Dynamics of the entanglement spectrum in spin chains

  title={Dynamics of the entanglement spectrum in spin chains},
  author={Giacomo Torlai and Luca Tagliacozzo and Gabriele De Chiara},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
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… 

Splitting a critical spin chain

We study a quench protocol that conserves the entanglement spectrum of a bipartition of a quantum system. As an example we consider the splitting of a critical Ising chain into two chains and compare

Entanglement Hamiltonians in 1D free lattice models after a global quantum quench

We study the temporal evolution of the entanglement Hamiltonian of an interval after a global quantum quench in free lattice models in one spatial dimension. In a harmonic chain we explore a quench

Relaxation of the entanglement spectrum in quench dynamics of topological systems

In this paper, we investigate how the entanglement spectrum relaxes to its steady-state values in one-dimensional quadratic systems after a quantum quench. In particular, we apply saddle-point

Signatures of information scrambling in the dynamics of the entanglement spectrum

We examine the time evolution of the entanglement spectrum of a small subsystem of a non-integrable spin chain following a quench from a product state. We identify signatures in this entanglement

Critical Scaling Behaviors of Entanglement Spectra*

We investigate the evolution of entanglement spectra under a global quantum quench from a short-range correlated state to the quantum critical point. Motivated by the conformal mapping, we find that

Schmidt gap in random spin chains

We numerically investigate the low-lying entanglement spectrum of the ground state of random one-dimensional spin chains obtained after partition of the chain into two equal halves. We consider two

On entanglement Hamiltonians of an interval in massless harmonic chains

We study the continuum limit of the entanglement Hamiltonians of a block of consecutive sites in massless harmonic chains. This block is either in the chain on the infinite line or at the beginning

Meson content of entanglement spectra after integrable and nonintegrable quantum quenches

We use tensor network simulations to calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. We

Operator content of entanglement spectra in the transverse field Ising chain after global quenches

We consider the time evolution of the gaps of the entanglement spectrum for a block of consecutive sites in finite transverse field Ising chains after sudden quenches of the magnetic field. We

Floquet dynamical phase transition and entanglement spectrum

We explore both pure and mixed states Floquet dynamical quantum phase transitions (FDQFTs) in the one-dimensional p-wave superconductor with a time-driven pairing phase. In the Fourier space, the



Evolution of entanglement entropy in one-dimensional systems

We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length and its complement, starting from a pure state

Entanglement spectrum and entangled modes of random XX spin chains

We study in this work the ground state entanglement properties of finite XX spin-1/2 chains with random couplings, using Jordan-Wigner transformation. We divide the system into two parts and study

Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition

We study the time evolution of entanglement entropy and entanglement spectrum in a finite-size system which crosses a quantum phase transition at different speeds. We focus on the Ising model with a

Reduced density matrices and entanglement entropy in free lattice models

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a

Energy and multipartite entanglement in multidimensional and frustrated spin models

We investigate the relation between the entanglement properties of a quantum state and its energy for macroscopic spin models. To this aim, we develop a general method to compute energy bounds for

Entanglement spectra of quantum Heisenberg ladders.

This work analyzes the entanglement spectrum of gapped two-leg quantum Heisenberg ladders on a periodic ribbon partitioned into two identical periodic chains, stating a direct correspondence between the low-energy entangler spectrum of a partitioned system and the true spectrum of the virtual edges.

Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry

We study the entanglement spectrum of spin-$1/2$ $XXZ$ ladders both analytically and numerically. Our analytical approach is based on perturbation theory starting either from the limit of strong rung

Entanglement spectrum of a topological phase in one dimension

We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of

Entanglement spectrum of one-dimensional extended Bose-Hubbard models

The entanglement spectrum provides crucial information about correlated quantum systems. We show that the study of the blocklike nature of the reduced density matrix in number sectors and the

Nonlocal order in gapless systems: entanglement spectrum in spin chains.

We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high "entanglement energy" levels, from a