arXiv:2207.06866 · Physics Letters B

Overlaps for matrix product states of arbitrary bond dimension in ABJM theory

Tamás Gombor, Charlotte Kristjansen

Published Sep 1, 2022• 19 citations

Abstract

We find a closed formula for the overlap of Bethe eigenstates of an alternating SU(4) spin chain, describing the scalar sector of ABJM theory, and matrix product states of any bond dimension representing 1/2 BPS co-dimension one domain walls in the field theory. One point functions of the defect CFTs involved, being directly expressible in terms of these overlaps, are hence completely determined.

DOI: 10.1016/j.physletb.2022.137428

Related papers

Scalar one-point functions and matrix product states of AdS/dCFT

Marius de Leeuw, Charlotte Kristjansen, Γεώργιος Λιναρδόπουλος

arXiv:1802.01598Physics Letters BApr 4, 201890 citations

Exact overlaps for all integrable two-site boundary states of gl(N) symmetric spin chains

T. Gombor

Jan 1, 20241 citation

Exact overlaps for all integrable two-site boundary states of $$ \mathfrak{gl} $$(N) symmetric spin chains

Tamás Gombor

A bstract We find closed formulas for the overlaps of Bethe eigenstates of $$ \mathfrak{gl} $$ gl ( N ) symmetric spin chains and integrable boundary states. We derive the general overlap formulas for $$ \mathfrak{gl} $$ gl ( M ) ⊕ $$ \mathfrak{gl} $$ gl ( N − M ) symmetric boundary states and give a well-established conjecture for the $$ \mathfrak{sp} $$ sp ( N ) symmetric case. Combining these results with the previously derived $$ \mathfrak{so} $$ so ( N ) symmetric formula, now we have the overlap functions for all integrable boundary states of the $$ \mathfrak{gl} $$ gl ( N ) spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the SO(6) and the alternating SU(4) spin chains which describe the scalar sectors of $$ \mathcal{N} $$ N = 4 super Yang-Mills and ABJM theories which are important application areas of our results.

arXiv:2311.04870Journal of High Energy PhysicsMay 16, 202413 citations

Derivations for the MPS overlap formulas of rational spin chains

Tamás Gombor

A bstract We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in $$ {\mathfrak{gl}}_N $$ gl N symmetric spin chains. This formula expresses the normalized overlap as a product of a MPS-independent Gaudin-determinant ratio and a MPS-dependent scalar factor constructed from eigenvalues of commuting operators, defined via the K -matrix associated with the MPS. Our proof is fully representation-independent and relies solely on algebraic Bethe Ansatz techniques and the KT -relation. We also propose a generalization of the overlap formula to $$ {\mathfrak{so}}_N $$ so N and $$ {\mathfrak{sp}}_N $$ sp N spin chains, supported by algebra embeddings and low-rank isomorphisms. These results significantly broaden the class of integrable initial states for which exact overlap formulas are available, with implications for quantum quenches and defect CFTs.

arXiv:2505.20234Journal of High Energy PhysicsOct 3, 20251 citation

Exact Overlaps for All Integrable Matrix Product States of Rational Spin Chains

Tamás Gombor

The overlaps between integrable matrix product states (MPSs) and Bethe states are important in both the nonequilibrium statistical physics and the AdS/CFT duality. We present the general MPS overlap formula. The result is a product of a ratio of Gaudin determinants and a prefactor. The Gaudin determinants depend on the spin chain but not on the MPS. The MPS dependent prefactor is given for all integrable MPSs of the gl_{N}, o_{N}, and sp_{N} symmetric spin chains with arbitrary representations.

arXiv:2410.23282Physical Review LettersSep 19, 20255 citations

On exact overlaps of integrable matrix product states: inhomogeneities, twists and dressing formulas

Tamás Gombor, Charlotte Kristjansen, Vasileios Moustakis +1 more

arXiv:2410.23117Journal of High Energy PhysicsFeb 18, 20253 citations

arXiv:2207.06866 · Physics Letters B

Overlaps for matrix product states of arbitrary bond dimension in ABJM theory

Tamás Gombor, Charlotte Kristjansen

Published Sep 1, 2022• 19 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.physletb.2022.137428

Related papers

Scalar one-point functions and matrix product states of AdS/dCFT

Marius de Leeuw, Charlotte Kristjansen, Γεώργιος Λιναρδόπουλος

We determine in a closed form all scalar one-point functions of the defect CFT dual to the D3–D5 probe brane system with k units of flux which amounts to calculating the overlap between a Bethe eigenstate of the integrable SO(6) spin chain and a certain matrix product state of bond dimension k. In particular, we show that the matrix product state is annihilated by all the parity odd charges of the spin chain which has recently been suggested as the criterion for such a state to correspond to an integrable initial state. Finally, we discuss the properties of the analogous matrix product state for the SO(5) symmetric D3–D7 probe brane set-up.We determine in a closed form all scalar one-point functions of the defect CFT dual to the D3–D5 probe brane system with k units of flux which amounts to calculating the overlap between a Bethe eigenstate of the integrable SO(6) spin chain and a certain matrix product state of bond dimension k. In particular, we show that the matrix product state is annihilated by all the parity odd charges of the spin chain which has recently been suggested as the criterion for such a state to correspond to an integrable initial state. Finally, we discuss the properties of the analogous matrix product state for the SO(5) symmetric D3–D7 probe brane set-up.

