Scaling theory of entanglement entropy in confinements near quantum critical points

Abstract

We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics subjected to a linear driving along with a finite system size. Competition among the three scales as well as the correlation length of the system is analysed in details. Interesting regimes and their complicated crossovers together with their characteristics follow naturally. The theory is verified with the one-dimensional transverse-field Ising model under a linear driving.

arXiv comment10 pages, 8 figures

References in corpus (56)

• Quantum entanglement
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• Area laws for the entanglement entropy - a review
• Nonequilibrium dynamics of closed interacting quantum systems
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Efficient classical simulation of slightly entangled quantum computations
• Detecting topological order in a ground state wave function
• Scaling of Entanglement close to a Quantum Phase Transitions
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement in a simple quantum phase transition
• Entanglement spectrum of a topological phase in one dimension
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Quantum criticality in an Ising chain: experimental evidence for emergent E8 symmetry
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Identifying Topological Order by Entanglement Entropy
• Quantum Phase Transitions and Bipartite Entanglement
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Entanglement entropy of random quantum critical points in one dimension
• Universality of Phase Transition Dynamics: Topological Defects from Symmetry Breaking
• Scaling of entanglement support for Matrix Product States
• Entanglement in a second order quantum phase transition
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Entanglement growth in quench dynamics with variable range interactions
• Entanglement Theory and the Second Law of Thermodynamics
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Time evolution algorithms for Matrix Product States and DMRG
• Scaling of Entanglement Entropy in the Random Singlet Phase
• Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains
• Dynamics after a sweep through a quantum critical point
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Quantum critical behavior of ultracold atoms in two-dimensional optical lattices
• How universal is the entanglement spectrum?
• Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition
• Dynamic scaling at classical phase transitions approached through non-equilibrium quenching
• Nonequilibrium quantum criticality in open systems: The dissipation rate as an additional indispensable scaling variable
• Half the entanglement in critical systems is distillable from a single specimen
• Kibble-Zurek Mechanism and Finite-Time Scaling
• Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions
• Dynamics of the entanglement spectrum in spin chains
• Density Matrix Renormalization Group of Gapless Systems
• Entanglement entropy in one-dimensional disordered interacting system: The role of localization
• Universal short-time quantum critical dynamics in imaginary time
• Off-equilibrium scaling behaviors driven by time-dependent external fields in three-dimensional O(N) vector models
• Scaling of the entanglement spectrum in driving critical dynamics
• Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI model
• Kibble-Zurek mechanism beyond adiabaticity: Finite-time scaling with critical initial slip
• Entanglement entropy scaling of the XXZ chain
• Non universality of entanglement convertibility

Cited by in corpus (9)

• Kibble-Zurek mechanism in a one-dimensional incarnation of deconfined quantum critical point
• Scaling Theories of Kosterlitz-Thouless Phase Transitions
• Nonequilibrium critical dynamics in the quantum chiral clock model
• Driving Driven Lattice Gases to Identify Their Universality Classes
• Self-similarity breaking: Anomalous nonequilibrium finite-size scaling and finite-time scaling
• Theory of Critical Phenomena with Memory
• Theory of Critical Phenomena with Long-Range Temporal Interaction
• Is there Kibble-Zurek scaling of topological defects in first-order phase transitions?
• Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry