Dynamics of the entanglement spectrum in spin chains

Abstract

We study the dynamics of the entanglement spectrum, that is the time evolution of the eigenvalues of the reduced density matrices after a bipartition of a one-dimensional spin chain. Starting from the ground state of an initial Hamiltonian, the state of the system is evolved in time with a new Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the system Hamiltonian across a quantum phase transition. We analyse the Ising model that can be exactly solved and the XXZ for which we employ the time-dependent density matrix renormalisation group algorithm. Our results show once more a connection between the Schmidt gap, i.e. the difference of the two largest eigenvalues of the reduced density matrix and order parameters, in this case the spontaneous magnetisation.

16 pages, 8 figures, comments are welcome! Version published in JSTAT special issue on "Quantum Entanglement In Condensed Matter Physics"

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• Rényi entropies after releasing the Néel state in the XXZ spin-chain
• Quenching small quantum gases: Genesis of the orthogonality catastrophe
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• On entanglement hamiltonians of an interval in massless harmonic chains
• Edge-entanglement spectrum correspondence in a nonchiral topological phase and Kramers-Wannier duality
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• Exact work statistics of quantum quenches in the anisotropic XY model
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• Scaling of the entanglement spectrum in driving critical dynamics
• Loschmidt amplitude spectrum in dynamical quantum phase transitions
• On the continuum limit of the entanglement Hamiltonian of a sphere for the free massless scalar field
• Entanglement and precession in two-dimensional dynamical quantum phase transitions
• Topological and dynamical properties of a generalized cluster model in one dimension
• Dynamics of the quantum search and quench-induced first-order phase transitions
• Signatures of information scrambling in the dynamics of the entanglement spectrum
• Quantum spin fluctuations in dynamical quantum phase transitions
• Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement
• Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems
• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Universal Single-Frequency Oscillations in a Quantum Impurity System After a Local Quench
• Momentum-Space Entanglement in Heisenberg Spin-Half Ladders
• Scaling theory of entanglement entropy in confinements near quantum critical points
• Survival of time-evolved correlations depends on whether quenching is across critical point in XY spin chain
• Critical Scaling Behaviors of Entanglement Spectra
• Splitting a critical spin chain
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches
• Schmidt gap in random spin chains
• Quantum coherence assisted dynamical phase transition
• On quenches to the critical point of the three states Potts model -- Matrix Product State simulations and CFT
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Relaxation of the entanglement spectrum in quench dynamics of topological systems
• Dynamics of Entanglement and the Schmidt Gap in a Driven Light-Matter System
• Entanglement-informed Construction of Variational Quantum Circuits
• Pauli weight requirement of the matrix elements in time-evolved local operators: dependence beyond the equilibration temperature
• Fermionic Approach to Elementary Excitations and Magnetization Plateaus in an S=1/2 XX Hybrid Trimer-Dimer Chain