[en] We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolution given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems, but it otherwise depends only linearly on the system size. We present simulations involving quantum spins and fermions in one spatial dimension

[en] In the context of characterizing the structure of quantum entanglement in many-body systems, we introduce the entanglement contour, a tool to identify which real-space degrees of freedom contribute, and how much, to the entanglement of a region A with the rest of the system B. The entanglement contour provides a complementary, more refined approach to characterizing entanglement than just considering the entanglement entropy between A and B, with several concrete advantages. We illustrate this in the context of ground states and quantum quenches in fermionic quadratic systems. For instance, in a quantum critical system in D = 1 spatial dimensions, the entanglement contour allows us to determine the central charge of the underlying conformal field theory from just a single partition of the system into regions A and B (using the entanglement entropy for the same task requires considering several partitions). In D ⩾ 2 dimensions, the entanglement contour can distinguish between gapped and gapless phases that obey the same boundary law for entanglement entropy. During a local or global quantum quench, the time-dependent contour provides a detailed account of the dynamics of entanglement, including propagating entanglement waves, which offers a microscopic explanation of the behavior of the entanglement entropy as a function of time. (paper)

[en] Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

[en] We present a study of the hard-core Bose-Hubbard model at zero temperature on an infinite square lattice using the infinite projected entangled pair state algorithm [J. Jordan, R. Orus, G. Vidal, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 101, 250602 (2008)]. Throughout the whole phase diagram our values for the ground-state energy, particle density, and condensate fraction accurately reproduce those previously obtained by other methods. We also explore ground-state entanglement, compute two-point correlators, and conduct a fidelity-based analysis of the phase diagram. Furthermore, for illustrative purposes we simulate the response of the system when a perturbation is suddenly added to the Hamiltonian.

[en] In this paper, we describe a refined matrix product representation for many-body states that are invariant under SU(2) transformations and use it to extend the time-evolving block decimation (TEBD) algorithm to the simulation of time evolution in the presence of an SU(2) symmetry. The resulting algorithm, when tested in a critical quantum spin chain, proved to be more efficient than the standard TEBD.

[en] We propose an algorithm to simulate interacting fermions on a two-dimensional lattice. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related multiscale entanglement renormalization ansatz. Benchmark calculations for free and interacting fermions on lattices ranging from 6x6 to 162x162 sites with periodic boundary conditions confirm the validity of this proposal.