Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials

Abstract

Aimed at a more realistic classical description of natural quantum systems, we present a two-dimensional tensor network algorithm to study finite temperature properties of frustrated model quantum systems and real quantum materials. For this purpose, we introduce the infinite projected entangled simplex operator ansatz to study thermodynamic properties. To obtain state-of-the-art benchmarking results, we explore the highly challenging spin-1/2 Heisenberg anti-ferromagnet on the Kagome lattice, a system for which we investigate the melting of the magnetization plateaus at finite magnetic field and temperature. Making close connection to actual experimental data of real quantum materials, we go on to studying the finite temperature properties of Ca${}_{10}$Cr${}_7$O${}_{28}$. We compare the magnetization curve of this material in the presence of an external magnetic field at finite temperature with classically simulated data. As a first theoretical tool that incorporates both thermal fluctuations as well as quantum correlations in the study of this material, our work contributes to settling the existing controversy between the experimental data and previous theoretical works on the magnetization process.

arXiv comment9 pages, 11 figures

References in corpus (64)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Area laws for the entanglement entropy - a review
• 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
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Identifying Topological Order by Entanglement Entropy
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Corner Transfer Matrix Renormalization Group Method
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• 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
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• The computational complexity of PEPS
• Tensor network decompositions in the presence of a global symmetry
• The iPEPS algorithm, improved: fast full update and gauge fixing
• What limits the simulation of quantum computers?
• A positive tensor network approach for simulating open quantum many-body systems
• 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
• Computational advantage of quantum random sampling
• Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• A simple tensor network algorithm for two-dimensional steady states
• Sample-efficient learning of quantum many-body systems
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Magnetism of the N=42 kagome lattice antiferromagnet
• Spin-S Kagome quantum antiferromagnets in a field with tensor networks
• The Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A high-order coupled cluster treatment
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Exponential Thermal Tensor Network Approach for Quantum Lattice Models
• Kosterlitz-Thouless Melting of Magnetic Order in the Triangular Quantum Ising Material TmMgGaO${}_4$
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• A tensor network annealing algorithm for two-dimensional thermal states
• Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet
• Time evolution of many-body localized systems in two spatial dimensions
• Efficient tensor network simulation of IBM's largest quantum processors
• Competition between intermediate plaquette phases in SrCu${}_2$(BO${}_3$)${}_2$ under pressure
• Thermodynamics of Spin-1/2 Kagomé Heisenberg Antiferromagnet: Algebraic Paramagnetic Liquid and Finite-Temperature Phase Diagram
• Time-dependent study of disordered models with infinite projected entangled pair states
• Contracting projected entangled pair states is average-case hard
• Tensor network study of the $m=1/2$ magnetization plateau in the Shastry-Sutherland model at finite temperature
• Series-Expansion Thermal Tensor Network Approach for Quantum Lattice Models
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Nematic and supernematic phases in Kagome quantum antiferromagnets under a magnetic field
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Quantum time crystals with programmable disorder in higher dimensions
• The magnetic Hamiltonian and phase diagram of the quantum spin liquid Ca10Cr7O28
• Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
• A programming guide for tensor networks with global $SU(2)$ symmetry
• Theory of Ca${}_{10}$Cr${}_7$O${}_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics
• How many spin liquids are there in Ca${}_{10}$Cr${}_7$O${}_{28}$?
• Tensor network simulation of the Kitaev-Heisenberg model at finite temperature
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
• Two-body repulsive bound pairs in multi-body interacting Bose-Hubbard model
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Bilayer Linearized Tensor Renormalization Group Approach for Thermal Tensor Networks
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets

Cited by in corpus (2)

• Tensor network analysis of the maple-leaf antiferromagnet spangolite
• Variational Neural and Tensor Network Approximations of Thermal States