Infinite coherence time of edge spins in finite-length chains

Motivated by the recent observation that exponentially long coherence times can be achieved for edge spins in models with strong zero modes, we study the impact of level crossings in finite-length spin chains on the dynamics of the edge spins. Focussing on the XY spin-1=2 chain with transverse or longitudinal magnetic field, two models relevant to understand recent experimental results on cobalt adatoms, we show that the edge spins can remain coherent for an infinite time even for a finite-length chain if the magnetic field is tuned to a value at which there is a level crossing. Furthermore, we show that the edge spins remain coherent for any initial state for the integrable case of transverse field because all states have level crossings at the same value of the field, while the coherence time is increasingly large for lower temperatures in the case of longitudinal field, which is non-integrable.Comment: 7 pages, 6 figure

Anticollinear magnetic order induced by impurities in the frustrated Heisenberg model of pnictides

We present Monte Carlo simulations for a classical antiferromagnetic Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) exchange couplings on the square lattice in the presence of non-magnetic impurities. We show that the order-by-disorder entropy selection, associated with the Ising-like phase transition that appears for $J_2/J_1>1/2$ in the pure spin model, is quenched at low temperature due to the presence of non-magnetic impurities. Evidences that a new competing order is stabilized around the impurities, and in turn induces a re-entrance phase transition are reported. Implications for local magnetic measurement of the parent compound of iron pnictides are briefly discussed

Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets

Motivated by the possibility to load multi-color fermionic atoms in optical lattices, we study the entropy dependence of the properties of the one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model of the SU(N) Hubbard model with one particle per site (filling 1/N). Using continuous-time world line Monte Carlo simulations for N=2 to 5, we show that characteristic short-range correlations develop at low temperature as a precursor of the ground state algebraic correlations. We also calculate the entropy as a function of temperature, and we show that the first sign of short-range order appears at an entropy per particle that increases with N and already reaches 0.8k_B at N=4, in the range of experimentally accessible values.Comment: 5 pages, 3 figures, 2 table

Semiclassical approach to ground-state properties of hard-core bosons in two dimensions

Motivated by some inconsistencies in the way quantum fluctuations are included beyond the classical treatment of hard-core bosons on a lattice in the recent literature, we revisit the large-S semi-classical approach to hard-core bosons on the square lattice at T=0. First of all, we show that, if one stays at the purely harmonic level, the only correct way to get the 1/S correction to the density is to extract it from the derivative of the ground state energy with respect to the chemical potential, and that to extract it from a calculation of the ground state expectation value of the particle number operator, it is necessary to include 1/\sqrt{S} corrections to the harmonic ground state. Building on this alternative approach to get 1/S corrections, we provide the first semiclassical derivation of the momentum distribution, and we revisit the calculation of the condensate density. The results of these as well as other physically relevant quantities such as the superfluid density are systematically compared to quantum Monte Carlo simulations. This comparison shows that the logarithmic corrections in the dilute Bose gas limit are only captured by the semi-classical approach if the 1/S corrections are properly calculated, and that the semi-classical approach is able to reproduce the 1/k divergence of the momentum distribution at k=0. Finally, the effect of 1/S^2 corrections is briefly discussed.Comment: 14 pages, 8 figure

Floating, critical and dimerized phases in a frustrated spin-3/2 chain

We study spontaneous dimerization and emergent criticality in a spin-3/2 chain with antiferromagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$ and three-site $J_3$ interactions. In the absence of three-site interaction $J_3$, we provide evidence that the model undergoes a remarkable sequence of three phase transitions as a function of $J_2/J_1$, going successively through a critical commesurate phase, a partially dimerized gapped phase, a critical floating phase with quasi-long-range incommensurate order, to end up in a fully dimerized phase at very large $J_2/J_1$. In the field theory language, this implies that the coupling constant of the marginal operator responsible for dimerization changes sign three times. For large enough $J_3$, the fully dimerized phase is stabilized for all $J_2$, and the phase transitions between the critical phases and this phase are both Wess-Zumino-Witten (WZW) SU(2)$_3$ along part of the boundary and turn first order at some point due to the presence of a marginal operator in the WZW SU(2)$_3$ model. By contrast, the transition between the two dimerized phase is always first order, and the phase transitions between the partially dimerized phase and the critical phases are Kosterlitz-Thouless. Finally, we discuss the intriguing spin-1/2 edge states that emerge in the partially dimerized phase for even chains. Unlike their counterparts in the spin-1 chain, they are not confined and disappear upon increasing $J_2$ in favour of a reorganization of the dimerization pattern.Comment: 14 pages, 23 figure

Variational Monte-Carlo investigation of SU(NN) Heisenberg chains

Motivated by recent experimental progress in the context of ultra-cold multi-color fermionic atoms in optical lattices, we have investigated the properties of the SU($N$) Heisenberg chain with totally antisymmetric irreducible representations, the effective model of Mott phases with $m < N$ particles per site. These models have been studied for arbitrary $N$ and $m$ with non-abelian bosonization [I. Affleck, Nuclear Physics B 265, 409 (1986); 305, 582 (1988)], leading to predictions about the nature of the ground state (gapped or critical) in most but not all cases. Using exact diagonalization and variational Monte-Carlo based on Gutzwiller projected fermionic wave functions, we have been able to verify these predictions for a representative number of cases with $N \leq 10$ and $m \leq N/2$, and we have shown that the opening of a gap is associated to a spontaneous dimerization or trimerization depending on the value of m and N. We have also investigated the marginal cases where abelian bosonization did not lead to any prediction. In these cases, variational Monte-Carlo predicts that the ground state is critical with exponents consistent with conformal field theory.Comment: 9 pages, 10 figures, 3 table