Fermionic Projected Entangled Pair States at Finite Temperature

Abstract

An algorithm for imaginary time evolution of a fermionic projected entangled pair state (PEPS) with ancillas from infinite temperature down to a finite temperature state is presented. As a benchmark application, it is applied to spinless fermions hopping on a square lattice subject to $p$-wave pairing interactions. With a tiny bias it allows to evolve the system across a high-temperature continuous symmetry-breaking phase transition.

7 pages, 11 figures; new results on a high-Tc phase transition were added

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• 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
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Controlling sign problems in spin models using tensor renormalization
• Fourier transform of fermionic systems and the spectral tensor network
• Numerical Study of Spin-1/2 XXZ Model on Square Lattice from Tensor Product States
• Real time evolution at finite temperatures with operator space matrix product states

Cited by in corpus (29)

• Lecture Notes of Tensor Network Contractions
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Orbital-selective Superconductivity in the Pressurized Bilayer Nickelate La${}_3$Ni${}_2$O${}_7$: An Infinite Projected Entangled-Pair State Study
• Tensor network study of the $m=1/2$ magnetization plateau in the Shastry-Sutherland model at finite temperature
• 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
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• 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
• SU(3) Fermions on the Honeycomb Lattice at 1/3-Filling
• 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
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Finite-temperature fidelity and von Neumann entropy in the honeycomb spin lattice with quantum Ising interaction
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
• Learning Effective Spin Hamiltonian of Quantum Magnet
• Isometric tensor network representations of two-dimensional thermal states
• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States
• Rényi free energy and variational approximations to thermal states
• Frustration-Induced Superconductivity in the $t$-$t^{\prime }$ Hubbard Model
• Forestalled Phase Separation as the Precursor to Stripe Order
• Energy of fermionic ground states with low-entanglement single-reference expansions, and tensor-based strong-coupling extensions of the coupled-cluster method