Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912143584002048 |
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| author | Luo, Xiao Kuramashi, Yoshinobu |
| author_facet | Luo, Xiao Kuramashi, Yoshinobu |
| contents | We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension $D_{\rm cut}\rightarrow \infty$. At the vanishing chemical potential $μ=0$, we investigate the von Neumann and Rényi types of entanglement entropies. The central charge is determined to be $c=1.97(9)$ by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with $μ\ne 0$, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point $μ_{\rm c}$ and the critical exponent of the correlation length $ν$ from the $μ$ dependence of the number density in the thermodynamic limit. The dynamical critical exponent $z$ is also extracted from the scaling behavior of the temporal correlation length as a function of $μ$. This is the first successful calculation of the dynamical critical exponent with the TRG method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential Luo, Xiao Kuramashi, Yoshinobu High Energy Physics - Lattice We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension $D_{\rm cut}\rightarrow \infty$. At the vanishing chemical potential $μ=0$, we investigate the von Neumann and Rényi types of entanglement entropies. The central charge is determined to be $c=1.97(9)$ by using the asymptotic scaling properties of the entropies. We also examine the consistency between two entropies. In the finite density region with $μ\ne 0$, where this model suffers from the sign problem in the standard Monte Carlo approach, we investigate the properties of the quantum phase transition. We determine the transition point $μ_{\rm c}$ and the critical exponent of the correlation length $ν$ from the $μ$ dependence of the number density in the thermodynamic limit. The dynamical critical exponent $z$ is also extracted from the scaling behavior of the temporal correlation length as a function of $μ$. This is the first successful calculation of the dynamical critical exponent with the TRG method. |
| title | Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2412.02995 |