Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1810.12038 · International Symposium on Lattice Field Theory (LATTICE)

Investigation of the 1+1 dimensional Thirring model using the method of matrix product states

C.-J. David Lin, Mari Carmen Bañuls, Krzysztof Cichy, Ying-Jer Kao, Yu-Ping Lin, Tao-Lin Tan

Published May 29, 2019• 5 citations
arXivHTMLPDF

Abstract

We present preliminary results of a study on the non-thermal phase structure of the (1+1) dimensional massive Thirring model, employing the method of matrix product states. Through investigating the entanglement entropy, the fermion correlators and the chiral condensate, it is found that this approach enables us to observe numerical evidence of a Kosterlitz-Thouless phase transition in the model.

DOI
10.22323/1.334.0229

Related papers

Phase structure of the ( 1+1 )-dimensional massive Thirring model from matrix product states

Mari Carmen Bañuls, Krzysztof Cichy, Ying-Jer Kao +3 more

Employing matrix product states as an ansatz, we study the nonthermal phase structure of the ($1+1$)-dimensional massive Thirring model in the sector of a vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate, and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with the nonzero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behavior, and they serve as an important ingredient for controlling the continuum extrapolation of the model.

arXiv:1908.04536•Physical review. D/Physical review. D.•Nov 20, 2019•17 citations

Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method

C.-J. David Lin, Mari Carmen Bañuls, Krzysztof Cichy +4 more

We present concluding results from our study for zero-temperature phase structure of the massive Thirring model in 1+1 dimensions with staggered regularisation. Employing the method of matrix product states, several quantities, including two types of correlators, are investigated, leading to numerical evidence of a Berezinskii-Kosterlitz-Thouless phase transition. Exploratory results for real-time dynamics pertaining to this transition, obtained using the approaches of variational uniform matrix product state and time-dependent variational principle, are also discussed.

arXiv:1912.07343•International Symposium on Lattice Field Theory (LATTICE)•Jan 3, 2020•1 citation

Tensor Network study of the (1+1)-dimensional Thirring Model

Mari Carmen Bañuls, Krzysztof Cichy, Ying-Jer Kao +3 more

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the massive Thirring model. We also show the possibility of studying soliton dynamics and topological phase transition via the Thirring model.

arXiv:1710.09993•EPJ Web of Conferences•Jan 1, 2018•1 citation

Tensor Network study of the (1+1)-dimensional Thirring Model

Carmen Bañuls Mari, Krzysztof Cichy, Ying-Jer Kao +3 more

Tensor Network methods have been established as a powerful technique for simulating low dimensional strongly-correlated systems for over two decades. Employing the formalism of Matrix Product States, we investigate the phase diagram of the massive Thirring model. We also show the possibility of studying soliton dynamics and topological phase transition via the Thirring model.

•Jan 1, 2018•8 citations

Quantum simulation of the phase transition of the massive Thirring model

Jia-Qi Gong, Ji-Chong Yang

A bstract Recent advancements in quantum computing technology have enabled the study of fermionic systems at finite temperature via quantum simulations. This presents a novel approach to investigating the chiral phase transition in such systems. Among these, the quantum minimally entangled typical thermal states (QMETTS) algorithm has recently attracted considerable interest. The massive Thirring model, which exhibits a variety of phenomena at low temperatures, includes both a chiral phase transition and a topologically non-trivial ground state. It therefore raises the intriguing question of whether its phase transition can be studied using a quantum simulation approach. In this study, the chiral phase transition of the massive Thirring model and its dual topological phase transition are studied using the QMETTS algorithm. Numerical results are obtained on a classical computer simulating circuit-based quantum computations. The results show that QMETTS is able to accurately reproduce the phase transition and thermodynamic properties of the massive Thirring model.

arXiv:2412.00803•Journal of High Energy Physics•Sep 16, 2025•4 citations

Thermal evolution of the one-flavour Schwinger model using Matrix Product States

H. Saito, Mari Carmen Bañuls, Krzysztof Cichy +2 more

The Schwinger model, or 1+1 dimensional QED, offers an interesting object of study, both at zero and non-zero temperature, because of its similarities to QCD. In this proceeding, we present the a full calculation of the temperature dependent chiral condensate of this model in the continuum limit using Matrix Product States (MPS). MPS methods, in general tensor networks, constitute a very promising technique for the non-perturbative study of Hamiltonian quantum systems. In the last few years, they have shown their suitability as ansatzes for ground states and low-lying excita- tions of lattice gauge theories. We show the feasibility of the approach also for finite temperature, both in the massless and in the massive case.

arXiv:1511.00794•Proceedings of Science•Nov 3, 2015•11 citations
We present preliminary results of a study on the non-thermal phase structure of the (1+1) dimensional massive Thirring model, employing the method of matrix product states. Through investigating the entanglement entropy, the fermion correlators and the chiral condensate, it is found that this approach enables us to observe numerical evidence of a Kosterlitz-Thouless phase transition in the model.
Employing matrix product states as an ansatz, we study the nonthermal phase structure of the (1+11+11+1)-dimensional massive Thirring model in the sector of a vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate, and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with the nonzero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behavior, and they serve as an important ingredient for controlling the continuum extrapolation of the model.
We present concluding results from our study for zero-temperature phase structure of the massive Thirring model in 1+1 dimensions with staggered regularisation. Employing the method of matrix product states, several quantities, including two types of correlators, are investigated, leading to numerical evidence of a Berezinskii-Kosterlitz-Thouless phase transition. Exploratory results for real-time dynamics pertaining to this transition, obtained using the approaches of variational uniform matrix product state and time-dependent variational principle, are also discussed.
A bstract Recent advancements in quantum computing technology have enabled the study of fermionic systems at finite temperature via quantum simulations. This presents a novel approach to investigating the chiral phase transition in such systems. Among these, the quantum minimally entangled typical thermal states (QMETTS) algorithm has recently attracted considerable interest. The massive Thirring model, which exhibits a variety of phenomena at low temperatures, includes both a chiral phase transition and a topologically non-trivial ground state. It therefore raises the intriguing question of whether its phase transition can be studied using a quantum simulation approach. In this study, the chiral phase transition of the massive Thirring model and its dual topological phase transition are studied using the QMETTS algorithm. Numerical results are obtained on a classical computer simulating circuit-based quantum computations. The results show that QMETTS is able to accurately reproduce the phase transition and thermodynamic properties of the massive Thirring model.
The Schwinger model, or 1+1 dimensional QED, offers an interesting object of study, both at zero and non-zero temperature, because of its similarities to QCD. In this proceeding, we present the a full calculation of the temperature dependent chiral condensate of this model in the continuum limit using Matrix Product States (MPS). MPS methods, in general tensor networks, constitute a very promising technique for the non-perturbative study of Hamiltonian quantum systems. In the last few years, they have shown their suitability as ansatzes for ground states and low-lying excita- tions of lattice gauge theories. We show the feasibility of the approach also for finite temperature, both in the massless and in the massive case.