Symmetry breaking and criticality in tensor-product states

Abstract

We discuss variationally optimized matrix-product states for the transverse-field Ising chain, using D*D matrices with small D=2-10. For finite system size N there are energy minimums for symmetric as well as symmetry-broken states, which cross each other at a field value hc(N,D); thus the transition is first-order. A continuous transition develops as N->infinity. The asymptotic critical behavior is then always of mean-field type (the magnetization exponent beta=1/2), but a window of field strengths where true Ising scaling holds (beta=1/8) emerges with increasing D. We also demonstrate asymptotic mean-field behavior for infinite-size two-dimensional tensor-product (iPEPS) states with small tensors.

4 pages, 5 figures

References in corpus (10)

• 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 one spatial dimension
• Matrix product states represent ground states faithfully
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Criticality, the area law, and the computational power of PEPS
• Scaling of entanglement support for Matrix Product States
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Entropy and Entanglement in Quantum Ground States
• Variational quantum Monte Carlo simulations with tensor-network states
• The Quantum Transverse Field Ising Model on an Infinite Tree from Matrix Product States

Cited by in corpus (7)

• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Entanglement renormalization and gauge symmetry
• Monte Carlo simulation with Tensor Network States
• Critical behavior of the two-dimensional icosahedron model
• Correlated valence-bond states
• Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain
• Uniform Matrix Product State in the Thermodynamic Limit