Bela Bauer

The ALPS project release 2.0: open source software for strongly correlated systems

We present release 2.0 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. The code development is centered on common XML and HDF5 data formats, libraries to simplify and speed up code development, common evaluation and plotting tools, and simulation programs. The programs enable non-experts to start carrying out serial or parallel numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), the density matrix renormalization group (DMRG) both in a static version and a dynamic time-evolving block decimation (TEBD) code, and quantum Monte Carlo solvers for dynamical mean field theory (DMFT). The ALPS libraries provide a powerful framework for programmers to develop their own applications, which, for instance, greatly simplify the steps of porting a serial code onto a parallel, distributed memory machine. Major changes in release 2.0 include the use of HDF5 for binary data, evaluation tools in Python, support for the Windows operating system, the use of CMake as build system and binary installation packages for Mac OS X and Windows, and integration with the VisTrails workflow provenance tool. The software is available from our web server at http://alps.comp-phys.org/.

Area laws in a many-body localized state and its implications for topological order

The question whether Anderson insulators can persist to finite-strength interactions?a scenario dubbed many-body localization?has recently received a great deal of interest. The origin of such a many-body localized phase has been described as localization in Fock space, a picture we examine numerically. We then formulate a precise sense in which a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator. We call such a state a many-body localized state and define a many-body localized phase as one in which almost all states are many-body localized states. We explore the possible consequences of this; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. We present the results of numerical calculations for a one-dimensional system of spinless fermions. Our results are consistent with an area law and, by implication, many-body localization for almost all states and almost all regions for weak enough interactions and strong disorder. However, there are rare regions and rare states with much larger entanglement entropies. Furthermore, we study the implications that many-body localization may have for topological phases and self-correcting quantum memories. We find that there are scenarios in which many-body localization can help to stabilize topological order at non-zero energy density, and we propose potentially useful criteria to confirm these scenarios.

Floquet Time Crystals

We define what it means for time translation symmetry to be spontaneously broken in a quantum system and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.

Gate-count estimates for performing quantum chemistry on small quantum computers

As quantum computing technology improves and quantum computers with a small but non-trivial number of N > 100 qubits appear feasible in the near future the question of possible applications of small quantum computers gains importance. One frequently mentioned application is Feynmans original proposal of simulating quantum systems, and in particular the electronic structure of molecules and materials. In this paper, we analyze the computational requirements for one of the standard algorithms to perform quantum chemistry on a quantum computer. We focus on the quantum resources required to find the ground state of a molecule twice as large as what current classical computers can solve exactly. We find that while such a problem requires about a ten-fold increase in the number of qubits over current technology, the required increase in the number of gates that can be coherently executed is many orders of magnitude larger. This suggests that for quantum computation to become useful for quantum chemistry problems, drastic algorithmic improvements will be needed.

Complete-graph tensor network states: a new fermionic wave function ansatz for molecules

We present a class of tensor network states specifically designed to capture the electron correlation within a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a complete-graph tensor network (CGTN) ansatz, which implements an efficient reduction of the number of variational parameters by breaking down the complexity of the high-dimensional coefficient tensor of a full-configuration-interaction (FCI) wave function. This ansatz applied to molecules is new and based on a tensor network wave function recently studied in lattice problems. We demonstrate that CGTN states approximate ground states of molecules accurately by comparison of the CGTN and FCI expansion coefficients. The CGTN parametrization is not biased towards any reference configuration, in contrast to many standard quantum chemical methods. This feature allows one to obtain accurate relative energies between CGTN states, which is central to molecular physics and chemistry. We discuss the implications for quantum chemistry and focus on the spin-state problem. Our CGTN approach is applied to the energy splitting of states of different spins for methylene and the strongly correlated ozone molecule at a transition state structure. The parameters of the tensor network ansatz are variationally optimized by means of a parallel-tempering Monte Carlo algorithm.

Simulation of strongly correlated fermions in two spatial dimensions with fermionic projected entangled-pair states

We explain how to implement, in the context of projected entangled-pair states (PEPSs), the general procedure of fermionization of a tensor network introduced in P. Corboz and G. Vidal, Phys. Rev. B 80, 165129 (2009). The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the t-J model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.

A Provenance-Based Infrastructure to Support the Life Cycle of Executable Papers

As publishers establish a greater online presence as well as infrastructure to support the distribution of more varied information, the idea of an executable paper that enables greater interaction has developed. An executable paper provides more information for computational experiments and results than the text, tables, and figures of standard papers. Executable papers can bundle computational content that allow readers and reviewers to interact, validate, and explore experiments. By including such content, authors facilitate future discoveries by lowering the barrier to reproducing and extending results. We present an infrastructure for creating, disseminating, and maintaining executable papers. Our approach is rooted in provenance, the documentation of exactly how data, experiments, and results were generated. We seek to improve the experience for everyone involved in the life cycle of an executable paper. The automated capture of provenance information allows authors to easily integrate and update results into papers as they write, and also helps reviewers better evaluate approaches by enabling them to explore experimental results by varying parameters or data. With a provenance-based system, readers are able to examine exactly how a result was developed to better understand and extend published findings.

Hybrid Quantum-Classical Approach to Correlated Materials

Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.

Implementing global Abelian symmetries in projected entangled-pair state algorithms

Due to the unfavorable scaling of tensor-network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states, in particular for gapless, strongly entangled systems. In one-dimensional density matrix renormalization group methods, the use of Abelian symmetries has led to large computational gain. In higher-dimensional tensor networks, this is associated with significant technical efforts and additional approximations. We explain a formalism to implement such symmetries in two-dimensional tensor-network states and present benchmark results that confirm the validity of these approximations in the context of projected entangled-pair state algorithms.

Bridging workflow and data provenance using strong links

As scientists continue to migrate their work to computational methods, it is important to track not only the steps involved in the computation but also the data consumed and produced. While this provenance information can be captured, in existing approaches, it often contains only weak references between data and provenance. When data files or provenance are moved or modified, it can be difficult to find the data associated with the provenance or to find the provenance associated with the data. We propose a persistent storage mechanism that manages input, intermediate, and output data files, strengthening the links between provenance and data. This mechanism provides better support for reproducibility because it ensures the data referenced in provenance information can be readily located. Another important benefit of such management is that it allows caching of intermediate data which can then be shared with other users. We present an implemented infrastructure for managing data in a provenance-aware manner and demonstrate its application in scientific projects.