Periodic Reporting for period 3 - TENSORNETSIM (Accurate simulations of strongly correlated systems with tensor network methods)
Reporting period: 2019-09-01 to 2021-02-28
This project focuses on the development and application of so-called two-dimensional tensor network methods to simulate challenging open problems in quantum many-body physics. A tensor network is an ansatz for quantum many-body states in which the accuracy can be systematically controlled by the so-called bond dimension.
On the methods development side, the main goals of this project include:
- the development of new techniques to optimize a tensor network ansatz and methods to extrapolate data to the exact infinite bond dimension limit
- the development of tensor network methods at finite temperature
- the development of algorithms to compute excitation spectra based on tensor networks
- tools to characterize and classify topological states of matter using tensor networks
- new types of tensor networks and algorithms to perform realistic simulations of high-temperature superconductors
- extensions of tensor network methods to quantum systems in 3 dimensions
- parallelization of tensor network codes
On the application side the main goals include:
- Simulations of the two-dimensional Hubbard model and multi-band Hubbard models to get new insights into high-temperature superconductivity, at zero and at finite temperature.
- Simulations of the SU(N) Hubbard and SU(N) Heisenberg models to predict new phases of matter which can be realized in experiments on ultra-cold alkaline earth atoms in optical lattices
- Simulations of realistic frustrated spin systems in two and three dimensions at zero and finite temperature for a quantitative understanding of frustrated materials
- the development of new algorithms to optimize the tensors by performing an energy minimization which provides more accurate results than previous techniques.
- the development of an extrapolation technique based on a so-called truncation error which yields accurate estimates of ground state energies in the infinite bond dimension limit.
- a breakthrough in the study of 2D quantum critical systems based on a so-called finite correlation length scaling, enabling the accurate determination of critical couplings and universal critical exponents
- the development and testing of tensor network methods to compute properties at finite temperature
- the implementation and testing of new schemes to compute excitations with tensor networks
- testing and benchmarking tensor network approaches for 3D quantum systems
On the application side of this project the main achievements so far include:
- a major breakthrough in simulating the 2D Hubbard model where were able to obtain, for the first time, a conclusive answer regarding the nature of the ground state at a particularly challenging point in the phase diagram (U/t=8, 1/8 doping), namely that the ground state is a stripe state and not a uniform state.
- extension of these simulations to an extended 2D Hubbard model with an additional next-nearest neighbor hopping which yields the same stripe period as observed in experiments
- simulations of the SU(6) Heisenberg model on the honeycomb lattice which revealed a plaquette state
- pioneering tensor network simulations of an SU(N) Hubbard model, for the case N=3 on the honeycomb lattice, which clearly demonstrates that these models have become within reach of state-of-the-art tensor network simulations
- discovery of an unexpected Haldane phase in S=1 spin systems
- new insights into the physics of the frustrated material SrCu2(BO3)2 described by the Shastry-Sutherland model, including a new explanation for the new anomalies in the magnetization process observed in experiments, and new theory for the system under pressure described by a deformed Shastry-Sutherland model
Our pioneering work on the SU(N) Hubbard models clearly show that these challenging systems can now be accurately studied by 2D tensor network simulations, offering a unique opportunity to predict new phases of matter which can potentially be realized in future quantum simulators with alkaline-earth atoms in optical lattices.
Our studies of frustrated spin systems further establish 2D tensor network as a reliable and powerful tool to study these systems in order to understand the physics of frustrated materials. First results at finite temperature also demonstrate that tensor networks can help to shed new light onto challenging problems at finite temperature where quantum Monte Carlo fails due to the negative sign problem. Also our first benchmarks in 3D look promising, and we expect to be able to address challenging problems in 3D in the second part of this project.
With the rapid progress on the methodological side so far we expect to have established and fully developed all methodological goals until the end of the project.