Frustrated three-leg spin tubes: from spin 1/2 with chirality to spin 3/2

Motivated by the recent discovery of the spin tube [(CuCl$_2$tachH)$_3$Cl]Cl$_2$, we investigate the properties of a frustrated three-leg spin tube with antiferromagnetic intra-ring and inter-ring couplings. We pay special attention to the evolution of the properties from weak to strong inter-ring coupling and show on the basis of extensive density matrix renormalization group and exact diagonalization calculations that the system undergoes a first-order phase transition between a dimerized gapped phase at weak coupling that can be described by the usual spin-chirality model and a gapless critical phase at strong coupling that can be described by an effective spin-3/2 model. We also show that there is a magnetization plateau at 1/3 in the gapped phase and slightly beyond. The implications for [(CuCl$_2$tachH)$_3$Cl]Cl$_2$ are discussed, with the conclusion that this system behaves essentially as a spin-3/2 chain.Comment: 8 pages, 9 figures, revised versio

The Density Matrix Renormalization Group applied to single-particle Quantum Mechanics

A simplified version of White's Density Matrix Renormalization Group (DMRG) algorithm has been used to find the ground state of the free particle on a tight-binding lattice. We generalize this algorithm to treat the tight-binding particle in an arbitrary potential and to find excited states. We thereby solve a discretized version of the single-particle Schr\"odinger equation, which we can then take to the continuum limit. This allows us to obtain very accurate results for the lowest energy levels of the quantum harmonic oscillator, anharmonic oscillator and double-well potential. We compare the DMRG results thus obtained with those achieved by other methods.Comment: REVTEX file, 21 pages, 3 Tables, 4 eps Figure

Charge order induced by electron-lattice interaction in NaV2O5

We present Density Matrix Renormalization Group calculations of the ground-state properties of quarter-filled ladders including static electron-lattice coupling. Isolated ladders and two coupled ladders are considered, with model parameters obtained from band-structure calculations for $\alpha^\prime$-NaV$_2$O$_5$. The relevant Holstein coupling to the lattice causes static out-of-plane lattice distortions, which appear concurrently with a charge-ordered state and which exhibit the same zigzag pattern observed in experiments. The inclusion of electron-lattice coupling drastically reduces the critical nearest-neighbor Coulomb repulsion $V_c$ needed to obtain the charge-ordered state. No spin gap is present in the ordered phase. The charge ordering is driven by the Coulomb repulsion and the electron-lattice interaction. With electron-lattice interaction, coupling two ladders has virtually no effect on $V_c$ or on the characteristics of the charge-ordered phase. At V=0.46\eV, a value consistent with previous estimates, the lattice distortion, charge gap, charge order parameter, and the effective spin coupling are in good agreement with experimental data for NaV$_2$O_5$.Comment: 7 pages, 9 figure

Coherent matter waves emerging from Mott-insulators

We study the formation of (quasi-)coherent matter waves emerging from a Mott insulator for strongly interacting bosons on a one-dimensional lattice. It has been shown previously that a quasi-condensate emerges at momentum k=\pi/2a, where a is the lattice constant, in the limit of infinitely strong repulsion (hard-core bosons). Here we show that this phenomenon persists for all values of the repulsive interaction that lead to a Mott insulator at a commensurate filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by means of a Jordan-Wigner transformation, and the generic case is studied using a time-dependent density matrix renormalization group technique. Different methods for controlling the emerging matter wave are discussed.Comment: 20 pages, 11 figures. Published versio

Time evolution of Matrix Product States

In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator. By comparing all methods with previous techniques based on Trotter decompositions we demonstrate that the Arnoldi method is the best one, reaching extremely good accuracy with moderate resources. Finally we apply this algorithm to studying the formation of molecules in an optical lattices when crossing a Feschbach resonance with a cloud of two-species hard-core bosons.Comment: More extensive comparison with all nearest-neighbor spin s=1/2 models. The results in this manuscript have been superseded by a more complete work in cond-mat/061021

Numerical study of a superconductor-insulator transition in a half-filled Hubbard chain with distant transfers

The ground state of a one-dimensional Hubbard model having the next-nearest neighbor hopping (t') as well as the nearest-neighbor one (t) is numerically investigated at half-filling. A quantum Monte Carlo result shows a slowly decaying pairing correlation for a sizeable interaction strength $(U \leq 2t)$, while the system is shown to become insulating for yet larger $U>U_C\sim 3t$ from a direct evaluation of the charge gap with the density-matrix renormalization group method. The results are consistent with Fabrizio's recent weak-coupling theory which suggests a transition from a superconductor into an insulator at a finite U.Comment: 4 pages, RevTeX, uses epsf.sty and multicol.st

Quantum criticality of dipolar spin chains

We show that a chain of Heisenberg spins interacting with long-range dipolar forces in a magnetic field h perpendicular to the chain exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory the magnon dispersion for small momenta k is [Delta^2 + v_k^2 k^2]^{1/2}, where Delta^2 \propto |h - h_c| and v_k^2 \propto |ln k|. For fields close to h_c linear spin-wave theory breaks down and we investigate the system using density-matrix and functional renormalization group methods. The Ginzburg regime where non-Gaussian fluctuations are important is found to be rather narrow on the ordered side of the transition, and very broad on the disordered side.Comment: 6 pages, 5 figure

Dielectric catastrophe at the Mott transition

We study the Mott transition as a function of interaction strength in the half-filled Hubbard chain with next-nearest-neighbor hopping t' by calculating the response to an external electric field using the Density Matrix Renormalization Group. The electric susceptibility chi diverges when approaching the critical point from the insulating side. We show that the correlation length xi characterizing this transition is directly proportional to fluctuations of the polarization and that chi ~ xi^2. The critical behavior shows that the transition is infinite-order for all t', whether or not a spin gap is present, and that hyperscaling holds.Comment: 4 pages, 4 eps figures, REVTe