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.

arXiv comment14 pages, 14 figures

References in corpus (99)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• An Area Law for One Dimensional Quantum Systems
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Area laws in quantum systems: mutual information and correlations
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Entropy scaling and simulability by Matrix Product States
• Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic Order in Hubbard Chains
• Coarse-graining renormalization by higher-order singular value decomposition
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Site-resolved Imaging of Fermionic Lithium-6 in an Optical Lattice
• Site-resolved measurement of the spin-correlation function in the Hubbard model
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Minimally Entangled Typical Thermal State Algorithms
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Minimally entangled typical quantum states at finite temperature
• Fermionic Projected Entangled Pair States
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Characterizing topological order by studying the ground states of an infinite cylinder
• Revealing Hidden Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators
• The one-dimensional Hubbard model: A reminiscence
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Algorithms for finite Projected Entangled Pair States
• Gradient methods for variational optimization of projected entangled-pair states
• Tangent-space methods for uniform matrix product states
• Site-resolved imaging of a fermionic Mott insulator
• Imaging magnetic polarons in the doped Fermi-Hubbard model
• String patterns in the doped Hubbard model
• Magnetization of SrCu2(BO3)2 in ultrahigh magnetic fields up to 118 T
• Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model
• Fermionic multi-scale entanglement renormalization ansatz
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• A simple tensor network algorithm for two-dimensional steady states
• Faster Methods for Contracting Infinite 2D Tensor Networks
• Unifying Projected Entangled Pair States contractions
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• A quantum magnetic analogue to the critical point of water
• Mott insulating states with competing orders in the triangular lattice Hubbard model
• Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Excitations and the tangent space of projected entangled-pair states
• Observation of 2D fermionic Mott insulators of ${}^{40}$K with single-site resolution
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Unitary circuits for strongly correlated fermions
• Exponential Thermal Tensor Network Approach for Quantum Lattice Models
• Finite correlation length scaling with infinite projected entangled-pair states
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• A tensor network annealing algorithm for two-dimensional thermal states
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
• Optimized Decimation of Tensor Networks with Super-orthogonalization for Two-Dimensional Quantum Lattice Models
• Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet
• Time evolution of many-body localized systems in two spatial dimensions
• Excitations with projected entangled pair states using the corner transfer matrix method
• Thermodynamics of Spin-1/2 Kagomé Heisenberg Antiferromagnet: Algebraic Paramagnetic Liquid and Finite-Temperature Phase Diagram
• Optimized contraction scheme for tensor-network states
• Time-dependent study of disordered models with infinite projected entangled pair states
• 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
• Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models
• 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
• Quantum time crystals with programmable disorder in higher dimensions
• 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
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Fermionic Projected Entangled Pair States at Finite Temperature
• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
• Quantum Many-Body Simulations of the 2D Fermi-Hubbard Model in Ultracold Optical Lattices
• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
• Tensor network simulation of the Kitaev-Heisenberg model at finite temperature
• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Emergent spin-1 trimerized valence bond crystal in the spin-1/2 Heisenberg model on the star lattice
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Approximate optimization, sampling and spin-glass droplets discovery with tensor networks
• Finite-temperature symmetric tensor network for spin-1/2 Heisenberg antiferromagnets on the square lattice
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet
• Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Efficient Quantum Simulation for Thermodynamics of Infinite-size Many-body Systems in Arbitrary Dimensions
• 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
• Collective Monte Carlo updates through tensor network renormalization
• Real-time dynamics of a critical Resonating Valence Bond spin liquid

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