Two-dimensional Quantum Antiferromagnets Research Articles

High T c cuprates as two-dimensional quantum antiferromagnets

The systematic evolution of the temperature-dependent resistivity R(T) in La 2−¢Sr ¢CuO 4 has been succesfully described over a wide temperature and composition range. Two important assumptions have been used to achieve a good quantitative fit of the R(T) curves: (i) the conductivity σ of the layered high T c cuprates is dominated by the universal two-dimensional quantum conductivity σ 2 D ≌ 4 e 2/ h x ln( Lø/ l) and (ii) the inelastic length Lø is given by the magnetic correlation length Lø ≌ ξ ≌ exp( J/T) of the two-dimensional quantum Heisenberg antiferromagnet. The enigmatic T-linear in-phase resistivity R( T) is then explained as a result of the mutual cancellation of the two inverse functions ( ln and exp), which leads to a linear R vs T dependence with the slope being inversely proportional to the exchange coupling J.

QED 3 and two-dimensional superconductivity without parity violation

We investigate a recently proposed parity-invariant model of two-dimensional superconductivity. The model consists of two-species of fermions coupled with opposite sign to an abelian gauge field and is closely related to QED 3. The first part of the paper is devoted to a detailed analysis of the relevant properties of QED 3. In particular we study the dynamical generation of a parity-conserving fermion mass and the finite-temperature symmetry restoration transition. We show how the parity-invariant model arises as an effective long-wavelength theory of the dynamics of holes in a two-dimensional quantum antiferromagnet. The model exhibits type-II superconductivity without parity or time-reversal symmetry violation, a high value of 2 Δ/ k B T c, flux quantization with quantum hc/2 e and a two-dimensional Meissner effect. We discuss the possible relevance of this model to the high- T c superconductors

Low-temperature properties of two-dimensional frustrated quantum antiferromagnets.

Though much of the recent work on 2D quantum canted antiferromagnets has been devoted to the study of disordered states, there is evidence that some of these systems have N\'eel ground states, even for spin 1/2. Following Chakravarty, Halperin, and Nelson, we study the quantum nonlinear sigma model suited to these systems and obtain, for the correlation length, \ensuremath{\xi}=${\mathit{C}}_{\ensuremath{\xi}}$[A/(${\mathit{k}}_{\mathit{B}}$T${)}^{1/2}$]${\mathit{e}}_{\mathit{B}}^{2\mathrm{\ensuremath{\pi}}\mathit{B}/\mathit{k}}$T, where A and B depend on the spin stiffness and spin-wave velocities renormalized by quantum fluctuations. We discuss experiments on $^{3}\mathrm{He}$ adsorbed on Grafoil.

Variational description of a quasihole excitation in a quantum antiferromagnet.

An accurate variational ansatz is proposed for a single quasihole excitation in a two-dimensional quantum antiferromagnet. The trial state includes spin-hole and spin-hole-spin correlations, in addition to background antiferromagnetic spin-spin correlations. Background spin-spin correlations are induced by the Heisenberg antiferromagnetic exchange interaction and describe the zero-point motion of spin waves around the Ne\ifmmode\acute\else\textasciiacute\fi{}el state. Spin-hole and spin-hole correlations describe ``strings'' of spins displaced by one lattice site along the hole path. This is a generalization of the Brinkman-Rice approach to include quantum spin fluctuations. We have used the Monte Carlo method to compute the variational energy and the spectral weight of the quasihole state in the t-J model on the square lattice, with the proposed ansatz. Comparison with exact results for the 4\ifmmode\times\else\texttimes\fi{}4 lattice shows very good agreement for both energy and spectral weight, at k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2) in the range 0\ensuremath{\le}t/J\ensuremath{\le}5. We report results for lattices of several sizes up to 16\ifmmode\times\else\texttimes\fi{}16 in the above range of t/J and for the two values of k where the hole energy band attains its minimum [k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)] and maximum [k=(0,0)].

Crossover and order-disorder transition of two-dimensional quantum antiferromagnets at low temperatures.

We study the low-temperature behavior of quantum antiferromagnets in two space dimensions. Our model is the quantum nonlinear \ensuremath{\sigma} model (NL\ensuremath{\sigma}M), which is the long-wavelength limit of the two-dimensional quantum Heisenberg model. Introducing fermion fields in NL\ensuremath{\sigma}M, we propose a model of doped antiferromagnets. We show that renormalization-group theory predicts an order-disorder transition at finite hole concentration ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$. Very small doping changes the temperature dependence of the correlation length \ensuremath{\xi} from exponential to power law, \ensuremath{\xi}\ensuremath{\propto}1/T, for hole concentration \ensuremath{\delta}${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$. We also discuss a crossover between classical and quantum regions with varying coupling constant g.

Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model.

