arXiv subjects

Matthias Troyer

Publications and source records attributed to Matthias Troyer.

At least 235 records · Page 13Linked to original sources

arXiv1998

The Two-Dimensional S=1 Quantum Heisenberg Antiferromagnet at Finite Temperatures

The temperature dependence of the correlation length, susceptibilities and the magnetic structure factor of the two-dimensional spin-1 square lattice quantum Heisenberg antiferromagnet are computed by the quantum Monte Carlo loop algorithm (QMC). In the experimentally relevant temperature regime the theoretically predicted asymptotic low temperature behavior is found to be not valid. The QMC results however, agree reasonably well with the experimental measurements of La2NiO4 even without considering anisotropies in the exchange interactions.

cond-mat.stat-mech↗

arXiv1998

Universal critical temperature for Kosterlitz-Thouless transitions in bilayer quantum magnets

Recent experiments show that double layer quantum Hall systems may have a ground state with canted antiferromagnetic order. In the experimentally accessible vicinity of a quantum critical point, the order vanishes at a temperature T_{KT} = κH, where H is the magnetic field and κis a universal number determined by the interactions and Berry phases of the thermal excitations. We present quantum Monte Carlo simulations on a model spin system which support the universality of κand determine its numerical value. This allows experimental tests of an intrinsically quantum-mechanical universal quantity, which is not also a property of a higher dimensional classical critical point.

cond-mat.str-el↗

arXiv1998

Thermodynamics of Random Ferromagnetic Antiferromagnetic Spin-1/2 Chains

Using the quantum Monte Carlo Loop algorithm, we calculate the temperature dependence of the uniform susceptibility, the specific heat, the correlation length, the generalized staggered susceptibility and magnetization of a spin-1/2 chain with random antiferromagnetic and ferromagnetic couplings, down to very low temperatures. Our data show a consistent scaling behavior in all the quantities and support strongly the conjecture drawn from the approximate real-space renormalization group treatment.A statistical analysis scheme is developed which will be useful for the search of scaling behavior in numerical and experimental data of random spin chains.

cond-mat↗

arXiv1998

Thermodynamics of the one-dimensional SU(4) symmetric spin-orbital model

The ground state properties and the thermodynamics of the one-dimensional SU(4) symmetric spin system with orbital degeneracy are investigated using the quantum Monte Carlo loop algorithm. The spin-spin correlation functions exhibit a 4-site periodicity, and their low temperature behavior is controlled by two correlation lengths that diverge like the inverse temperature, while the entropy is linear in temperature and its slope is consistent with three gapless modes of velocity $π/2$. The physical implications of these results are discussed.

cond-mat↗

arXiv1998

Quantum Monte Carlo Simulation of the Trellis Lattice Heisenberg Model for SrCu$_2$O$_3$ and CaV$_2$O$_5$

We study the spin-1/2 trellis lattice Heisenberg model, a coupled spin ladder system, both by perturbation around the dimer limit and by quantum Monte Carlo simulations. We discuss the influence of the inter-ladder coupling on the spin gap and the dispersion, and present results for the temperature dependence of the uniform susceptibility. The latter was found to be parameterized well by a mean-field type scaling ansatz. Finally we discuss fits of experimental measurements on SrCu$_2$O$_3$ and CaV$_2$O$_5$ to our results.

cond-mat.str-el↗

arXiv1998

Spin-spin Correlation lengths of Bilayer Antiferromagnets

The spin-spin correlation length and the static structure factor for bilayer antiferromagnets, such as YBa$_2$Cu$_3$O$_{6}$, are calculated using field theoretical and numerical methods. It is shown that these quantities can be directly measured in neutron scattering experiments using energy integrated two-axis scan despite the strong intensity modulation perpendicular to the layers. Our calculations show that the correlation length of the bilayer antiferromagnet diverges considerably more rapidly, as the temperature tends to zero, than the correlation length of the corresponding single layer antiferromagnet typified by La$_2$CuO$_4$. This rapid divergence may have important consequences with respect to magnetic fluctuations of the doped superconductors.

