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Register a new userMinimally Entangled Typical Thermal States Algorithms for Finite Temperature Matsubara Green Functions
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We extend finite-temperature tensor network methods to compute Matsubara imaginary-time correlation functions, building on the minimally entangled typical thermal states (METTS) and purification algorithms. While imaginary-time correlation functions are straightforward to formulate with these methods, care is needed to avoid convergence issues that would result from naive estimators. As a benchmark, we study the single-band Anderson impurity model, even though the algorithm is quite general and applies to lattice models. The special structure of the impurity model benchmark system and our choice of basis enable techniques such as reuse of high-probability METTS for increasing algorithm efficiency. The results are competitive with state-of-the-art continuous time Monte Carlo. We discuss the behavior of computation time and error as a function of the number of purified sites in the Hamiltonian.
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The minimally entangled typical thermal states algorithm is applied to fermionic systems using the Krylov-space approach to evolve the system in imaginary time. The convergence of local observables is studied in a tight-binding system with a site-dependent potential. The temperature dependence of the superconducting correlations of the attractive Hubbard model is analyzed on chains, showing an exponential decay with distance and exponents proportional to the temperature at low temperatures, as expected. In addition, the non-local parity correlator is calculated at finite temperature. Other possible applications of the minimally entangled typical thermal states algorithm to fermionic systems are also discussed.
We improve the efficiency of the minimally entangled typical thermal states (METTS) algorithm without breaking the Abelian symmetries. By adding the operation of Trotter gates that respects the Abelian symmetries to the METTS algorithm, we find that a correlation between successive states in Markov-chain Monte Carlo sampling decreases by orders of magnitude. We measure the performance of the improved METTS algorithm through the simulations of the canonical ensemble of the Bose-Hubbard model and confirm that the reduction of the autocorrelation leads to the reduction of computation time. We show that our protocol using the operation of Trotter gates is effective also for the simulations of the grand canonical ensemble.
Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing with finite projected entangled pair states, which allows significantly enlarged system size and improves the accuracy of tensor network simulation. We demonstrate our method on the square-lattice antiferromagnetic Heisenberg model up to $32 times 32$ sites, as well as a highly frustrated $J_1-J_2$ model up to $24times 24$ sites. The results, including ground state energy and spin correlations, are in excellent agreement with those of the available quantum Monte Carlo or density matrix renormalization group methods. Therefore, our method substantially advances the calculation of 2D tensor networks for finite systems, and potentially opens a new door towards resolving many challenging strongly correlated quantum many-body problems.
We analyze a criterion which guarantees that the ground states of certain many body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the low energy physics arising from local interactions. In order to assess stability in the framework of PEPS, one thus needs to understand how physically allowed perturbations of the local tensor affect the properties of the global state. In this paper, we show that a restricted version of the Local Topological Quantum Order (LTQO) condition provides a checkable criterion which allows to assess the stability of local properties of PEPS under physical perturbations. We moreover show that LTQO itself is stable under perturbations which preserve the spectral gap, leading to nontrivial examples of PEPS which possess LTQO and are thus stable under arbitrary perturbations.
While general quantum many-body systems require exponential resources to be simulated on a classical computer, systems of non-interacting fermions can be simulated exactly using polynomially scaling resources. Such systems may be of interest in their own right, but also occur as effective models in numerical methods for interacting systems, such as Hartree-Fock, density functional theory, and many others. Often it is desirable to solve systems of many thousand constituent particles, rendering these simulations computationally costly despite their polynomial scaling. We demonstrate how this scaling can be improved by adapting methods based on matrix product states, which have been enormously successful for low-dimensional interacting quantum systems, to the case of free fermions. Compared to the case of interacting systems, our methods achieve an exponential speedup in the entanglement entropy of the state. We demonstrate their use to solve systems of up to one million sites with an effective MPS bond dimension of 10^15.
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