the spin-1/2 kagome lattice Heisenberg antiferromagnet which is of prime interest in the search of spin liquids.

Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu3(OH)6Cl2

“…Although our results for herbertsmithite comply with the recent convergence of models toward a Dirac spin liquid, we note, for completeness, that (i) very recent results from series expansion [31] and exact diagonalizations [43] point to a maximum of the susceptibility at T (χ max ) of the order of 0.1 − 0.15 J, significantly lower than our value ∼ 0.3 J. If confirmed, these results would signal that herbertsmithite is possibly not as close to the ideal case as one could believe and, as a counterpart, the behavior of the susceptibility is dramatically sensitive to other details in the Hamiltonian.…”

“…The main reason lies in the existence of a proliferation of states close-by in energy which have led to theoretical proposals spanning from valence bond crystals [24] -made of local spin dimers-to spin liquids, either gapped like the resonating valence bond state, or not, like the Dirac U(1) spin liquid [25]. Each novel round in the debate has resulted from challenging developments of the numerical techniques [26][27][28][29][30][31][32][33]. While Density Matrix Renomalization Group (DMRG) first concluded that a gapped RVB state could be stabilized [27,28], variational Monte-Carlo (VMC) [29] methods, exact diagonalizations (ED) for a 48 spins cluster [30], "grand canonical analysis" [31] and further works using DMRG suggested that this is in fact not the case, recently pointing to a gapless Dirac state [32] which is also found using Tensor Network States (TNS) [33].…”

Fine structure of heating in a quasiperiodically driven critical quantum system

“…In order to make analytical progress, we compensate for the lack of time and space translation symmetry by allowing ourselves access to the infinitely generated conformal symmetry group. Concretely, we study a driven conformal field theory (CFT), where the time-evolution operator alternates between a uniform (1 + 1)-dimensional CFT and one of its nonhomogeneous versions known as sine-square deformation (SSD) [17][18][19][20][21][22], first introduced in the context of lattice systems as an efficient way to suppress boundary effects [23][24][25][26][27][28]. This setup has been previously studied with a periodic Floquet drive, where it displays a rich phase diagram with both heating and nonheating phases [29][30][31].…”

Dimensional reduction in quantum spin-1/2 system on a 1/7-depleted triangular lattice

“…Such development of peak is the characteristic feature of the two-dimensional highly frustrated antiferromagnet, e.g. a kagome lattice ones 47 .…”

“…where besides J 1d xy one can adjust J 1d z > J 1d xy to fit the susceptibility as well as the spin gap. The temperature dependence of χ is obtained by a size-free calculation using a sine-square deformation combined with the TPQ method 47 which gives χ of the thermodynamic limit.…”