Finite correlation length scaling with infinite projected entangled pair states at finite temperature

Abstract

We study second order finite temperature phase transitions of the 2D quantum Ising and interacting honeycomb fermions models using infinite projected entangled pair states (iPEPS). We obtain an iPEPS thermal state representation by Variational Tensor Network Renormalization (VTNR). We find that at the critical temperature $T_c$ the iPEPS correlation length is finite for the computationally accessible values of the iPEPS bond dimension $D$. Motivated by this observation we investigate the application of Finite Correlation Length Scaling (FCLS), which has been previously used for iPEPS simulations of quantum critical points at $T=0$, to obtain precise values of $T_c$ and the universal critical exponents. We find that in the vicinity of $T_c$ the behavior of observables follows well the one predicted by FCLS. Using FCLS we obtain $T_c$ and the critical exponents in agreement with Quantum Monte Carlo (QMC) results except for couplings close to the quantum critical points where larger bond dimensions are required.

12 pages, 11 figures, published version, presentation improved

References in corpus (15)

• 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
• Scaling of entanglement support for Matrix Product States
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Algorithms for finite Projected Entangled Pair States
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• 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
• Phase diagram of interacting spinless fermions on the honeycomb lattice
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet

Cited by in corpus (8)

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• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• 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
• Tensor Network Based Finite-Size Scaling for Two-Dimensional Classical Models
• Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network