Automatic differentiation applied to excitations with projected  entangled pair states

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite projected entangled-pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.

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Hyper-optimized tensor network contraction

Quantum ◽

10.22331/q-2021-03-15-410 ◽

2021 ◽

Vol 5 ◽

pp. 410

Author(s):

Johnnie Gray ◽

Stefanos Kourtis

Keyword(s):

Computation Time ◽

Quantum Circuit ◽

Optimization Approach ◽

Many Body ◽

Tensor Networks ◽

Randomized Protocols ◽

Classical Simulation ◽

Tensor Network ◽

Speed Up ◽

Many Body Systems

Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to tensor networks with irregular geometries. Finding the best possible contraction path for such networks is a central problem, with an exponential effect on computation time and memory footprint. In this work, we implement new randomized protocols that find very high quality contraction paths for arbitrary and large tensor networks. We test our methods on a variety of benchmarks, including the random quantum circuit instances recently implemented on Google quantum chips. We find that the paths obtained can be very close to optimal, and often many orders or magnitude better than the most established approaches. As different underlying geometries suit different methods, we also introduce a hyper-optimization approach, where both the method applied and its algorithmic parameters are tuned during the path finding. The increase in quality of contraction schemes found has significant practical implications for the simulation of quantum many-body systems and particularly for the benchmarking of new quantum chips. Concretely, we estimate a speed-up of over 10,000× compared to the original expectation for the classical simulation of the Sycamore `supremacy' circuits.

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Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)

10.21468/scipostphyslectnotes.5 ◽

2018 ◽

Cited By ~ 38

Author(s):

Johannes Hauschild ◽

Frank Pollmann

Keyword(s):

Matrix Product ◽

Many Body ◽

Density Matrix Renormalization ◽

Tensor Networks ◽

Condensed Matter Theory ◽

Tensor Network ◽

Matter Theory ◽

Particle Number Conservation ◽

Many Body Systems ◽

The One

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.

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Ultrafast dynamical Lifshitz transition

Science Advances ◽

10.1126/sciadv.abd9275 ◽

2021 ◽

Vol 7 (17) ◽

pp. eabd9275

Author(s):

Samuel Beaulieu ◽

Shuo Dong ◽

Nicolas Tancogne-Dejean ◽

Maciej Dendzik ◽

Tommaso Pincelli ◽

...

Keyword(s):

Fermi Surface ◽

Colossal Magnetoresistance ◽

Surface Topology ◽

Strongly Correlated ◽

Many Body ◽

Time Resolved ◽

Weyl Semimetal ◽

Lifshitz Transition ◽

Fermi Surface Topology ◽

Many Body Systems

Fermi surface is at the heart of our understanding of metals and strongly correlated many-body systems. An abrupt change in the Fermi surface topology, also called Lifshitz transition, can lead to the emergence of fascinating phenomena like colossal magnetoresistance and superconductivity. While Lifshitz transitions have been demonstrated for a broad range of materials by equilibrium tuning of macroscopic parameters such as strain, doping, pressure, and temperature, a nonequilibrium dynamical route toward ultrafast modification of the Fermi surface topology has not been experimentally demonstrated. Combining time-resolved multidimensional photoemission spectroscopy with state-of-the-art TDDFT+U simulations, we introduce a scheme for driving an ultrafast Lifshitz transition in the correlated type-II Weyl semimetal Td-MoTe2. We demonstrate that this nonequilibrium topological electronic transition finds its microscopic origin in the dynamical modification of the effective electronic correlations. These results shed light on a previously unexplored ultrafast scheme for controlling the Fermi surface topology in correlated quantum materials.

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Understanding strongly correlated many-body systems with quantum Monte Carlo simulations

physica status solidi (b) ◽

10.1002/pssb.200440065 ◽

2005 ◽

Vol 242 (10) ◽

pp. 1957-1968 ◽

Cited By ~ 1

Author(s):

Catia Lavalle ◽

Marcos Rigol ◽

Alejandro Muramatsu

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Quantum Monte Carlo ◽

Strongly Correlated ◽

Many Body ◽

Many Body Systems ◽

Quantum Monte Carlo Simulations

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Virial expansion coefficients in the unitary Fermi gas

SciPost Physics Proceedings ◽

10.21468/scipostphysproc.3.049 ◽

2020 ◽

Author(s):

