Entanglement entropy of excited states in the quantum Lifshitz model

Angel-Ramelli, J.

doi:10.1088/1742-5468/abcd35

Cited by 12 publications

(8 citation statements)

References 65 publications

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“…In previous works [52,54] and the present paper, we have focused on one-dimensional quantum systems. The entanglement in excited states of higher dimensional free and interacting quantum systems has been investigated in for example [45,51], suggesting that there are simple formulas as in one dimensions. It would be interesting to adapt the subsystem mode method to higher dimensions and check the results in various higher dimensional quantum systems.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Entanglement of magnon excitations in spin chains

Zhang

Rajabpour

2022

J. High Energ. Phys.

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We calculate exactly the entanglement content of magnon excited states in the integrable spin-1/2 XXX and XXZ chains in the scaling limit. In particular, we show that as far as the number of excited magnons with respect to the size of the system is small one can decompose the entanglement content, in the scaling limit, to the sum of the entanglement of particular excited states of free fermionic or bosonic theories. In addition we conjecture that the entanglement content of the generic translational invariant free fermionic and bosonic Hamiltonians can be also classified, in the scaling limit, with respect to the entanglement content of the fermionic and bosonic chains with the number operator as the Hamiltonian in certain circumstances. Our results effectively classify the entanglement content of wide range of integrable spin chains in the scaling limit.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Entanglement of magnon excitations in spin chains

Zhang

Rajabpour

2022

J. High Energ. Phys.

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“…Connected correlations with an exponential bound Ce −m(x2−x1) are characteristic of a gapped phase with mass m. We identify ξ = ω −1 = √ κ/m as the correlation length, and recover the quantum critical Lifshitz boson in the massless limit. Expressions (36) and (37) do not depend on the choice of boundary conditions. We are surprised to find that when the correlation length is infinite (requiring both ω → 0 and L → ∞ to be effective), the theory develops an IR divergence in bulk correlations.…”

Section: A Correlations In the Groundstatementioning

confidence: 99%

“…Because of their simple form and relation to a lower-dimensional classical theory, RK states offer a useful and controlled framework to analytically compute, e.g., correlation functions and entanglement measures such as entanglement entropy, which is notoriously hard to achieve in quantum many-body systems in general. Systems poised at a RK point have been extensively studied, in particular their entanglement properties [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

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confidence: 99%

Entanglement and separability in continuum Rokhsar-Kivelson states

Boudreault¹,

Berthiere²,

Witczak-Krempa³

2021

Preprint

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Starting from the (d + 1)-dimensional Lifshitz critical boson with dynamical exponent z = 2, we propose two nontrivial deformations that preserve the Rokhsar-Kivelson structure where the groundstate is encoded in an underlying, local d-dimensional QFT. Specializing to d = 1 spatial dimension, the first deformation maps the groundstate to the quantum harmonic oscillator, leading to a gap for the scalar. We study the resulting correlation functions, and find that Cluster Decomposition is restored. The special form of the groundstate allows to analytically compute the c-function for the entanglement entropy along a renormalization group (RG) flow for the wavefunction, which is found to be strictly decreasing as in conformal field theories (CFTs). From the entropic c-function, we obtain the corner term for the z = 2 Lifshitz critical boson in (2+1)D in the small angle limit. The second deformation is non-Gaussian and yields a groundstate described by SL(2, R)-conformal quantum mechanics. This deformation preserves the conformal spatial symmetry of the groundstate, and constrains the form of the correlators and entanglement entropy. As a byproduct of our calculations, we obtain explicit results for the capacity of entanglement in Lifshitz theories and discuss their interpretation. We also prove the separability of the reduced density matrix of two disconnected subsystems for real-valued RK wavefunctions, implying the vanishing of logarithmic negativity. Finally, we comment on the relations to certain stoquastic quantum spin chains, the Motzkin and Fredkin chains.

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“…Entanglement entropy for Lifshitz bosons also have been studied, such as in the quantum Lifshitz model with z = 2 in 2+1 dimensions (see e.g. [18][19][20][21][22][23][24][25] for a partial list of references), and more generally for z = d + 1 in [26][27][28]. More recently studies for generic z were carried out in in e.g.…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropy with Lifshitz fermions

Hartmann

Kavanagh

2021

SciPost Phys.

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We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent z. Remarkably, in the ground state the entanglement entropy vanishes for even values of z, whereas for odd values it is independent of z and equal to the relativistic case with z=1. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of z and T which we plot using the lattice correlation method. The dependence on the even- or oddness of z still shows for small temperatures, but is washed out for large temperatures or large values of z.

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Entanglement entropy of excited states in the quantum Lifshitz model

Cited by 12 publications

References 65 publications

Entanglement of magnon excitations in spin chains

Entanglement of magnon excitations in spin chains

Entanglement and separability in continuum Rokhsar-Kivelson states

Entanglement entropy with Lifshitz fermions

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