Minimally entangled typical thermal state algorithms

By E. Stoudenmire, S. White. 2010

309 citations recorded by the source corpus.

We discuss a method based on sampling minimally entangled typical thermal states (METTS) that can simulate finite temperature quantum systems with a computational cost comparable to the ground state density matrix renormalization group (DMRG). Detailed implementation of each step of the method is presented, along with efficient algorithms for working with matrix product states and matrix product operators. Furthermore, we explore how the properties of METTS can reveal characteristic order and excitations of systems and discuss why METTS form an efficient basis for sampling. Finally, we explore the extent to which the average entanglement of a METTS ensemble is minimal.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/fe4ba71baf0295c4db320027640355bcd582d53d

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum trajectories and open many-body quantum systems (2014, background): “Initial states can be directly constructed or computed if they are pure states, or known mixtures of pure states, and finite temperature states could also potentially be sampled as minimally entangled thermal states [229].”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “, via the “zip-up” method proposed by (Stoudenmire and White, 2010).”
Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy) (2018, unknown): “, next-to-nearest-neighbor couplings) by introducing so-called swap gates [61].”
Time-evolution methods for matrix-product states (2019, background): “ 0 1 2 0 3 w0 w1 w2 w3 1 2 3 M0˙1 1;w0m0;w1m1 w 0m0 s1 s 0 1 m1 m2 m3 1 2 0 3 w1 w2 w3 2 3 SVD(M0˙1 1;w0m0;w1m1 ) M0˙2 2;s1;w2m2 ! Figure9: Theessentialstepsofthezip-upmethodproposedinRef.[64]. (left)Initialtensornetworkthatshallbecontracted, consistingofaright-canonicalMPSandanMPOthatonlyslightly”
Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model (2020, background): “One notable exception is the minimally entangled typical thermal state method (METTS) and related approaches, which combine together tensor network representations and stochastic sampling [40–42].”
The ITensor Software Library for Tensor Network Calculations (2020, methodology): “ITensor has also been used for studying continuum electronic systems such as quantum chemistry calculations of hydrogen chains [15,30,31]; for finite-temperature studies, primarily in the context of the minimally entangled typical thermal state (METTS) algorithm [32–35]; and for calculations involvi”