Dynamics of one-dimensional Bose liquids: Andreev-like reflection at Y-junctions and absence of the Aharonov-Bohm effect

We study one dimensional Bose liquids of interacting ultracold atoms in the Y-shaped potential when each branch is filled with atoms. We find that the excitation packet incident on a single Y-junction should experience a negative density reflection analogous to the Andreev reflection at normal-superconductor interfaces, although the present system does not contain fermions. In a ring interferometer type configuration, we find that the transport is completely insensitive to the (effective) flux contained in the ring, in contrast to the Aharonov-Bohm effect of a single particle in the same geometry.Comment: 4 pages, 2 figures, final versio

Quantum phase transitions in three-leg spin tubes

We investigate the properties of a three-leg quantum spin tube using several techniques such as the density matrix renormalization group method, strong coupling approaches and the non linear sigma model. For integer spins S, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of 2S phase transitions. They can be accurately identified by the behavior of a non local string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions are further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases S = 1. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first order phase transition but at the close proximity of a tricritical point separating a gapless and a first order transition line in the phase diagram of the quantum spin tube.Comment: 20 pages, 18 figure

Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.Comment: 6 pages, LaTeX 2.09, 3 PostScript figure

Fractional statistics and duality: strong tunneling behavior of edge states of quantum Hall liquids in the Jain sequence

While the values for the fractional charge and fractional statistics coincide for fractional Hall (FQH) states in the Laughlin sequence, they do not for more general FQH states, such as those in the Jain sequence. This mismatch leads to additional phase factors in the weak coupling expansion for tunneling between edge states which alter the nature of the strong tunneling limit. We show here how to construct a weak-strong coupling duality for generalized FQH states with simple unreconstructed edges. The correct dualization of quasiparticles into integer charged fermions is a consistency requirement for a theory of FQH edge states with a simple edge. We show that this duality also applies for weakly reconstructed edges.Comment: 4+epsilon page

Coupled S=1/2S=1/2 Heisenberg antiferromagnetic chains in an effective staggered field

We present a systematic study of coupled $S=1/2$ Heisenberg antiferromagnetic chains in an effective staggered field. We investigate several effects of the staggered field in the {\em higher} ({\em two or three}) {\em dimensional} spin system analytically. In particular, in the case where the staggered field and the inter-chain interaction compete with each other, we predict, using mean-field theory, a characteristic phase transition. The spin-wave theory predicts that the behavior of the gaps induced by the staggered field is different between the competitive case and the non-competitive case. When the inter-chain interactions are sufficiently weak, we can improve the mean-field phase diagram by using chain mean-field theory and the analytical results of field theories. The ordered phase region predicted by the chain mean-field theory is substantially smaller than that by the mean-field theory.Comment: 13pages, 12figures, to be published in PR

Symmetry protection of topological order in one-dimensional quantum spin systems

We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $\pi$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys. Rev. B \textbf{81}, 064439 (2010)]. On the other hand, an even-$S$ Haldane phase is not topologically protected (i.e., it is indistinct from a trivial, site-factorizable phase). We show some numerical evidence that supports these claims, using concrete examples.Comment: 9 pages, 6 figures, extended version: several new examples and numerical results added. Journal reference adde

Universal temperature dependence of the magnetization of gapped spin chains

Temperature dependence of the magnetization of the Haldane spin chain at finite magnetic field is analyzed systematically. Quantum Monte Carlo data indicates a clear minimum of magnetization as a function of temperature in the gapless regime. On the basis of the Tomonaga-Luttinger liquid theory, we argue that this minimum is rather universal and can be observed for general axially symmetric quasi-one-dimensional spin systems. Our argument is confirmed by the magnetic-field dependence of the spin-wave velocity obtained numerically. One can estimate a magnitude of the gap of any such systems by fitting the experimental data with the magnetization minimum.Comment: 9 pages, 7 figure