A numerical canonical transformation approach to quantum many body problems

We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of numerical canonical transformations.Comment: 10 pages, 3 encapsulated figures. Parts of the paper are substantially revised to refer to previous similar method

Neel order in square and triangular lattice Heisenberg models

Using examples of the square- and triangular-lattice Heisenberg models we demonstrate that the density matrix renormalization group method (DMRG) can be effectively used to study magnetic ordering in two-dimensional lattice spin models. We show that local quantities in DMRG calculations, such as the on-site magnetization M, should be extrapolated with the truncation error, not with its square root, as previously assumed. We also introduce convenient sequences of clusters, using cylindrical boundary conditions and pinning magnetic fields, which provide for rapidly converging finite-size scaling. This scaling behavior on our clusters is clarified using finite-size analysis of the effective sigma-model and finite-size spin-wave theory. The resulting greatly improved extrapolations allow us to determine the thermodynamic limit of M for the square lattice with an error comparable to quantum Monte Carlo. For the triangular lattice, we verify the existence of three-sublattice magnetic order, and estimate the order parameter to be M = 0.205(15).Comment: 4 pages, 5 figures, typo fixed, reference adde

Enhanced Pairing in the "Checkerboard" Hubbard Ladder

We study signatures of superconductivity in a 2--leg "checkerboard" Hubbard ladder model, defined as a one--dimensional (period 2) array of square plaquettes with an intra-plaquette hopping $t$ and inter-plaquette hopping $t'$, using the density matrix renormalization group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half filling, $U\approx 6t$ and $t'/t \approx 0.6$. Other forms of modulated hopping parameters, with periods of either 1 or 3 lattice constants, are also found to enhance pairing relative to the uniform two--leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.Comment: 9 pages, 9 figures; Journal reference adde

Weak plaquette valence bond order in the S=1/2S=1/2 honeycomb J1−J2J_1-J_2 Heisenberg model

Using the density matrix renormalization group, we investigate the $S=1/2$ Heisenberg model on the honeycomb lattice with first- ($J_1$) and second-neighbor ($J_2$) interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For $J_2/J_1$ near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for $J_2\lesssim 0.26$ and by a valence bond crystal for $J_2\gtrsim 0.36$. The longest correlation length that we find in this intermediate phase is for plaquette valence bond (PVB) order. This correlation length grows strongly with cylinder circumference, indicating either quantum criticality or weak PVB order.Comment: 9 pages, 15 figures, minor changes are made for publication in Phys. Rev. Let

Unexpected z-Direction Ising Antiferromagnetic Order in a frustrated Spin-1/2 J1−J2J_1-J_2 XY Model on the Honeycomb Lattice

Using the density matrix renormalization group (DMRG) on wide cylinders, we study the phase diagram of the spin-1/2 XY model on the honeycomb lattice, with first-neighbor ($J_1 = 1$) and frustrating second-neighbor ($J_2>0$) interactions. For the intermediate frustration regime $0.22\lesssim J_2\lesssim0.36$, we find a surprising antiferromagnetic Ising phase, with ordered moments pointing along the z axis, despite the absence of any S_z_z interactions in the Hamiltonian. Surrounding this phase as a function of $J_2$ are antiferromagnetic phases with the moments pointing in the $x-y$ plane for small $J_2$ and a close competition between an $x-y$ plane magnetic collinear phase and a dimer phase for large values of $J_2$. We do not find any spin liquid phases in this model.Comment: 5 pages, 5 figures, minor changes made for publication on PR

Dynamical Correlation Functions using the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) method allows for very precise calculations of ground state properties in low-dimensional strongly correlated systems. We investigate two methods to expand the DMRG to calculations of dynamical properties. In the Lanczos vector method the DMRG basis is optimized to represent Lanczos vectors, which are then used to calculate the spectra. This method is fast and relatively easy to implement, but the accuracy at higher frequencies is limited. Alternatively, one can optimize the basis to represent a correction vector for a particular frequency. The correction vectors can be used to calculate the dynamical correlation functions at these frequencies with high accuracy. By separately calculating correction vectors at different frequencies, the dynamical correlation functions can be interpolated and pieced together from these results. For systems with open boundaries we discuss how to construct operators for specific wavevectors using filter functions.Comment: minor revision, 10 pages, 15 figure

Real time evolution using the density matrix renormalization group

We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation functions is discussed and illustrated in several examples. We simulate a scattering process in a spin chain which generates a spatially non-local entangled wavefunction.Comment: 4 pages, 4 eps figures, some minor corrections in text and Eq.(3

Topography of Spin Liquids on a Triangular Lattice

Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization group and mapped out the topography of the region that can harbor a spin liquid. We find that this spin-liquid phase is continuously connected to a previously discovered spin-liquid phase of the isotropic $J_1\!-\!J_2$ model. The two limits show nearly identical spin correlations, making the case that their respective spin liquids are isomorphic to each other.Comment: Accepted to PRL; 5 p., 11+ p. supplemental; main text is longer than the accepted versio

Disorder-Induced Mimicry of a Spin Liquid in YbMgGaO4_4

We suggest that a randomization of the pseudo-dipolar interaction in the spin-orbit-generated low-energy Hamiltonian of YbMgGaO$_4$ due to an inhomogeneous charge environment from a natural mixing of Mg$^{2+}$ and Ga$^{3+}$ can give rise to orientational spin disorder and mimic a spin-liquid-like state. In the absence of such quenched disorder, $1/S$ and density matrix renormalization group calculations both show robust ordered states for the physically relevant phases of the model. Our scenario is consistent with the available experimental data and further experiments are proposed to support it.Comment: 5+ main text, 7+ supplemental, text asymptotically close to PR

Binding of holons and spinons in the one-dimensional anisotropic t-J model

We study the binding of a holon and a spinon in the one-dimensional anisotropic t-J model using a Bethe-Salpeter equation approach, exact diagonalization, and density matrix renormalization group methods on chains of up to 128 sites. We find that holon-spinon binding changes dramatically as a function of anisotropy parameter \alpha=J_\perp/J_z: it evolves from an exactly deducible impurity-like result in the Ising limit to an exponentially shallow bound state near the isotropic case. A remarkable agreement between the theory and numerical results suggests that such a change is controlled by the corresponding evolution of the spinon energy spectrum.Comment: 4 pages, 5 figures, published versio