Shimpei Endo

Keyword(s):

Recent Progress ◽

Cold Atoms ◽

Virial Coefficient ◽

Fermi Gas ◽

Virial Expansion ◽

Strongly Correlated ◽

Many Body ◽

Unitary Fermi Gas ◽

Expansion Coefficients ◽

Many Body Systems

Virial expansion is widely used in cold atoms to analyze high temperature strongly correlated many-body systems. As the n-th order virial expansion coefficient can be accurately obtained by exactly solving up to n-body problems, the virial expansion offers a few-body approach to study strongly correlated many-body problems. In particular, the virial expansion has successfully been applied to unitary Fermi gas. We review recent progress of the virial expansion studies in the unitary Fermi gas, in particular the fourth order virial coefficient.

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Mutual Information Scaling for Tensor Network Machine Learning

Machine Learning: Science and Technology ◽

10.1088/2632-2153/ac44a9 ◽

2021 ◽

Author(s):

Ian Convy ◽

William Huggins ◽

Haoran Liao ◽

K Birgitta Whaley

Keyword(s):

Machine Learning ◽

Mutual Information ◽

Many Body ◽

Learning Tasks ◽

Tensor Networks ◽

Tensor Network ◽

Logistic Regression Algorithm ◽

Entanglement Structure ◽

Insight Into ◽

Specific Learning

Abstract Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part on how well it can reproduce the underlying entanglement structure of the target state, with different network designs favoring different scaling patterns. We demonstrate here how a related correlation analysis can be applied to tensor network machine learning, and explore whether classical data possess correlation scaling patterns similar to those found in quantum states which might indicate the best network to use for a given dataset. We utilize mutual information as measure of correlations in classical data, and show that it can serve as a lower-bound on the entanglement needed for a probabilistic tensor network classifier. We then develop a logistic regression algorithm to estimate the mutual information between bipartitions of data features, and verify its accuracy on a set of Gaussian distributions designed to mimic different correlation patterns. Using this algorithm, we characterize the scaling patterns in the MNIST and Tiny Images datasets, and find clear evidence of boundary-law scaling in the latter. This quantum-inspired classical analysis offers insight into the design of tensor networks which are best suited for specific learning tasks.

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Exceptional band touching for strongly correlated systems in equilibrium

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptaa059 ◽

2020 ◽

Vol 2020 (12) ◽

Cited By ~ 3

Author(s):

Tsuneya Yoshida ◽

Robert Peters ◽

Norio Kawakami ◽

Yasuhiro Hatsugai

Keyword(s):

Green's Functions ◽

Green’S Functions ◽

Strongly Correlated Systems ◽

Strongly Correlated ◽

Many Body ◽

Band Structures ◽

Correlated Systems ◽

Concise Review ◽

Open Questions ◽

Many Body Systems

Abstract Quasi-particles described by Green‘s functions of equilibrium systems exhibit non-Hermitian topological phenomena because of their finite lifetime. This non-Hermitian perspective on equilibrium systems provides new insights into correlated systems and attracts much interest because of its potential to solve open questions in correlated compounds. We provide a concise review of the non-Hermitian topological band structures for quantum many-body systems in equilibrium, as well as their classification.

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Thermal bosons in 3d optical lattices via tensor networks

Scientific Reports ◽

10.1038/s41598-020-75548-x ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Saeed S. Jahromi ◽

Román Orús

Keyword(s):

Optical Lattice ◽

Optical Lattices ◽

Numerical Algorithms ◽

Hard Core ◽

Strongly Correlated ◽

Cubic Lattices ◽

Tensor Networks ◽

Tensor Network ◽

Ideal Tool ◽

Thermal States

Abstract Ultracold atoms in optical lattices are one of the most promising experimental setups to simulate strongly correlated systems. However, efficient numerical algorithms able to benchmark experiments at low-temperatures in interesting 3d lattices are lacking. To this aim, here we introduce an efficient tensor network algorithm to accurately simulate thermal states of local Hamiltonians in any infinite lattice, and in any dimension. We apply the method to simulate thermal bosons in optical lattices. In particular, we study the physics of the (soft-core and hard-core) Bose–Hubbard model on the infinite pyrochlore and cubic lattices with unprecedented accuracy. Our technique is therefore an ideal tool to benchmark realistic and interesting optical-lattice experiments.

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