The Ising model on a three-dimensional cubic lattice with all plaquettes in the x-y frustrated plane is studied by use of a Monte Carlo technique; the exchange constants are of equal magnitude, but have varying signs. At zero temperature, the model has a finite entropy and no long-range order. The low-temperature phase is characterized by an order parameter measuring the ${\mathit{openZ}}_{4}$ symmetry of lattice rotations which is invariant under Mattis gauge transformation; fluctuations lead to the alignment of frustrated bonds into columns and a fourfold degeneracy. An additional factor-of-2 degeneracy is obtained from a global spin flip. The order vanishes at a critical temperature by a transition that appears to be in the universality class of the D=3, XY model. These results are consistent with the theoretical predictions of Blankschtein et al. This Ising model is related by duality to phenomenological models of two-dimensional frustrated quantum antiferromagnets.

Spectral function of a single hole in a two-dimensional quantum antiferromagnet.

The spectral function of a single hole moving in a two-dimensional antiferromagnetic background is calculated, using the self-consistent Born approximation for the self-energy. For small systems, good agreement is found with the results of exact diagonalization studies. In the thermodynamic limit, the quasiparticle residue, the effective mass, and the incoherent multiple spin-wave background are determined as functions of the ratio of Heisenberg exchange J and hopping amplitude t. The relevance of the single-hole results to the physical problem of a finite hole concentration is briefly discussed.

Quantum Monte Carlo Simulations of Models Related to High-Tc Superconductivity on a Transputer Network

Much of the insight into the low temperature behaviour of two-dimensional quantum antiferromagnets has been recently obtained by extensive Monte Carlo. These models are relevant in the study of the magnetic behaviour of high Tc compounds containing copper-oxide layers. While of little technical importance, the physical properties of these models are certainly important for the understanding of the new type of behaviour that leads to superconductivity under certain conditions.

Coherent motion of a hole in high-temperature superconductors

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional quantum antiferromagnet is discussed. We investigate the hole motion for the t - J model. The influence of spin fluctuations in the ground state on the hole motion is also considered. The calculations are based on the introduction of a new trial wave function. It generalizes a wave function which was originally proposed by Shraiman and Siggia for the motion in the pure Néel state. The different mechanisms for the coherent propagation are treated on the same footing. Due to spin fluctuations in the ground state the excitation energy for the hole has a bandwidth, which is reduced by a factor 0.7 as compared to the case without spin fluctuations.

A single hole in a quantum antiferromagnet: selfconsistent Green’s function approach

We solved numerically the integral equation for the selfenergy which describes the motion of a single hole in a two-dimensional quantum antiferromagnet (AF) within the selfconsistent Born approximation. This formulation stresses the similarity of the AF-spin polaron with the standard polaron problem. We confine our calculation to finite cluster geometries and compare with results from previous exact diagonalization studies. The spectral function is characterized by a narrow quasiparticle (qp) peak at the low energy side of the spectra, which appears to be well separated from the incoherent band part for large enough J values. For small J we find a reduced width of ~7t for the incoherent band. The bottom of the coherent qp band always occurs at (±π/2, ±π/2). Its bandwidth initially increases with J until J≃t and then decreases as 2t2/J. A complete characterization of our solution is given, including the dispersion relation and effective masses of this quasiparticle. The comparison with exact diagonalization studies for a 4×4 cluster is remarkably good. From our results we see that a lattice of 16×16 sites describes adequately the thermodynamic limit. We conclude that the simple Born approximation is a valuable scheme to characterize the dynamics of one hole in the t-J model. both in the perturbative and the strong coupling regimes.

Series investigations of magnetically disordered ground states in two-dimensional frustrated quantum antiferromagnets.

An extensive series-expansion study of the square-lattice, spin-1/2 Heisenberg antiferromagnet with nearest- and second-neighbor couplings has been carried out to investigate the nature of the ground state for ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\approxeq}1/2. In agreement with an earlier numerical study along similar lines, we find that the magnetically disordered phase exhibits columnar spontaneous dimerization, but the magnitude of such order may not be as large as had been suggested previously. Although the magnetically disordered phase is not critical, it appears to have both spin-spin and energy-energy correlations of range greater than a few lattice spacings. The possibility of ``spin-nematic'' order, as proposed by Chandra, Coleman, and Larkin, has not been directly ruled out, but the balance of circumstantial evidence weighs against it in this system.

