Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States

Abstract

The Minimally Entangled Typical Thermal States (METTS) are an ensemble of pure states, equivalent to the Gibbs thermal state, that can be efficiently represented by tensor networks. In this article, we use the Projected Entangled Pair States (PEPS) ansatz as to represent METTS on a two-dimensional (2D) lattice. While Matrix Product States (MPS) are less efficient for 2D systems due to their complexity growing exponentially with the lattice size, PEPS provide a more tractable approach. To substantiate the prowess of PEPS in modeling METTS (dubbed as PEPS-METTS), we benchmark it against the purification method for the 2D quantum Ising model at its critical temperature. Our analysis reveals that PEPS-METTS achieves accurate long-range correlations with significantly lower bond dimensions. We further corroborate this finding in the 2D Fermi Hubbard model at half-filling. At a technical level, we introduce an efficient \textit{zipper} method to obtain PEPS boundary matrix product states needed to compute expectation values. The imaginary time evolution is performed with the neighbourhood tensor update.

14 pages, 14 figures

References in corpus (29)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Area laws in quantum systems: mutual information and correlations
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Entropy scaling and simulability by Matrix Product States
• Minimally Entangled Typical Thermal State Algorithms
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Characterizing topological order by studying the ground states of an infinite cylinder
• Algorithms for finite Projected Entangled Pair States
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Spin Excitation Spectra of Anisotropic Spin-$1/2$ Triangular Lattice Heisenberg Antiferromagnets
• Tensor network study of the $m=1/2$ magnetization plateau in the Shastry-Sutherland model at finite temperature
• Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t-J model
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Projected Entangled Pair States at Finite Temperature: Iterative Self-Consistent Bond Renormalization for Exact Imaginary Time Evolution
• Thermal Tensor Renormalization Group Simulations of Square-Lattice Quantum Spin Models
• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
• Isometric tensor network representations of two-dimensional thermal states
• Real-time dynamics of a critical Resonating Valence Bond spin liquid

Cited by in corpus (6)

• Low-temperature Gibbs states with tensor networks
• Forestalled Phase Separation as the Precursor to Stripe Order
• Limitations of tensor network approaches for optimization and sampling: A comparison to quantum and classical Ising machines
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
• Scalable projected entangled-pair state representation of random quantum circuit states