arXiv subjects

B. Bernu

Publications and source records attributed to B. Bernu.

31 records · Page 2Linked to original sources

arXiv2005

Path Integral Calculations of exchange in solid 4He

Recently there have been experimental indications that solid 4He might be a supersolid. We discuss the relation of supersolid behavior to ring exchange. The tunnelling frequencies for ring exchanges in quantum solids are calculated using Path Integral Monte Carlo by finding the free energy for making a path that begins with the atoms in one configuration and ends with a permutation of those positions. We find that the exchange frequencies in solid 4He are described by a simple lattice model which does not show supersolid behavior. Thus, the PIMC calculations constrain the mechanism for the supersolid behavior. We also look at the characteristics of very long exchanges needed for macroscopic mass transport.

cond-mat.other↗

arXiv2004

Ring exchanges and the supersolid phase of 4He

Using Path Integral Monte Carlo we calculate exchange frequencies in bulk hcp 4He as atoms undergo ring exchange. We fit the frequencies to a lattice model and examine whether such atoms could become a supersolid, that is have a non-classical rotational inertia. We find that the scaling with respect to the number of exchanging atoms is such that superfluid behavior will not be observed in a perfect 4He crystal.

cond-mat.stat-mech↗

arXiv2004

The Magnetic Ordering of the 3d Wigner Crystal

Using Path Integral Monte Carlo, we have calculated exchange frequencies as electrons undergo ring exchanges of 2, 3 and 4 electrons in a ``clean'' 3d Wigner crystal (bcc lattice) as a function of density. We find pair exchange dominates and estimate the critical temperature for the transition to antiferromagnetic ordering to be roughly $1 \times 10^{-8}$Ry at melting. In contrast to the situation in 2d, the 3d Wigner crystal is different from the solid bcc 3He in that the pair exchange dominates because of the softer interparticle potential. We discuss implications for the magnetic phase diagram of the electron gas.

cond-mat.str-el↗

arXiv2003

Multi-spin exchange model the near melting transition of the 2D Wigner crystal

The low temperature properties of fermionic solids are governed by spin exchanges. Near the melting transition, the spin-exchange energy increases as well as the relative contribution of large loops. In this paper, we check the convergence of the multi-spin exchange model and the validity of the Thouless theory near the melting of the Wigner crystal in two dimensions. Exchange energies are computed using Path Integral Monte Carlo for loop sizes up to 8, at $r_s=40$, 50 and 75. The data are then fitted to a geometric model. Then the exchange energies are extrapolated to larger sizes in order to evaluate their contributions to the leading term of the magnetic susceptibility and the specific heat. These results are used to check the convergence of the multi-spin exchange model.

cond-mat.str-el↗

arXiv2003

Determination of the exchange energies in Li2VOSiO4 from a high-temperature series analysis of the square lattice J1-J2 Heisenberg model

We present a high-temperature expansion (HTE) of the magnetic susceptibility and specific heat data of Melzi et al. on Li2VOSiO4 [Phys. Rev. B 64, 024409 (2001)]. The data are very well reproduced by the J1-J2 Heisenberg model on the square lattice with exchange energies J1=1.25+-0.5 K and J2=5.95+-0.2 K. The maximum of the specific heat Cv^{max}(T_{max}) is obtained as a function J2/J1 from an improved method based on HTE.

cond-mat.str-el↗

arXiv2000

Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions

We have developed a new method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system and the low-temperature expected behavior of the specific heat as well as the ground-state energy. By the choice of an appropriate variable (entropy as a function of energy), a stable interpolation scheme between low and high temperature is performed. Contrary to previous methods, the constraint that the total entropy is log(2S+1) for a spin S on each site is automatically satisfied. We present some applications to quantum spin models on one- and two- dimensional lattices. Remarkably, in most cases, a good accuracy is obtained down to zero temperature.

cond-mat.str-el↗

arXiv2000

Exchange Frequencies in the 2d Wigner crystal

Using Path Integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a ``clean'' 2d Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for r_s \leq 175 \pm 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.

cond-mat.str-el↗

arXiv1998

Spin Liquid in the Multiple-Spin Exchange model on the Triangular lattice: 3He on graphite

Using exact diagonalizations, we investigate the T=0 phase diagram of the Multi-Spin Exchange (MSE) model on the triangular lattice: we find a transition separating a ferromagnetic phase from a non-magnetic gapped Spin Liquid phase. Systems far enough from the ferromagnetic transition have a metamagnetic behavior with magnetization plateaus at m/m_sat=0 and 1/2. The MSE has been proposed to describe solid 3He films adsorbed onto graphite, thus we compute the MSE heat capacity for parameters in the low density range of the 2nd layer and find a double-peak structure.

cond-mat.str-el↗

arXiv1998

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic ($ΔS=1$) excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic ($ΔS=0$) excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets.

cond-mat.stat-mech↗

arXiv1997

Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis

A group symmetry analysis of the low lying levels of the spin-1/2 kagomé Heisenberg antiferromagnet is performed for small samples up to N=27. This approach allows to follow the effect of quantum fluctuations when the sample size increases. The results contradict the scenario of ``order by disorder'' which has been advanced on the basis of large S calculations. A large enough second neighbor ferromagnetic exchange coupling is needed to stabilize the $\sqrt 3 \times \sqrt 3$ pattern: the finite size analysis indicates a quantum critical transition at a non zero coupling.

cond-mat.str-el↗

arXiv1996

Molecular Dissociation in Hot, Dense Hydrogen

We present a path-integral Monte Carlo study of dissociation in dense hydrogen ($1.75 \leq r_s \leq 2.2$, with $r_s$ the Wigner sphere radius). As temperature is lowered from $10^5$ to 5000 K, a molecular hydrogen gas forms spontaneously from a neutral system of protons and electrons. At high density, $r_s < 2.0$, thermally activated dissociation is accompanied by decreasing pressure, signaling the presence of a first order transition and critical point. The decrease in electron kinetic energy during dissociation is responsible for the pressure decrease and transition. At lower density the phase transition disappears.

cond-mat↗

arXiv1995

$J_1-J_2$ quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder

On the triangular lattice, for $J_2/J_1$ between $1/8$ and $1$, the classical Heisenberg model with first and second neighbor interactions presents four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and Jolicoeur\cite{cj92} and Korshunov\cite{k93} suggest that quantum fluctuations select amongst these states a colinear two-sublattice order. From theoretical requirements, we develop the full symmetry analysis of the low lying levels of the spin-1/2 Hamiltonian in the hypotheses of either a four or a two-sublattice order. We show on the exact spectra of periodic samples ($N=12,16$ and $28$) how quantum fluctuations select the colinear order from the four-sublattice order.

cond-mat↗

arXiv1994

Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice

Exact spectra of periodic samples are computed up to $ N=36 $. Evidence of an extensive set of low lying levels, lower than the softest magnons, is exhibited. These low lying quantum states are degenerated in the thermodynamic limit; their symmetries and dynamics as well as their finite-size scaling are strong arguments in favor of Néel order. It is shown that the Néel order parameter agrees with first-order spin-wave calculations. A simple explanation of the low energy dynamics is given as well as the numerical determinations of the energies, order parameter and spin susceptibilities of the studied samples. It is shown how suitable boundary conditions, which do not frustrate Néel order, allow the study of samples with $ N=3p+1 $ spins. A thorough study of these situations is done in parallel with the more conventional case $ N=3p $.

cond-mat↗