arXiv:1802.01598Physics Letters BApr 4, 201890 citations

Exact overlaps for all integrable two-site boundary states of gl(N) symmetric spin chains

T. Gombor

We find closed formulas for the overlaps of Bethe eigenstates of $\\mathfrak{gl}(N)$ symmetric spin chains and integrable boundary states. We derive the general overlap formulas for $\\mathfrak{gl}(M)\\oplus\\mathfrak{gl}(N-M)$ symmetric boundary states and give a well-established conjecture for the $\\mathfrak{sp}(N)$ symmetric case. Combining these results with the previously derived $\\mathfrak{so}(N)$ symmetric formula, now we have the overlap functions for all integrable boundary states of the $\\mathfrak{gl}(N)$ spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the $SO(6)$ and the alternating $SU(4)$ spin chains which describe the scalar sectors of $\\mathcal{N}=4$ super Yang-Mills and ABJM theories which are important application areas of our results.We find closed formulas for the overlaps of Bethe eigenstates of $\\mathfrak{gl}(N)$ symmetric spin chains and integrable boundary states. We derive the general overlap formulas for $\\mathfrak{gl}(M)\\oplus\\mathfrak{gl}(N-M)$ symmetric boundary states and give a well-established conjecture for the $\\mathfrak{sp}(N)$ symmetric case. Combining these results with the previously derived $\\mathfrak{so}(N)$ symmetric formula, now we have the overlap functions for all integrable boundary states of the $\\mathfrak{gl}(N)$ spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the $SO(6)$ and the alternating $SU(4)$ spin chains which describe the scalar sectors of $\\mathcal{N}=4$ super Yang-Mills and ABJM theories which are important application areas of our results.

Jan 1, 20241 citation

Exact overlaps for all integrable two-site boundary states of $\mathfrak{gl}$ (N) symmetric spin chainsExact overlaps for all integrable two-site boundary states of $$ \mathfrak{gl} $$(N) symmetric spin chains

Tamás Gombor

A bstract We find closed formulas for the overlaps of Bethe eigenstates of $\mathfrak{gl}$ gl ( N ) symmetric spin chains and integrable boundary states. We derive the general overlap formulas for $\mathfrak{gl}$ gl ( M ) ⊕ $\mathfrak{gl}$ gl ( N − M ) symmetric boundary states and give a well-established conjecture for the $\mathfrak{sp}$ sp ( N ) symmetric case. Combining these results with the previously derived $\mathfrak{so}$ so ( N ) symmetric formula, now we have the overlap functions for all integrable boundary states of the $\mathfrak{gl}$ gl ( N ) spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the SO(6) and the alternating SU(4) spin chains which describe the scalar sectors of $\mathcal{N}$ N = 4 super Yang-Mills and ABJM theories which are important application areas of our results.A bstract We find closed formulas for the overlaps of Bethe eigenstates of $$ \mathfrak{gl} $$ gl ( N ) symmetric spin chains and integrable boundary states. We derive the general overlap formulas for $$ \mathfrak{gl} $$ gl ( M ) ⊕ $$ \mathfrak{gl} $$ gl ( N − M ) symmetric boundary states and give a well-established conjecture for the $$ \mathfrak{sp} $$ sp ( N ) symmetric case. Combining these results with the previously derived $$ \mathfrak{so} $$ so ( N ) symmetric formula, now we have the overlap functions for all integrable boundary states of the $$ \mathfrak{gl} $$ gl ( N ) spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the SO(6) and the alternating SU(4) spin chains which describe the scalar sectors of $$ \mathcal{N} $$ N = 4 super Yang-Mills and ABJM theories which are important application areas of our results.

arXiv:2311.04870Journal of High Energy PhysicsMay 16, 202413 citations

Derivations for the MPS overlap formulas of rational spin chains

Tamás Gombor

A bstract We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in ${\mathfrak{gl}}_N$ gl N symmetric spin chains. This formula expresses the normalized overlap as a product of a MPS-independent Gaudin-determinant ratio and a MPS-dependent scalar factor constructed from eigenvalues of commuting operators, defined via the K -matrix associated with the MPS. Our proof is fully representation-independent and relies solely on algebraic Bethe Ansatz techniques and the KT -relation. We also propose a generalization of the overlap formula to ${\mathfrak{so}}_N$ so N and ${\mathfrak{sp}}_N$ sp N spin chains, supported by algebra embeddings and low-rank isomorphisms. These results significantly broaden the class of integrable initial states for which exact overlap formulas are available, with implications for quantum quenches and defect CFTs.A bstract We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in $$ {\mathfrak{gl}}_N $$ gl N symmetric spin chains. This formula expresses the normalized overlap as a product of a MPS-independent Gaudin-determinant ratio and a MPS-dependent scalar factor constructed from eigenvalues of commuting operators, defined via the K -matrix associated with the MPS. Our proof is fully representation-independent and relies solely on algebraic Bethe Ansatz techniques and the KT -relation. We also propose a generalization of the overlap formula to $$ {\mathfrak{so}}_N $$ so N and $$ {\mathfrak{sp}}_N $$ sp N spin chains, supported by algebra embeddings and low-rank isomorphisms. These results significantly broaden the class of integrable initial states for which exact overlap formulas are available, with implications for quantum quenches and defect CFTs.

