arXiv:2306.07784

$T\bar{T}$-deformed Entanglement Entropy for Integrable Quantum Field Theory

Miao He, Jue Hou, Yunfeng Jiang

Published Jun 13, 2023• 0 citations

Abstract

We calculate the $T\bar{T}$-deformed entanglement entropy for integrable quantum field theories (IQFTs) using the form factor bootstrap approach. We solve the form factor bootstrap axioms for the branch-point twist fields and obtain the deformed form factors. Using these form factors, we compute the deformed von Neuman entropy up to two particle contributions. The solution of the form factor axioms is not unique. We find that for the simplest solution of the bootstrap axioms, the UV limit of the entanglement entropy takes the same form as the undeformed one, but the effective central charge is deformed. For solutions with additional CDD-like factors, we can have different behaviors. The IR corrections, which only depends on the particle spectrum is untouched.

DOI: 10.48550/arxiv.2306.07784

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$$ T\overline{T} $$-deformed entanglement entropy for IQFT

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arXiv:2306.07784

$T\bar{T}$ -deformed Entanglement Entropy for Integrable Quantum Field Theory$T\bar{T}$-deformed Entanglement Entropy for Integrable Quantum Field Theory

Miao He, Jue Hou, Yunfeng Jiang

Published Jun 13, 2023• 0 citations

arXiv HTML PDF

Abstract

We calculate the

T\bar{T}

-deformed entanglement entropy for integrable quantum field theories (IQFTs) using the form factor bootstrap approach. We solve the form factor bootstrap axioms for the branch-point twist fields and obtain the deformed form factors. Using these form factors, we compute the deformed von Neuman entropy up to two particle contributions. The solution of the form factor axioms is not unique. We find that for the simplest solution of the bootstrap axioms, the UV limit of the entanglement entropy takes the same form as the undeformed one, but the effective central charge is deformed. For solutions with additional CDD-like factors, we can have different behaviors. The IR corrections, which only depends on the particle spectrum is untouched.

DOI: 10.48550/arxiv.2306.07784

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Entanglement entropy from form factors in $\textrm{T}\overline{\textrm{T}}$ -deformed integrable quantum field theoriesEntanglement entropy from form factors in $$ \textrm{T}\overline{\textrm{T}} $$-deformed integrable quantum field theories

Olalla A. Castro-Alvaredo, Stefano Negro, Fabio Sailis

Abstract In two recent papers [1, 2] we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised $\textrm{T}\overline{\textrm{T}}$ T T ¯ -deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to $\textrm{T}\overline{\textrm{T}}$ T T ¯ -perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for $\textrm{T}\overline{\textrm{T}}$ T T ¯ -perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of the recent publication [3] where the same problem has been addressed.Abstract In two recent papers [1, 2] we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ -deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ -perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for $$ \textrm{T}\overline{\textrm{T}} $$ T T ¯ -perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of the recent publication [3] where the same problem has been addressed.

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Olalla A. Castro-Alvaredo, Stefano Negro, Fabio Sailis

In two recent papers we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised $\mathrm{T}\bar{\mathrm{T}}$ -deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to $\mathrm{T}\bar{\mathrm{T}}$ -perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for $\mathrm{T}\bar{\mathrm{T}}$ -perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of a recent publication where the same problem has been addressed.In two recent papers we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised $\mathrm{T}\bar{\mathrm{T}}$-deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to $\mathrm{T}\bar{\mathrm{T}}$-perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for $\mathrm{T}\bar{\mathrm{T}}$-perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of a recent publication where the same problem has been addressed.

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T\bar{T}

-deformed Entanglement Entropy for Integrable Quantum Field Theory

We calculate the

T\bar{T}

T\overline{T}

-deformed entanglement entropy for IQFT

A bstract We calculate the

T\overline{T}

T T ¯ -deformed entanglement entropy for integrable quantum field theories (IQFTs) using the form factor bootstrap approach. We solve the form factor bootstrap axioms for the branch-point twist fields and obtain the deformed form factors. Using these form factors, we compute the deformed von Neuman entropy up to two particle contributions. The solution of the form factor axioms is not unique. We find that for the simplest solution of the bootstrap axioms, the UV limit of the entanglement entropy takes the same form as the undeformed one, but the effective central charge is deformed. For solutions with additional CDD-like factors, we can have different behaviors. The IR corrections, which only depends on the particle spectrum is untouched.

\frac{c_{\text{eff}}}{3}\log \ell

where

c_{\text{eff}}

is the effective central charge of the theory (a positive number related to the central charge) and

\ell

is the size of the region. Furthermore the form factor expansion of twist fields allows us to explore the large region limit of the entanglement entropy and find the next-to-leading order correction to saturation. We find that this correction is very different from its counterpart in unitary models. Whereas in the latter case, it had a form depending only on few parameters of the model (the particle spectrum), it appears to be much more model-dependent for non-unitary models.

Entanglement entropy from form factors in

\textrm{T}\overline{\textrm{T}}

-deformed integrable quantum field theories

Abstract In two recent papers [1, 2] we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised

\textrm{T}\overline{\textrm{T}}

T T ¯ -deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to

\textrm{T}\overline{\textrm{T}}

T T ¯ -perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for

\textrm{T}\overline{\textrm{T}}

T T ¯ -perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of the recent publication [3] where the same problem has been addressed.

Entanglement Entropy from Form Factors in

\mathrm{T}\bar{\mathrm{T}}

-Deformed Integrable Quantum Field Theories

In two recent papers we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised

\mathrm{T}\bar{\mathrm{T}}

-deformed integrable quantum field theories. This new program, based on the construction of form factors, opens many avenues for future study, one of which we address in this paper: computing entanglement measures employing branch point twist fields. Indeed, over the past 15 years, this has become one the leading methods for the computation of entanglement measures, both in conformal field theory and integrable quantum field theory. Thus the generalisation of this program to

\mathrm{T}\bar{\mathrm{T}}

-perturbed theories offers a promising new tool for the study of entanglement measures in the presence of irrelevant perturbations. In this paper, we show that the natural two-particle form factor solution for branch point twist fields in replica theories with diagonal scattering admits a simple generalisation to a solution for

\mathrm{T}\bar{\mathrm{T}}

-perturbed theories. Starting with this solution, some of the known properties of entanglement measures in massive integrable quantum field theories can be generalised to the perturbed models. We show this by focusing on the Ising field theory. During the completion of this paper, we became aware of a recent publication where the same problem has been addressed.