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arXiv:2107.13941 · Physical review. B./Physical review. B

Minimally entangled typical thermal state algorithms for finite temperature Matsubara Green functions

Daniel Bauernfeind, Xiaodong Cao, Edwin Miles Stoudenmire, Olivier Parcollet

Published May 6, 2022• 3 citations
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Abstract

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 the 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.

DOI
10.1103/physrevb.105.195107

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Minimally Entangled Typical Thermal States for Classical and Quantum Simulation of 1+1-Dimensional Z2\mathbb Z_2Z2​ Lattice Gauge Theory at Finite Temperature and Density
Simulating strongly coupled gauge theories at finite temperature and density is a longstanding challenge in nuclear and high-energy physics that also has fundamental implications for condensed matter physics. In this work, we use minimally entangled typical thermal state (METTS) approaches to facilitate both classical and quantum computational studies of such systems. METTS techniques combine classical random sampling with imaginary time evolution, which can be performed on either a classical or a quantum computer, to estimate thermal averages of observables. We study 1+1-dimensional Z2\mathbb{Z}_2Z2​ gauge theory coupled to spinless fermionic matter, which maps onto a local quantum spin chain. We benchmark both a classical matrix-product-state implementation of METTS and a recently proposed adaptive variational approach that is a promising candidate for implementation on near-term quantum devices, focusing on the equation of state as well as on various measures of fermion confinement. Of particular importance is the choice of basis for obtaining new METTS samples, which impacts both the classical sampling complexity (a key factor in both classical and quantum simulation applications) and complexity of circuits used in the quantum computing approach. Our work sets the stage for future studies of strongly coupled gauge theories with both classical and quantum hardware.