Periodic Reporting for period 2 - NexGenTeN (State-of-the-art simulations of quantum many-body systems with the next-generation tensor network algorithms)
Reporting period: 2023-06-01 to 2024-11-30
One of the central goals in physics is to understand the emergent properties in systems made of many strongly interacting quantum particles. These so-called strongly correlated systems give rise to remarkable phenomena, such as high-temperature superconductivity (HTSC), quantum spin liquids with topological order, and other novel states of matter. In many cases accurate and efficient numerical techniques are indispensable for gaining insight into the properties of these systems. One of the most powerful approaches is Quantum Monte Carlo (QMC), however, it fails for important classes of systems (fermionic and frustrated systems) due to the infamous negative sign problem, which is the main reason why many relevant models are still unsolved. A well-known example is the two-dimensional (2D) Hubbard model which is believed to be relevant for understanding HTSC. Despite immense effort over the last three decades, the Hubbard model and its generalizations are is still not fully solved and a consensus about the mechanism leading to HTSC is still lacking. Thus, to make progress in many-body physics and for the design of future quantum technologies it is essential to develop accurate numerical techniques that go beyond today’s state-of-the-art.
In recent years, groundbreaking progress in the simulation of strongly correlated systems has been achieved with tensor network algorithms, an interdisciplinary field which emerged at the interface between quantum information science and condensed matter physics. A tensor network is a variational ansatz in which a state is efficiently represented by a trace over a product of tensors, where the accuracy can be systematically controlled by the so-called bond dimension D. The best-known example is the matrix product state (MPS) - a very efficient ansatz for quasi-1D systems - which has had an enormous impact on the understanding of low-dimensional systems in the last three decades. Progress in quantum information science has led to the development of tensor networks for 2D systems, such as projected entangled-pair states (PEPS) or the multi-scale entanglement renormalization ansatz (MERA). A particularly powerful ansatz is infinite PEPS (iPEPS) which represents a 2D state directly in the thermodynamic limit, thereby overcoming the problem of finite-size and boundary effects.
Building upon recent breakthroughs with iPEPS, the main goal of this project is to develop and use the next generation of tensor network methods for groundbreaking simulations of challenging open problems in several fields, in order to make major advances in our fundamental understanding of strongly correlated systems. This includes novel powerful algorithms for ground states, time evolution, spectral functions, finite temperature, open systems, and multi-scale approaches, which are used for state-of-the-art simulations of realistic models of HTSC and frustrated materials, and for accurate predictions and benchmarks for experimental quantum simulators of SU(N) and open quantum systems.
In recent years, groundbreaking progress in the simulation of strongly correlated systems has been achieved with tensor network algorithms, an interdisciplinary field which emerged at the interface between quantum information science and condensed matter physics. A tensor network is a variational ansatz in which a state is efficiently represented by a trace over a product of tensors, where the accuracy can be systematically controlled by the so-called bond dimension D. The best-known example is the matrix product state (MPS) - a very efficient ansatz for quasi-1D systems - which has had an enormous impact on the understanding of low-dimensional systems in the last three decades. Progress in quantum information science has led to the development of tensor networks for 2D systems, such as projected entangled-pair states (PEPS) or the multi-scale entanglement renormalization ansatz (MERA). A particularly powerful ansatz is infinite PEPS (iPEPS) which represents a 2D state directly in the thermodynamic limit, thereby overcoming the problem of finite-size and boundary effects.
Building upon recent breakthroughs with iPEPS, the main goal of this project is to develop and use the next generation of tensor network methods for groundbreaking simulations of challenging open problems in several fields, in order to make major advances in our fundamental understanding of strongly correlated systems. This includes novel powerful algorithms for ground states, time evolution, spectral functions, finite temperature, open systems, and multi-scale approaches, which are used for state-of-the-art simulations of realistic models of HTSC and frustrated materials, and for accurate predictions and benchmarks for experimental quantum simulators of SU(N) and open quantum systems.
We have made substantial progress in reaching several of the main objectives and milestones of this project, both on the methods development side and on the application side. Key results include:
- We developed an efficient iPEPS approach to simulate layered systems in 3D, which is computationally substantially cheaper than standard 3D approaches. We applied this approach to the Shastry-Sutherland model with an interlayer coupling, relevant for the compound SrCu2(BO3)2, and showed that the inclusion of the interlayer couplings leads to better agreement of the phase diagram between theory and experiment.
- We conducted state-of-the-art simulations of the three-band Hubbard model using a special iPEPS ansatz to simulate the copper-oxygen planes of the cuprate high-Tc superconductors. Our simulations revealed superconducting stripes over an extended doping range, with a period compatible with experiments.