arXiv:2505.20234Journal of High Energy PhysicsOct 3, 20251 citation

Exact Overlaps for All Integrable Matrix Product States of Rational Spin Chains

Tamás Gombor

arXiv:2410.23282Physical Review LettersSep 19, 20255 citations

On exact overlaps of integrable matrix product states: inhomogeneities, twists and dressing formulas

Tamás Gombor, Charlotte Kristjansen, Vasileios Moustakis +1 more

A bstract Invoking a quantum dressing procedure as well as the representation theory of twisted Yangians we derive a number of summation formulas for the overlap between integrable matrix product states and Bethe eigenstates which involve only eigenvalues of fused transfer matrices and which are valid in the presence of inhomogeneities as well as twists. Although the method is general we specialize to the SO(6) spin chain for which integrable matrix product states corresponding to evaluation representations of the twisted Yangian Y + (4) encode the information about one-point functions of the D3-D5 domain wall version of $\mathcal{N}$ N = 4 SYM. Considering the untwisted and homogeneous limit of our summation formulas we finally fill the last gap in the analytical understanding of the overlap formula for the SO(6) sector of the D3-D5 domain wall system.A bstract Invoking a quantum dressing procedure as well as the representation theory of twisted Yangians we derive a number of summation formulas for the overlap between integrable matrix product states and Bethe eigenstates which involve only eigenvalues of fused transfer matrices and which are valid in the presence of inhomogeneities as well as twists. Although the method is general we specialize to the SO(6) spin chain for which integrable matrix product states corresponding to evaluation representations of the twisted Yangian Y + (4) encode the information about one-point functions of the D3-D5 domain wall version of $$ \mathcal{N} $$ N = 4 SYM. Considering the untwisted and homogeneous limit of our summation formulas we finally fill the last gap in the analytical understanding of the overlap formula for the SO(6) sector of the D3-D5 domain wall system.

arXiv:2410.23117Journal of High Energy PhysicsFeb 18, 20253 citations

We find closed formulas for the overlaps of Bethe eigenstates of

\\mathfrak{gl}(N)

symmetric spin chains and integrable boundary states. We derive the general overlap formulas for

\\mathfrak{gl}(M)\\oplus\\mathfrak{gl}(N-M)

symmetric boundary states and give a well-established conjecture for the

\\mathfrak{sp}(N)

symmetric case. Combining these results with the previously derived

\\mathfrak{so}(N)

symmetric formula, now we have the overlap functions for all integrable boundary states of the

\\mathfrak{gl}(N)

spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the

SO(6)

and the alternating

SU(4)

spin chains which describe the scalar sectors of

\\mathcal{N}=4

super Yang-Mills and ABJM theories which are important application areas of our results.

Exact overlaps for all integrable two-site boundary states of

\mathfrak{gl}

(N) symmetric spin chains

A bstract We find closed formulas for the overlaps of Bethe eigenstates of

\mathfrak{gl}

gl ( N ) symmetric spin chains and integrable boundary states. We derive the general overlap formulas for

\mathfrak{gl}

gl ( M ) ⊕

\mathfrak{gl}

gl ( N − M ) symmetric boundary states and give a well-established conjecture for the

\mathfrak{sp}

sp ( N ) symmetric case. Combining these results with the previously derived

\mathfrak{so}

so ( N ) symmetric formula, now we have the overlap functions for all integrable boundary states of the

\mathfrak{gl}

gl ( N ) spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the SO(6) and the alternating SU(4) spin chains which describe the scalar sectors of

\mathcal{N}

N = 4 super Yang-Mills and ABJM theories which are important application areas of our results.

A bstract We derive a universal formula for the overlaps between integrable matrix product states (MPS) and Bethe eigenstates in

{\mathfrak{gl}}_N

gl N symmetric spin chains. This formula expresses the normalized overlap as a product of a MPS-independent Gaudin-determinant ratio and a MPS-dependent scalar factor constructed from eigenvalues of commuting operators, defined via the K -matrix associated with the MPS. Our proof is fully representation-independent and relies solely on algebraic Bethe Ansatz techniques and the KT -relation. We also propose a generalization of the overlap formula to

{\mathfrak{so}}_N

so N and

{\mathfrak{sp}}_N

sp N spin chains, supported by algebra embeddings and low-rank isomorphisms. These results significantly broaden the class of integrable initial states for which exact overlap formulas are available, with implications for quantum quenches and defect CFTs.

\mathcal{N}

N = 4 SYM. Considering the untwisted and homogeneous limit of our summation formulas we finally fill the last gap in the analytical understanding of the overlap formula for the SO(6) sector of the D3-D5 domain wall system.