Coherent motion of a hole in a two-dimensional quantum antiferromagnet

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional quantum antiferromagnet is discussed. The system is described by two model Hamiltonians, thet-J model and thet-t′-J model, which have been used frequently to discuss strong electron-correlation effects present in high-T c superconductors. The calculations are based on the introduction of a new wave function which is constructed by use of equations derived by Shraiman and Siggia. The different mechanisms for the coherent propagation, which are due to the spin fluctuation and the hopping terms of the Hamiltonian, are treated on the same footing. As a result of the inclusion of an effective hopping mechanism along spiral paths-first discussed by Trugman-the minimum of the band is somewhat changed compared to results recently obtained in the literature. For large values of the ratiot/J an inversion of the whole dispersion relation occurs. The overall shapes of the dispersion within both models are found to agree quite well, though for small values oft/J the bandwidth within thet-J model becomes significantly smaller than that of thet-t′-J model.

Microscopic calculation of dynamical correlations in two-dimensional quantum antiferromagnets at low temperature (abstract)

We calculate the spin-spin relaxation function for a two-dimensional quantum antiferromagnet at low temperature from first principles. The calculation justifies the picture of the system as a weakly interacting Bose gas of spin waves. The long wavelength behavior at T=0 is qualitatively consistent with hydrodynamic predictions based upon the existence of long-range order, although the spin-wave velocity contains nontrivial dynamical shifts that cannot be calculated from thermodynamic parameters.

Erratum: Microscopic calculation of the dynamical correlations in two-dimensional quantum antiferromagnets at low temperaturesT=0 results [Phys. Rev. Lett. 63, 1004 (1989)

Erratum: Microscopic calculation of the dynamical correlations in two-dimensional quantum antiferromagnets at low temperatures<i>T</i>=0 results [Phys. Rev. Lett. 63, 1004 (1989)

Microscopic calculation of the dynamical correlations in two-dimensional quantum antiferromagnets at low temperatures: T=0 results.

Calcul de la fonction de relaxation spin-spin pour un antiferromagnetique quantique bidimensionnel de spin arbitraire a basse temperature. Le calcul justifie l'image des excitations du systeme comme un gaz de Base des ondes de spin interagissant faiblement

Sine-Gordon theory of the non-Néel phase of two-dimensional quantum antiferromagnets.

We examine a recently developed sine-Gordon model description of the non-N\'eel phase of quantum antiferromagnets on two-dimensional bipartite lattices. Using a spatial dimensionality d=1+\ensuremath{\epsilon} expansion we argue that the model always scales to its strong-coupling limit and displays spin Peierls or valence-bond-solid order. The structure of the theory in this strong-coupling limit bears a remarkable resemblance to a fermionic large-N limit of the nearest-neighbor SU(N) antiferromagnet.

Monte‐Carlo Study of Two‐Dimensional Quantum Antiferromagnets with Random Anisotropies and Spin S = 1

physica status solidi (b)Volume 153, Issue 1 p. K79-K84 Short Note Monte-Carlo Study of Two-Dimensional Quantum Antiferromagnets with Random Anisotropies and Spin S = 1 S. S. Aplesnin, S. S. Aplesnin L. V. Kirenskii Institute of Physics, Academy of Sciences of the USSR, Siberian Branch, Krasnoyarsk Search for more papers by this author S. S. Aplesnin, S. S. Aplesnin L. V. Kirenskii Institute of Physics, Academy of Sciences of the USSR, Siberian Branch, Krasnoyarsk Search for more papers by this author First published: 1 May 1989 https://doi.org/10.1002/pssb.2221530158Citations: 1 SU-660036 Krasnoyarsk, USSR. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume153, Issue11 May 1989Pages K79-K84 RelatedInformation

Exact-diagonalization study of the effective model for holes in the planar antiferromagnet.

The effective single-band Hamiltonian for holes in the two-dimensional quantum antiferromagnet, relevant for the ${\mathrm{CuO}}_{2}$ layers in copper-oxide superconductors, is studied by the exact diagonalization of a finite-size system with 16 cells. Single- and two-hole ground-state properties are calculated. Pair-binding-energy and hole-density correlation functions indicate that two holes bind for moderate exchange interactions, even in the case of the extreme anisotropic-Ising limit.

A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state

We continue the study of valence-bond solid antiferromagnetic quantum Hamiltonians. These Hamiltonians are invariant under rotations in spin space. We prove that a particular two-dimensional model from this class (the spin-3/2 model on the hexagonal lattice) has a unique ground state in the infinite-volume limit and hence no Neel order. Moreover, all truncated correlation functions decay exponentially in this ground state. We also characterize all the finite-volume ground states of these models (in every dimension), and prove that the two-point correlation function of the spin-2 square lattice model with periodic boundary conditions has exponential decay.

Absence of the Hopf invariant in the long-wavelength action of two-dimensional quantum antiferromagnets.

Contrary to recent theoretical suggestions, we show that the long-wavelength action of a two-dimensional quantum antiferromagnet on a square lattice can be mapped onto a classical (2+1) nonlinear $\ensuremath{\sigma}$ model without any additional topological term.