Meron-Cluster Solution of Fermion and Other Sign Problems

Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Important examples include QCD and other field theories at non-zero chemical potential, at non-zero vacuum angle, or with an odd number of flavors, as well as the Hubbard model for high-temperature superconductivity and quantum antiferromagnets in an external magnetic field. In all these cases standard simulation algorithms require an exponentially large statistics in large space-time volumes and are thus impossible to use in practice. Meron-cluster algorithms realize a general strategy to solve severe sign problems but must be constructed for each individual case. They lead to a complete solution of the sign problem in several of the above cases.Comment: 15 pages,LATTICE9

Systematic Effective Field Theory Investigation of Spiral Phases in Hole-Doped Antiferromagnets on the Honeycomb Lattice

Motivated by possible applications to the antiferromagnetic precursor of the high-temperature superconductor Na$_x$CoO$_2\cdot$yH$_2$O, we use a systematic low-energy effective field theory for magnons and holes to study different phases of doped antiferromagnets on the honeycomb lattice. The effective action contains a leading single-derivative term, similar to the Shraiman-Siggia term in the square lattice case, which gives rise to spirals in the staggered magnetization. Depending on the values of the low-energy parameters, either a homogeneous phase with four or a spiral phase with two filled hole pockets is energetically favored. Unlike in the square lattice case, at leading order the effective action has an accidental continuous spatial rotation symmetry. Consequently, the spiral may point in any direction and is not necessarily aligned with a lattice direction.Comment: 10 pages, 6 figure

Spiral phases and two-particle bound states from a systematic low-energy effective theory for magnons, electrons, and holes in an antiferromagnet

We have constructed a systematic low-energy effective theory for hole- and electron-doped antiferromagnets, where holes reside in momentum space pockets centered at $(\pm\frac{\pi}{2a},\pm\frac{\pi}{2a})$ and where electrons live in pockets centered at $(\frac{\pi}{a},0)$ or $(0,\frac{\pi}{a})$. The effective theory is used to investigate the magnon-mediated binding between two holes or two electrons in an otherwise undoped system. We derive the one-magnon exchange potential from the effective theory and then solve the corresponding two-quasiparticle Schr\"odinger equation. As a result, we find bound state wave functions that resemble $d_{x^2-y^2}$-like or $d_{xy}$-like symmetry. We also study possible ground states of lightly doped antiferromagnets.Comment: 2 Pages; Proc. of SCES'07, Housto

Constraint Effective Potential of the Staggered Magnetization in an Antiferromagnet

We employ an improved estimator to calculate the constraint effective potential of the staggered magnetization in the spin $\tfrac{1}{2}$ quantum Heisenberg model using a loop-cluster algorithm. The first and second moment of the probability distribution of the staggered magnetization are in excellent agreement with the predictions of the systematic low-energy magnon effective field theory. We also compare the Monte Carlo data with the universal shape of the constraint effective potential of the staggered magnetization and study its approach to the convex effective potential in the infinite volume limit. In this way the higher-order low-energy parameter $k_0$ is determined from a fit to the numerical data

Random RNA under tension

The Laessig-Wiese (LW) field theory for the freezing transition of random RNA secondary structures is generalized to the situation of an external force. We find a second-order phase transition at a critical applied force f = f_c. For f f_c, the extension L as a function of pulling force f scales as (f-f_c)^(1/gamma-1). The exponent gamma is calculated in an epsilon-expansion: At 1-loop order gamma = epsilon/2 = 1/2, equivalent to the disorder-free case. 2-loop results yielding gamma = 0.6 are briefly mentioned. Using a locking argument, we speculate that this result extends to the strong-disorder phase.Comment: 6 pages, 10 figures. v2: corrected typos, discussion on locking argument improve