Entanglement signatures of phase transition in higher-derivative quantum field theories

Ghosh, Suman; Shankaranarayanan, S.

doi:10.1103/physrevd.86.125011

Cited by 7 publications

(12 citation statements)

References 32 publications

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“…The importance of the higher derivative spatial terms were studied in Refs. [18,19] and can be used to understand some quantum phase transitions. Unlike the Wilsonian type renormalization [10][11][12], the higher derivative terms introduce Next-to-Next-to-Next interaction in the lattice.…”

Section: The Model: Massless Self Interacting Scalar Fieldmentioning

confidence: 99%

Role of spatial higher order derivatives in momentum space entanglement

Kumar

Shankaranarayanan

2017

Phys. Rev. D

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We study the momentum space entanglement between different energy modes of interacting scalar fields propagating in general (D + 1)-dimensional flat space-time. As opposed to some of the recent works [1], we use Lorentz invariant normalized ground state to obtain the momentum space entanglement entropy. We show that the Lorenz invariant definition removes the spurious power-law behaviour obtained in the earlier works [1]. More specifically, we show that the cubic interacting scalar field in (1 + 1) dimensions leads to logarithmic divergence of the entanglement entropy and consistent with the results from real space entanglement calculations. We study the effects of the introduction of the Lorentz violating higher derivative terms in the presence of non-linear self interacting scalar field potential and show that the divergence structure of the entanglement entropy is improved in the presence of spatial higher derivative terms.

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Section: The Model: Massless Self Interacting Scalar Fieldmentioning

confidence: 99%

Role of spatial higher order derivatives in momentum space entanglement

Kumar

Shankaranarayanan

2017

Phys. Rev. D

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“…(ii) It is well-known that term with non-linear terms lead to classical Lifshitz transitions 40 , 41 . Here, we show that terms or NNN coupling drives QPT 42 . (iii) It is important to note the differences between quantum Lifshitz transitions and our case.…”

Section: Model and Setupmentioning

confidence: 66%

“…The model Hamiltonian in Eq. ( 1 ) was first studied in three dimensional space and concluded with the following salient remarks 42 : (i) EE violates area-law in three dimensional space. (ii) NNN coupling term is responsible for the change in the behaviour of EE and thus changes the ground system properties of the system at QCP.…”

Section: Resultsmentioning

confidence: 99%

“…A qualitative understanding of excitation of higher modes (for ) can be understood using the quantum mechanical model of a particle in a 2-dimensional box of length L 42 . It was explicitly shown that Equation ( 21 ) implies that, for , the ground state energy eigenvalue for case II is higher compared to that of canonical scalar field.…”

Section: Discussion and Future Outlookmentioning

confidence: 99%

“…The procedure to obtain the entanglement entropy is similar to the one discussed in refs 39 , 42 . We assume that the quantum state corresponding to the Hamiltonian of the N -harmonic oscillator system is the ground state i. e. .…”

Section: Model and Setupmentioning

confidence: 99%

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Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories

Kumar

Shankaranarayanan

2017

Sci Rep

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In a bipartite set-up, the vacuum state of a free Bosonic scalar field is entangled in real space and satisfies the area-law— entanglement entropy scales linearly with area of the boundary between the two partitions. In this work, we show that the area law is violated in two spatial dimensional model Hamiltonian having dynamical critical exponent z = 3. The model physically corresponds to next-to-next-to-next nearest neighbour coupling terms on a lattice. The result reported here is the first of its kind of violation of area law in Bosonic systems in higher dimensions and signals the evidence of a quantum phase transition. We provide evidence for quantum phase transition both numerically and analytically using quantum Information tools like entanglement spectra, quantum fidelity, and gap in the energy spectra. We identify the cause for this transition due to the accumulation of large number of angular zero modes around the critical point which catalyses the change in the ground state wave function due to the next-to-next-to-next nearest neighbor coupling. Lastly, using Hubbard-Stratanovich transformation, we show that the effective Bosonic Hamiltonian can be obtained from an interacting fermionic theory and provide possible implications for condensed matter systems.

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