Fusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebraFusion approach for quantum integrable system associated with the $\mathfrak{gl}(1|1)$ Lie superalgebra

Xiaotian Xu, Wen, Wuxiao, Tao Yang +2 more

In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$ , both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the $U(1)$ symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra $\mathfrak{gl}(1|1)$, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the $U(1)$ symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.

arXiv:2510.27312Oct 31, 20250 citations

Dynamical symmetry of integrable quantum systems

Alexander A. Belavin

Nuclear Physics BMar 1, 1981255 citations

Fusion approach for quantum integrable system associated with the gl(1|1) Lie superalgebra

Xiaotian Xu, Wuxiao Wen, Tao Yang +2 more

In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra \mathfrak{gl}(1|1) 𝔤 𝔩 ( 1 | 1 ) , both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe Ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the U(1) U ( 1 ) symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra \mathfrak{gl}(1|1) 𝔤 𝔩 ( 1 | 1 ) , both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe Ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the U(1) U ( 1 ) symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.

SciPost PhysicsFeb 26, 20260 citations

Wave functions of quantum integrable systems

Михаил Аронович Ольшанецкий

Theoretical and Mathematical PhysicsOct 1, 19833 citations

4D beyond-cohomology topological phase protected by C2 symmetry and its boundary theories

Sheng-Jie Huang

This works uses the two dimensional rotational invariant plane in bosonic symmetry protected topological phases with ${C}_{2}$ rotational symmetry in four dimensions to classify the phases and obtain a boundary field theory as well as an anomalous topological order for the phase that is not captured by the group cohomology classification.This works uses the two dimensional rotational invariant plane in bosonic symmetry protected topological phases with ${C}_{2}$ rotational symmetry in four dimensions to classify the phases and obtain a boundary field theory as well as an anomalous topological order for the phase that is not captured by the group cohomology classification.

arXiv:2001.07772Physical Review ResearchAug 11, 20207 citations

Fusion approach for quantum integrable system associated with the

\mathfrak{gl}(1|1)

Lie superalgebra

In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra

\mathfrak{gl}(1|1)

, both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the

U(1)

symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.

This works uses the two dimensional rotational invariant plane in bosonic symmetry protected topological phases with

{C}_{2}

rotational symmetry in four dimensions to classify the phases and obtain a boundary field theory as well as an anomalous topological order for the phase that is not captured by the group cohomology classification.