Research

Scientific Interests

Strongly correlated systems, including heavy fermion materials and transition metal oxides; valence bond descriptions of Mott insulator physics; quantum phase transitions; simulation techniques for interacting electrons and quantum magnets; modern C++ libraries for use in computational physics

Recent Work

The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study

K. S. D. Beach, Fabien Alet, Matthieu Mambrini, and Sylvain Capponi

We present exact numerical results for the square-lattice SU(N) Heisenberg model, computed using a singlet projector algorithm that is not restricted to integer values of N. Finite-size scaling of the data suggests a direct, continuous phase transition between a Néel-ordered phase and a crystalline bond-ordered phase at a single critical value N_c=4.57(5) with critical exponents z=1 and β/ν = 0.81(3). LINK

Coherence and metamagnetism in the two-dimensional Kondo lattice model

K. S. D. Beach and F. F. Assaad

We report the results of dynamical mean field calculations for the metallic Kondo lattice model subject to an applied magnetic field. High-quality spectral functions reveal that the picture of rigid, hybridized bands, Zeeman-shifted in proportion to the field strength, is qualitatively correct. We find evidence of a zero-temperature magnetization plateau, whose onset coincides with the chemical potential entering the spin up hybridization gap. The plateau appears at the field scale predicted by (static) large-N mean field theory and has a magnetization value consistent with that of x=1-n_c spin-polarized heavy holes, where n_c < 1 is the conduction band filling of the noninteracting system. We argue that the emergence of the plateau at low temperature marks the onset of quasiparticle coherence. LINK

Comment on “Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets”

K. S. D. Beach, Matthieu Mambrini, and Fabien Alet

Quantum Monte Carlo methods are sophisticated numerical techniques for simulating interacting quantum systems. In some cases, however, they suffer from the notorious "sign problem" and become too inefficient to be useful. A recent publication [J. Wojtkiewicz, Phys. Rev. B 75, 174421 (2007)] claims to have solved the sign problem for a certain class of frustrated quantum spin systems through the use of a bipartite valence bond basis. We show in this Comment that the apparent positivity of the path integral is due to a misconception about the resolution of the identity operator in this basis, and that consequently the sign problem remains a severe obstacle for the simulation of frustrated quantum magnets. LINK

Mean Field study of the heavy fermion metamagnetic transition

S. Viola Kusminskiy, K. S. D. Beach, A. H. Castro Neto, and David K. Campbell

We investigate the evolution of the heavy fermion ground state under application of a strong external magnetic field. We present a richer version of the usual hybridization mean field theory that allows for hybridization in both the singlet and triplet channels and incorporates a self-consistent Weiss field. We show that for a magnetic field strength B*, a filling-dependent fraction of the zero-field hybridization gap, the spin up quasiparticle band becomes fully polarized—an event marked by a sudden jump in the magnetic susceptibility. The system exhibits a kind of quantum rigidity in which the susceptibility (and several other physical observables) are insensitive to further increases in field strength. This behavior ends abruptly with the collapse of the hybridization order parameter in a first-order transition to the normal metallic state. We argue that the feature at B* corresponds to the "metamagnetic transition" in YbRh₂Si₂. Our results are in good agreement with recent experimental measurements. LINK

Valence bond description of the long-range, nonfrustrated Heisenberg chain

K. S. D. Beach

The Heisenberg chain with antiferromagnetic, powerlaw exchange has a quantum phase transition separating spin liquid and Neel ordered phases at a critical value of the powerlaw exponent alpha. The behaviour of the system can be explained rather simply in terms of a resonating valence bond state in which the amplitude for a bond of length r goes as 1/r^α for α < 1, as 1/r^(1+α)/2 for 1 < α < 3, and as 1/r² for α > 3. Numerical evaluation of the staggered magnetic moment and Binder cumulant reveals a second order transition at α_c = 2.18(5), in excellent agreement with quantum Monte Carlo. The divergence of the magnetic correlation length is consistent with an exponent ν = 2/(3-α_c) = 2.4(2). LINK

Master equation approach to computing RVB bond amplitudes

K. S. D. Beach

We describe a “master equation” analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner dictated by the spin hamiltonian under consideration) toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J₁–J₂ antiferromagnetic Heisenberg model. Without frustration (J₂=0), the amplitudes are radially symmetric and fall off as 1/r³ in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J₂/J₁ < 0.418. It fails when the r=(2,1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J₂/J₁ = 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry. LINK