Low Temperature Behavior and Crossovers of the Square Lattice Quantum Heisenberg Antiferromagnet

Kim, Jaekwon; Troyer, Matthias

doi:10.1103/physrevlett.80.2705

Cited by 166 publications

(172 citation statements)

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“…Because of both advances in computational techniques and the implementation of finite-size scaling methods, QMC data now exist for ξ/a for the S = 1/2 nn 2DSLQHA for length scales varying from 1 to 350,000 lattice constants. QMC results of Beard et al [13] and Kim and Troyer [14] are plotted in Fig. 7 together with our experimental results in La 2 CuO 4 .…”

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confidence: 99%

“…This has, in fact, been confirmed in detail experimentally [10]; specifically, over a wide range of length scales the 2D correlation length measured in Sr 2 CuO 2 Cl 2 agrees quantitatively with results from quantum Monte Carlo (QMC) calculations carried out on the Hamiltonian Eq. (1) with S=1/2 [12][13][14]. The value for J for Sr 2 CuO 2 Cl 2 listed in Table (1) is deduced from two magnon Raman scattering measurements [15].…”

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confidence: 99%

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Instantaneous spin correlations inLa2CuO4

et al. 1999

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We have carried out a neutron scattering study of the instantaneous spin-spin correlations in La2CuO4 (TN = 325 K) over the temperature range 337 K to 824 K. Incident neutron energies varying from 14.7 meV to 115 meV have been employed in order to guarantee that the energy integration is carried out properly. The results so-obtained for the spin correlation length as a function of temperature when expressed in reduced units agree quantitatively both with previous results for the two dimensional (2D) tetragonal material Sr2CuO2Cl2 and with quantum Monte Carlo results for the nearest neighbor square lattice S=1/2 Heisenberg model. All of the experimental and numerical results for the correlation length are well described without any adjustable parameters by the behavior predicted for the quantum non-linear sigma model in the low temperature renormalized classical regime. The amplitude, on the other hand, deviates subtly from the predicted low temperature behavior. These results are discussed in the context of recent theory for the 2D quantum Heisenberg model. The physics of low dimensional quantum Heisenberg antiferromagnets has been the subject of research ever since the advent of modern quantum and statistical mechanics [1,2]. Interest in two dimensional (2D) systems was heightened by the discovery of high temperature superconductivity in the lamellar copper oxides [3]. Specifically, it was realized early on that the parent compounds such as La 2 CuO 4 correspond to rather good approximations to the S=1/2 2D square-lattice quantum Heisenberg antiferromagnet (2DSLQHA) [4,5]. It seems at least possible that the 2D magnetism may in some way be essential to the superconductivity in the charge carrier doped cuprates. Further, the magnetism itself is of fundamental interest as a quantum many body phenomenon in lower dimensions.Early experiments by Endoh and co-workers [5] showed that over a wide range of temperatures above the three dimensional Néel ordering transition in La 2 CuO 4+y (that is, La 2 CuO 4 with a small amount of excess oxygen) the instantaneous spin-spin correlations were purely two dimensional and that the correlation length diverged exponentially in 1/T. This led to a flurry of theoretical activity [2] including most especially work based on the quantum non-linear sigma model (QNLσM) by Chakravarty, Halperin and Nelson (CHN) [6] and Hasenfratz and Niedermayer (HN) [7]. These theories are all based on the 2D Heisenberg Hamiltonian which for nearest neighbor (nn) interactions alone takes the formwhere the summation is over nn pairs on a square lattice. In La 2 CuO 4 , for temperatures below the tetragonal (I4/mmm) -orthorhombic (Bmab) structural phase transition temperature of T st = 530 K, the leading terms in the spin Hamiltonian [8,9] areHere, α nnn , α xy , α ⊥j , and α DM represent the reduced next nearest neighbor in-plane Heisenberg exchange coupling, XY anisotropy, interlayer coupling and Dzyaloshinski-Moriya antisymmetric exchange, respectively, and S c i is the c component of the spin at site...

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Instantaneous spin correlations inLa2CuO4

et al. 1999

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“…In particular open questions still exist [13][14][15][16] on the low-temperature region, where the spin correlation length becomes of the order of 10 2 lattice spacings and the real magnets are seen to develop macroscopic areas of correlated spins.…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature ordering in two-dimensional magnets

et al. 2000

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We study the two dimensional quantum Heisenberg antiferromagnet on the square lattice with easyaxis exchange anisotropy. By the semiclassical method called pure-quantum self-consistent harmonic approximation we analyse several thermodynamic quantities and investigate the existence of a finite temperature transition, possibly describing the low-temperature critical behaviour experimentally observed in many layered real compounds. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of 10 −2 J (J being the intra-layer exchange integral), as in most experimental situations. On the other hand, typical features of the isotropic Heisenberg model are observed for both values of anisotropy considered, one in the quasi-isotropic limit and the other in a more markedly easy-axis region. The good agreement found between our theoretical results and the experimental data relative to the real compound Rb2MnF4 shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the experimental data, thus allowing to recognize in such anisotropy the main agent for the observed onset of finite temperature long-range order.

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“…Specifically, the spin-1/2 Heisenberg model on the square lattice is the appropriate model for understanding the undoped precursors of high T c cuprates (undoped antiferromagnets). Second, because of the availability of efficient Monte Carlo algorithms as well as the increased power of computing resources, properties of undoped antiferromagnets on geometrically non-frustrated lattices can be simulated with unprecedented accuracy [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] . As a consequence, these models are particular suitable for examining theoretical predictions and exploring ideas.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model

Jiang

2012

Phys. Rev. B

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Motivated by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of ρs12L and ρs22L, where L stands for the spatial box size used in the simulations and ρsi with i ∈ {1, 2} is the spin-stiffness in the i-direction. Remarkably, while we observe a large correction to scaling for the observable ρs12L, the data for ρs22L exhibit a good scaling behavior without any indication of a large correction. As a consequence, we are able to obtain a numerical value for the critical exponent ν which is consistent with the known O(3) result with moderate computational effort. Further, we additionally carry out an unconventional finitesize scaling analysis with which we assume that the ratio of the spatial winding numbers squared is fixed through all simulations. The theoretical correctness of our idea is argued and its validity is confirmed. Using this unconventional finite-size scaling method, even from ρs1L which receives the most serious correction among the observables considered in this study, we are able to arrive at a value for ν consistent with the expected O(3) value. A detailed investigation to compare these two finite-size scaling methods should be performed.

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Low Temperature Behavior and Crossovers of the Square Lattice Quantum Heisenberg Antiferromagnet

Cited by 166 publications

References 29 publications

Instantaneous spin correlations inLa2CuO4

Instantaneous spin correlations inLa2CuO4

Finite-temperature ordering in two-dimensional magnets

Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model

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