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.

arXiv comment4 pages, 5 figures

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Cited by in corpus (28)

• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• Entanglement renormalization and gauge symmetry
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Monte Carlo simulation with Tensor Network States
• Infinite boundary conditions for matrix product state calculations
• Deconfined quantum critical point in one dimension
• Quantum critical phase with infinite projected entangled paired states
• Breakdown of a perturbed Z_N topological phase
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• A scaling hypothesis for matrix product states
• Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets
• Renormalization group contraction of tensor networks in three dimensions
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• Plaquette Renormalization Scheme for Tensor Network States
• One-dimensional model for deconfined criticality with ${\mathbb{Z}}_3\times {\mathbb{Z}}_3$ symmetry
• Emergent conformal boundaries from finite-entanglement scaling in matrix product states
• Efficient evaluation of high-order moments and cumulants in tensor network states
• Phase diagram of the SO(n) bilinear-biquadratic chain from many-body entanglement
• 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
• Cumulants and Scaling Functions of Infinite Matrix Product States
• Uniform Matrix Product State in the Thermodynamic Limit
• Finite entanglement properties in the matrix product states of the one-dimensional Hubbard model
• Finite-size scaling analysis of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states
• Incommensurate Matrix Product State for Quantum Spin Systems
• Application of Uniform Matrix Product State to Quantum Phase Transition with a Periodicity Change