Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group (DMRG) method have long been applied to such systems, the spatial topology of DMRG-based methods allows efficient optimizations to be carried out with respect to one spatial dimension only. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Following Shi. et. al. [Phys. Rev. A, 74, 022320 (2006)], we treat a tree-like network ansatz with arbitrary coordination number z, where the z=2 case corresponds to the one-dimensional scheme. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, in contrast to the matrix-product ansatz, which deviates exponentially. The computational cost of the tree-tensor-network method is significantly smaller than that of previous DMRG-based attempts, which renormalize several blocks into a single block. In addition, we investigate the effect of unitary transformations on the local basis states and present a method for optimizing such transformations. For the 1-d interacting spinless fermion model, the optimized transformation interpolates smoothly between real space and momentum space. Calculations carried out on small quantum chemical systems support our approach

Adiabatic Preparation of a Heisenberg Antiferromagnet Using an Optical Superlattice

We analyze the possibility to prepare a Heisenberg antiferromagnet with cold fermions in optical lattices, starting from a band insulator and adiabatically changing the lattice potential. The numerical simulation of the dynamics in 1D allows us to identify the conditions for success, and to study the influence that the presence of holes in the initial state may have on the protocol. We also extend our results to two-dimensional systems.Comment: 5 pages, 4 figures + Supplementary Material (5 pages, 6 figures), published versio

Modified spin-wave theory with ordering vector optimization I: frustrated bosons on the spatially anisotropic triangular lattice

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a 1D quasi-ordered phase, a 2D Neel ordered phase, and a 2D spiraling ordered phase. We have strong indications that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory we also explore the finite-temperature phase diagram. We find that the zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a Berezinskii-Kosterlitz-Thouless temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that modified spin-wave theory is very well suited for describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast method for singling out Hamiltonians which may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator.Comment: 40 pages, 16 figure

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states

Matrix product operator representations

We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translational invariant matrix product operators suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We illustrate how those tools can be exploited for constructing new algorithms for simulating quantum spin systems

Programme informatique de formation à la médecine vétérinaire des petits mammifères de compagnie

Faisant suite à un premier logiciel d'apprentissage de la médecine des reptiles, l'auteur présente cet outil adapté aux petits mammifères de compagnie : furets, rongeurs et lagomorphes.NANTES-Ecole Nat.Vétérinaire (441092302) / SudocSudocFranceF