cond-mat.str-el↗

arXiv1997

Quantum Monte Carlo Loop Algorithm for the t-J Model

We propose a generalization of the Quantum Monte Carlo loop algorithm to the t-J model by a mapping to three coupled six-vertex models. The autocorrelation times are reduced by orders of magnitude compared to the conventional local algorithms. The method is completely ergodic and can be formulated directly in continuous time. We introduce improved estimators for simulations with a local sign problem. Some first results of finite temperature simulations are presented for a t-J chain, a frustrated Heisenberg chain, and t-J ladder models.

cond-mat.str-el↗

arXiv1997

Asymptotic scaling of the square lattice quantum Heisenberg antiferromagnet

We present thermodynamic measurements of various physical observables of the two dimensional S=1/2 isotropic quantum Heisenberg antiferromagnet on a square lattice, obtained by quantum Monte Carlo. In particular we have been able to measure the infinite volume limit of the uniform susceptibility up to the inverse temperature beta=40, the analysis of which reveals the correct asymptotic behavior in excellent agreement with the prediction of chiral perturbation theory. The controversy over the existence of a crossover from quantum critical to renormalized classical regime is resolved.

cond-mat.str-el↗

arXiv1997

Temperature dependent correlation length for the S=1/2 Quantum Heisenberg Antiferromagnet on the square lattice

We present an analysis of high precision Monte Carlo data for the two dimensional S=1/2 quantum Heisenberg antiferromagnet up to $ξ= 95.7(3)$ obtained by the continuous time version of the loop algorithm. Our data are in good agreement with a prediction of the recent theory (Phys. Rev. Lett. vol. 77, 3439 (1996)) in very high temperature regime, but they strongly disagree with it in the low temperature regime.

cond-mat.stat-mech↗

arXiv1997

Quantum critical exponents of a planar antiferromagne

We present high precision estimates of the exponents of a quantum phase transition in a planar antiferromagnet. This has been made possible by the recent development of cluster algorithms for quantum spin systems, the loop algorithms. Our results support the conjecture that the quantum Heisenberg antiferromagnet is in the same universality class as the O(3) nonlinear sigma model. The Berry phase in the Heisenbrg antiferromagnet do not seem to be relevant for the critical behavior.

cond-mat.str-el↗

arXiv1997

Critical exponents of the quantum phase transition in a planar antiferromagnet

We have performed a large scale quantum Monte Carlo study of the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9 structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical exponents beta, nu and eta agree within our errors with the classical 3D O(3) exponents, expected from a mapping to the nonlinear sigma model. This confirms the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously irrelevant.

cond-mat.str-el↗

arXiv1996

Nearly critical ground state of LaCuO2.5

Using a combination of analytical techniques and Quantum Monte Carlo simulations we investigate the coupled spin ladder system LaCuO2.5. At a critical ratio of the interladder to intraladder coupling (J'/J)_c \approx 0.11 we find a quantum phase transition between a Neel ordered and a disordered state. At criticality the uniform susceptibility behaves as χ(T)=aT^2 with a universal prefactor. At intermediate temperatures the system crosses over to a ``decoupled ladders regime'' with pseudo-gap type behavior, similar to uncoupled ladders. This can explain the gap-like experimental data for the magnetic susceptibility of LaCuO2.5 despite the presence of the long range Neel order.

cond-mat↗

arXiv1996

Susceptibility and Low Temperature Thermodynamics of Spin-1/2 Heisenberg Ladders

The temperature dependence of the uniform susceptibility and the ground state energy of antiferromagnetic Heisenberg ladders with up to 6 legs has been calculated, using the Monte Carlo loop algorithm. The susceptibilities of even-leg-ladders show spin gaps while these of odd-leg-ladders remain finite in the zero temperature limit. For small ratios of intra- to inter-leg couplings, odd-leg-ladders can be mapped at low temperatures to single chains. For equal couplings, the logarithmic corrections at low temperatures increase markedly with the number of legs.

