Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians

In a recent contribution [Phys. Rev. B 81, 165104 (2010)] fermionic Projected Entangled-Pair States (PEPS) were used to approximate the ground state of free and interacting spinless fermion models, as well as the $t$-$J$ model. This paper revisits these three models in the presence of an additional next-nearest hopping amplitude in the Hamiltonian. First we explain how to account for next-nearest neighbor Hamiltonian terms in the context of fermionic PEPS algorithms based on simulating time evolution. Then we present benchmark calculations for the three models of fermions, and compare our results against analytical, mean-field, and variational Monte Carlo results, respectively. Consistent with previous computations restricted to nearest-neighbor Hamiltonians, we systematically obtain more accurate (or better converged) results for gapped phases than for gapless ones.Comment: 10 pages, 11 figures, minor change

RVB superconductors with fermionic projected entangled pair states

We construct a family of simple fermionic projected entangled pair states (fPEPS) on the square lattice with bond dimension $D=3$ which are exactly hole-doped resonating valence bond (RVB) wavefunctions with short-range singlet bonds. Under doping the insulating RVB spin liquid evolves immediately into a superconductor with mixed $d+is$ pairing symmetry whose pair amplitude grows as the square-root of the doping. The relative weight between $s$-wave and $d$-wave components can be controlled by a single variational parameter $c$. We optimize our ansatz w.r.t. $c$ for the frustrated $t-J_1-J_2$ model (including both nearest and next-nearest neighbor antiferromagnetic interactions $J_1$ and $J_2$, respectively) for $J_2\simeq J_1/2$ and obtain an energy very close to the infinite-PEPS state (using full update optimization and same bond dimension). The orbital symmetry of the optimized RVB superconductor has predominant d-wave character, although we argue a residual (complex s-wave) time reversal symmetry breaking component should always be present. Connections of the results to the physics of superconducting cuprates and pnictides are outlined.Comment: 6 pages, 4 figures and Supplemental Material (3 pages, 2 figures). Updated version including new iPEPS results using full update optimization scheme, showing excellent agreement with RVB wave functio

Prenatal intuitive coparenting behaviors

Micro-analytic research on intuitive parenting behaviors has shed light on the temporal dynamics of parent and child interactions. Observations have shown that parents possess remarkable implicit communicative abilities allowing them to adapt to the clues infants give and therefore stimulate the development of many of the infants' abilities, such as communication skills. This work focused on observing intuitive parenting behaviors that were synchronized and coordinated between the parents. We call them prenatal intuitive coparenting behaviors and used an observation task - the Prenatal Lausanne Trilogue Play procedure - to observe them. For this task, the parents role-play their first encounter with their future baby, represented by a doll. Two cases from a study on pregnancy after assisted reproductive technology are provided to illustrate how these behaviors manifest themselves. The observations from the first case suggest that expectant parents can offer the baby a coparental framework, whereas the observations from the second case show that opportunities for episodes of prenatal intuitive coparenting can be missed due to certain relationship dynamics.These kinds of observations deepen our knowledge of the prenatal emergence of the coparenting relationship and allow us to hone our strategies for intervening during pregnancy with couples who experience coparenting difficulties. Furthermore, these observations provide a novel and complementary perspective on prenatal intuitive parenting and coparenting behaviors

High-resolution geophysical surveying at the Springfield Fault, New Zealand

To trace the active Springfield Fault (South Island, New Zealand) and map its character at shallow depths on a terrace where it exhibits no surface expression, we recorded 3-D georadar data across an approximately rectangular 110 x 40 m survey area. In addition, we carried out multi-electrode geoelectric measurements along a 198 m long profile that crossed the georadar survey area. Although the georadar depth penetration was limited to only ~5 m, the processed images revealed the presence of a prominent reflecting horizon disrupted by three main discontinuities. Semi-continuous subhorizontal reflection patterns were interpreted to represent sedimentary units within the fluvial deposits, whereas three detected discontinuities were interpreted as fault traces with small near-vertical offsets (~0.4 m). This interpretation was supported by vertical and lateral changes visible on the final inverted resistivity model indicating lithological boundaries and fault branches

Symmetry projection schemes for Gaussian Monte Carlo methods

A novel sign-free Monte Carlo method for the Hubbard model has recently been proposed by Corney and Drummond. High precision measurements on small clusters show that ground state correlation functions are not correctly reproduced. We argue that the origin of this mismatch lies in the fact that the low temperature density matrix does not have the symmetries of the Hamiltonian. Here we show that supplementing the algorithm with symmetry projection schemes provides reliable and accurate estimates of ground state properties.Comment: 10 pages, 3 figure

Thermodynamic properties of the Shastry-Sutherland model from quantum Monte Carlo simulations

We investigate the minus-sign problem that afflicts quantum Monte Carlo (QMC) simulations of frustrated quantum spin systems, focusing on spin S=1/2, two spatial dimensions, and the extended Shastry-Sutherland model. We show that formulating the Hamiltonian in the diagonal dimer basis leads to a sign problem that becomes negligible at low temperatures for small and intermediate values of the ratio of the inter- and intradimer couplings. This is a consequence of the fact that the product state of dimer singlets is the exact ground state both of the extended Shastry-Sutherland model and of a corresponding "sign-problem-free" model, obtained by changing the signs of all positive off-diagonal matrix elements in the dimer basis. By exploiting this insight, we map the sign problem throughout the extended parameter space from the Shastry-Sutherland to the fully frustrated bilayer model and compare it with the phase diagram computed by tensor-network methods. We use QMC to compute with high accuracy the temperature dependence of the magnetic specific heat and susceptibility of the Shastry-Sutherland model for large systems up to a coupling ratio of 0.526(1) and down to zero temperature. For larger coupling ratios, our QMC results assist us in benchmarking the evolution of the thermodynamic properties by systematic comparison with exact diagonalization calculations and interpolated high-temperature series expansions.Comment: 13 pages including 10 figures; published version with minor changes and correction

Comment on "Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice" by Poletti D. et al

In a recent letter [D. Poletti et al., EPL 93, 37008 (2011)] a model of attractive spinless fermions on the honeycomb lattice at half filling has been studied by mean-field theory, where distinct homogenous phases at rather large attraction strength $V>3.36$, separated by (topological) phase transitions, have been predicted. In this comment we argue that without additional interactions the ground states in these phases are not stable against phase separation. We determine the onset of phase separation at half filling $V_{ps}\approx 1.7$ by means of infinite projected entangled-pair states (iPEPS) and exact diagonalization.Comment: 2 pages, 1 figur

Entanglement renormalization and boundary critical phenomena

The multiscale entanglement renormalization ansatz is applied to the study of boundary critical phenomena. We compute averages of local operators as a function of the distance from the boundary and the surface contribution to the ground state energy. Furthermore, assuming a uniform tensor structure, we show that the multiscale entanglement renormalization ansatz implies an exact relation between bulk and boundary critical exponents known to exist for boundary critical systems.Comment: 6 pages, 4 figures; for a related work see arXiv:0912.164