Magnetization and entanglement after a geometric quench in the XXZ chain

Gruber, Matthias; Eisler, Viktor

doi:10.1103/physrevb.99.174403

Cited by 26 publications

(36 citation statements)

References 72 publications

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“…Consequently, the entanglement properties in the dynamical and static problems are identical. The entanglement entropy for a biased hopping chain was studied in [55,[57][58][59] between two parts of the chain, with the cut located somewhere along the emerging front. The growth was found to be logarithmic, however with a different prefactor as for the local (unbiased) quench.…”

Section: A Homogeneous Chainmentioning

confidence: 99%

Time evolution of entanglement negativity across a defect

Gruber¹,

Eisler²

2020

J. Phys. A: Math. Theor.

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We consider a quench in a free-fermion chain by joining two homogeneous half-chains via a defect. The time evolution of the entanglement negativity is studied between adjacent segments surrounding the defect. In case of equal initial fillings, the negativity grows logarithmically in time and essentially equals one-half of the Rényi mutual information with index α = 1/2 in the limit of large segments. In sharp contrast, in the biased case one finds a linear increase followed by the saturation at an extensive value for both quantities, which is due to the backscattering from the defect and can be reproduced in a quasiparticle picture. Furthermore, a closer inspection of the subleading corrections reveals that the negativity and the mutual information have a small but finite difference in the steady state. Finally, we also study a similar quench in the XXZ spin chain via density-matrix renormalization group methods and compare the results for the negativity to the fermionic case.

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Section: A Homogeneous Chainmentioning

confidence: 99%

Time evolution of entanglement negativity across a defect

Gruber¹,

Eisler²

2020

J. Phys. A: Math. Theor.

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“…Letting the system evolve, the domain wall starts to melt, giving rise to an expanding front region characterized by a nonzero spin current. The resulting magnetization profiles were studied in various integrable spin models such as the XX chain [6][7][8], the transverse Ising (TI) [9][10][11], the XY [12] as well as the XXZ chains [4,[13][14][15][16][17]. Rather generically one finds ballistic transport, with the exception of the isotropic Heisenberg chain where a diffusive behaviour is observed instead [18][19][20][21][22].…”

mentioning

confidence: 99%

Front dynamics in the XY chain after local excitations

Eisler

Maislinger

2020

SciPost Phys.

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We study the time evolution of magnetization and entanglement for initial states with local excitations, created upon the ferromagnetic ground state of the XY chain. For excitations corresponding to a single or two well separated domain walls, the magnetization profile has a simple hydrodynamic limit, which has a standard interpretation in terms of quasiparticles. In contrast, for a spin-flip we obtain an interference term, which has to do with the nonlocality of the excitation in the fermionic basis. Surprisingly, for the single domain wall the hydrodynamic limit of the entropy and magnetization profiles are found to be directly related. Furthermore, the entropy profile is additive for the double domain wall, whereas in case of the spin-flip excitation one has a nontrivial behaviour.

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“…Halfway between these two scenarios, a peculiar class of quantum quenches is that of bi-partitioning protocols see e.g. [9-11, 13, 30, 37, 64-71], where a logarithmic growth of entanglement [30,37,64,65,67] is associated with the integrability of the model. In this context, a remarkable example is the time-evolution of a domain-wall state |↑ .…”

Section: Introductionmentioning

confidence: 99%

“…↓ (in some literature this protocol is known as a geometric quench [65,67,72]). This setup has been studied intensively in the past and the exact expressions for the conserved charges and current profiles have been found for a spin-1/2 xxz model both in the free [68,73] and interacting [67] cases. Very recently, it was also shown that initial quantum correlations can suppress particle transport [74].…”

Section: Introductionmentioning

confidence: 99%

Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion

Scopa,

Krajenbrink,

Calabrese

et al. 2021

Preprint

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We consider the non-equilibrium dynamics of the entanglement entropy of a onedimensional quantum gas of hard-core particles, initially confined in a box potential at zero temperature. At t = 0 the right edge of the box is suddenly released and the system is let free to expand. During this expansion, the initially correlated region propagates with a non-homogeneous profile, leading to the growth of entanglement entropy. This setting is investigated in the hydrodynamic regime, with tools stemming from semi-classical Wigner function approach and with recent developments of quantum fluctuating hydrodynamics. Within this framework, the entanglement entropy can be associated to a correlation function of chiral twist-fields of the conformal field theory that lives along the Fermi contour and it can be exactly determined. Our predictions for the entanglement evolution are found in agreement with and generalize previous results in literature based on numerical calculations and heuristic arguments.

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Magnetization and entanglement after a geometric quench in the XXZ chain

Cited by 26 publications

References 72 publications

Time evolution of entanglement negativity across a defect

Time evolution of entanglement negativity across a defect

Front dynamics in the XY chain after local excitations

Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion

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