cond-mat↗

arXiv1995

Phase diagram of depleted Heisenberg model for CaV4O9

We have numerically investigated the 1/5-depleted Heisenberg square lattice representing CaV4O9 using the Quantum Monte Carlo loop algorithm. We have determined the phase diagram of the model as a function of the ratio of the two different couplings: bonds within a plaquette and dimer bonds between plaquettes. By calculating both the spin gap and the staggered magnetization we determine the range of stability of the long range ordered (LRO) phase. At isotropic coupling LRO survives the depletion. But the close vicinity of the isotropic point to the spin gap phase leads us to the conclusion that already a small frustrating next nearest neighbor interaction can drive the system into the quantum disordered phase and thus explain the spin gap behavior of CaV4O9.

cond-mat↗

arXiv1995

Properties of lightly doped t-J two-leg ladders

We have numerically investigated the doped t-J ladder using exact diagonalization. We have studied both the limit of strong inter-chain coupling and isotropic coupling. The ladder scales to the Luther-Emery liquid regime in the strong inter-chain coupling limit. In this strong coupling limit there is a simple picture of the excitation spectrum that can be continued to explain the behavior at isotropic coupling. At J=0 we have indications of a ferromagnetic ground state. At a large $J/t$ the ladder is phase separated into holes and a Heisenberg ladder. At intermediate coupling the ground state shows hole pairing with a modified d-wave symmetry. The excitation spectrum separates into a limited number of quasiparticles which carry charge $+|e|$ and spin ${1\over 2}$ and a triplet magnon mode. At half-filling the former vanish but the latter evolves continuously into the magnon band of the spin liquid. At low doping the quasiparticles form a dilute Fermi gas with a strong attraction but simultaneously the Fermi wave vector, as would be measured in photoemission, is large. The dynamical structure factors are calculated and are found to be very similar to calculations on 2D clusters.

cond-mat↗

arXiv1995

Effect of the Three-Site Hopping Term on the t-J Model

We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional {t-J} model including the three-site hopping term derived from the strong coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the {t-J} and Hubbard models. Phase separation, which exists in the t-J model is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values $J/t<2$. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at $J/t>2.8$ in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.

cond-mat↗

arXiv1994

Singlet Stripe Phases in the planar t-J Model

The energies of singlet stripe phases in which a plane is broken up into spin liquid ladders by lines of holes, is examined. If the holes were static then patterns containing spin liquids with a finite spin gap are favored. The case of dynamic holes is treated by assembling t-J ladders oriented perpendicular to the stripes. For a wide region around $J/t \approx 1$ the hole-hole correlations in a single ladder are found to be predominantly charge density wave type but an attraction between hole pairs on adjacent ladders leads to a stripe phase. A quantum mechanical melting of the hole lines at smaller $J/t$ values leads to a Bose condensate of hole pairs, i.e. a superconducting phase.

cond-mat↗

arXiv1994

Thermodynamics and spin gap of the Heisenberg ladder calculated by the look-ahead Lanczos algorithm

We have developed an improved version of the quantum transfer matrix algorithm. The extreme eigenvalues and eigenvectors of the transfer matrix are calculated by the recently developed look-ahead Lanczos algorithm for non-Hermitian matrices with higher efficiency and accuracy than by the power method. We have applied this method to the Heisenberg ladder. The temperature dependence of the susceptibility, specific heat, correlation length and nuclear spin relaxation rate $1/T_1$ are calculated. Our results support the existence of a spin gap of about $0.5 J$. The preprint is submitted as a uuencoded compressed PostScript file. In case of printing problems the original TeX file (without figures) can be retrieved by anonymous ftp to 'maggia.ethz.ch' filename 'CSSP/preprints/hblad.tex'. Alternatively from June 1, 1994 by WWW: URL "http://www.ips.id.ethz.ch/CSSP/preprints.html"

cond-mat↗