- We developed a time evolution method for the computation of spectral functions with iPEPS. A complementary route to compute spectral functions is provided by the iPEPS excitation ansatz, for which we developed a more efficient and accurate method than previous approaches.
- We achieved several breakthroughs in the study of SrCu2(BO3)2 under pressure and in a magnetic field, described by the Shastry-Sutherland model, in collaboration with experimental groups. We discovered several new exotic phases, including a new plateau phase that has a different nature than the other plateaus, and several so-called supersolid phases. The numerical results for the phase boundaries are in remarkable agreement with the experimental findings. We also extended the iPEPS simulations up to the saturation field and found a close agreement with experiments, including the value of the saturation field. Based on the iPEPS simulations, we were also able to gain an understanding of the drastic reduction of the sound velocity in the 1/2 plateau observed in experiments.
- We discovered a new phase in the triangular Kondo-necklace model, called central spin phase, which may be realized in certain heavy-fermion compounds.
- We developed a new iPEPS ansatz enabling the efficient simulation of spin spiral phases with arbitrary large wave vectors, overcoming the limitations of previous finite-size approaches. The application of this approach to the anisotropic triangular lattice Heisenberg model revealed a quantum spin liquid phase over an extended parameter range.
- We developed an efficient iPEPS approach to simulate layered systems in 3D, which is computationally substantially cheaper than standard 3D approaches. We applied this approach to the Shastry-Sutherland model with an interlayer coupling, relevant for the compound SrCu2(BO3)2, and showed that the inclusion of the interlayer couplings leads to better agreement of the phase diagram between theory and experiment.
- We conducted state-of-the-art simulations of the three-band Hubbard model using a special iPEPS ansatz to simulate the copper-oxygen planes of the cuprate high-Tc superconductors. Our simulations revealed superconducting stripes over an extended doping range, with a period compatible with experiments.
- We developed a time evolution method for the computation of spectral functions with iPEPS. A complementary route to compute spectral functions is provided by the iPEPS excitation ansatz, for which we developed a more efficient and accurate method than previous approaches.
- We achieved several breakthroughs in the study of SrCu2(BO3)2 under pressure and in a magnetic field, described by the Shastry-Sutherland model, in collaboration with experimental groups. We discovered several new exotic phases, including a new plateau phase that has a different nature than the other plateaus, and several so-called supersolid phases. The numerical results for the phase boundaries are in remarkable agreement with the experimental findings. We also extended the iPEPS simulations up to the saturation field and found a close agreement with experiments, including the value of the saturation field. Based on the iPEPS simulations, we were also able to gain an understanding of the drastic reduction of the sound velocity in the 1/2 plateau observed in experiments.
- We discovered a new phase in the triangular Kondo-necklace model, called central spin phase, which may be realized in certain heavy-fermion compounds.
- We developed a new iPEPS ansatz enabling the efficient simulation of spin spiral phases with arbitrary large wave vectors, overcoming the limitations of previous finite-size approaches. The application of this approach to the anisotropic triangular lattice Heisenberg model revealed a quantum spin liquid phase over an extended parameter range.
Each of the achievements discussed above constitutes a significant advancement beyond the previous state of the art. All models mentioned above are not tractable by conventional Monte Carlo methods due to the negative sign problem, and our results are not affected by finite size effects, unlike most other methods. Our next-generation methods developed so far provide powerful extensions to the existing tensor network toolbox, enabling us to address a broader range of problems with higher accuracy.
The second part of the project focuses on additional large-scale calculations of frustrated magnets, in particular triangular lattice compounds and (extended and doped) Shastry-Sutherland models, accurate simulations of SU(N) systems relevant for experiments on ultracold alkaline earth atoms in optical lattices, simulations of open systems, and extended doped t-J and Hubbard models. The methods side includes further refinements of the iPEPS excitation ansatz, improved methods for open systems and time evolution, exploring multi-scale approaches, higher-performance optimization and contraction techniques, improved finite temperature schemes, and more.
The second part of the project focuses on additional large-scale calculations of frustrated magnets, in particular triangular lattice compounds and (extended and doped) Shastry-Sutherland models, accurate simulations of SU(N) systems relevant for experiments on ultracold alkaline earth atoms in optical lattices, simulations of open systems, and extended doped t-J and Hubbard models. The methods side includes further refinements of the iPEPS excitation ansatz, improved methods for open systems and time evolution, exploring multi-scale approaches, higher-performance optimization and contraction techniques, improved finite temperature schemes, and more.