On quenches to the critical point of the three states Potts model -- Matrix Product State simulations and CFT

Abstract

Conformal Field Theories (CFTs) have been used extensively to understand the physics of critical lattice models at equilibrium. However, the applicability of CFT calculations to the behavior of the lattice systems in the out-of-equilibrium setting is not entirely understood. In this work, we compare the CFT results of the evolution of the entanglement spectrum after a quantum quench with numerical calculations of the entanglement spectrum of the three-state Potts model using matrix product state simulations. Our results lead us to conjecture that CFT does not describe the entanglement spectrum of the three-state Potts model at long times, contrary to what happens in the Ising model. We thus numerically simulate the out-of-equilibrium behaviour of the Potts model according to the CFT protocol - i.e. by taking a particular product state and "cooling" it, then quenching to the critical point and find that, in this case, the entanglement spectrum is indeed described by the CFT at long times.

arXiv comment9 pages 10 figures, all comments welcome

References in corpus (41)

• Entanglement Entropy and Quantum Field Theory
• Nonequilibrium dynamics of closed interacting quantum systems
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependence of correlation functions following a quantum quench
• Time-dependent variational principle for quantum lattices
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Spread of correlations in long-range interacting quantum systems
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Scaling of entanglement support for Matrix Product States
• Can One Trust Quantum Simulators?
• Entanglement entropy for the long range Ising chain
• Entanglement hamiltonians in two-dimensional conformal field theory
• Lecture Notes of Tensor Network Contractions
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects
• Entanglement negativity after a global quantum quench
• Numerical study of the chiral ${\mathbb{Z}}_3$ quantum phase transition in one spatial dimension
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Finite correlation length scaling with infinite projected entangled-pair states
• Numerical Renormalization Group at Criticality
• Evolution operators in conformal field theories and conformal mappings: the entanglement Hamiltonian, the sine-square deformation, and others
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Boundary Critical Phenomena in the Three-State Potts Model
• Conformal Data from Finite Entanglement Scaling
• Parafermionic conformal field theory on the lattice
• A scaling hypothesis for matrix product states
• Entanglement hamiltonians in 1D free lattice models after a global quantum quench
• On entanglement hamiltonians of an interval in massless harmonic chains
• Dynamics of the entanglement spectrum in spin chains
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Entanglement hamiltonian evolution during thermalization in conformal field theory
• Operator content of entanglement spectra after global quenches in the transverse field Ising chain
• Signatures of quantum phase transitions after quenches in quantum chaotic one-dimensional systems
• Simulating the out-of-equilibrium dynamics of local observables by trading entanglement for mixture
• Entanglement Hamiltonian of the 1+1-dimensional free, compactified boson conformal field theory
• Critical Scaling Behaviors of Entanglement Spectra

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