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:2308.02798 · Journal of High Energy Physics

Entanglement and Rényi entropies of (1+1)-dimensional O(3) nonlinear sigma model with tensor renormalization group

Xiao Luo, Y. Kuramashi

Published Mar 4, 2024• 4 citations
arXivHTMLPDF

Abstract

A bstract We investigate the entanglement and Rényi entropies for the (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method. The central charge is determined from the asymptotic scaling properties of both entropies. We also examine the consistency between the entanglement entropy and the n th-order Rényi entropy with n → 1.

DOI
10.1007/jhep03(2024)020

Related papers

Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential

Xiao Luo, Y. Kuramashi

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.

arXiv:2412.02995•Dec 4, 2024•0 citations

Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential

Y. Kuramashi, Xiao Luo

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 $\mu=0$, we investigate the von Neumann and R\'enyi 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 $\mu\ne 0$, 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 $\mu_{\rm c}$ and the critical exponent of the correlation length $\nu$ from the $\mu$ 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 $\mu$. This is the first successful calculation of the dynamical critical exponent with the TRG method.

International Symposium on Lattice Field Theory (LATTICE)•Dec 5, 2024•0 citations

Quantum phase transition of (1+1)-dimensional O(3) nonlinear sigma model at finite density with tensor renormalization group

Xiao Luo, Y. Kuramashi

A bstract We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential μ at a fixed coupling of β . We determine the transition point μ c and the critical exponent 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 .

arXiv:2406.08865•Journal of High Energy Physics•Nov 26, 2024•1 citation

O(3) nonlinear sigma model in 1+1 dimensions with matrix product states

Falk Bruckmann A, Karl Jansen, Stefan Kühn

We numerically study the spectral properties, the entanglement and the zero-temperature phase structure at nonvanishing chemical potential of the O(3) nonlinear sigma model. Using matrix product states, a particular kind of one-dimensional tensor network state, we show that we are able to reach the asymptotic scaling regime and to reproduce the analytical predictions for the mass gap at vanishing chemical potential. In addition, we study the scaling of the entanglement entropy towards the continuum limit obtaining a central charge consistent with 2. Moreover, our approach does not suffer from the sign problem and we also explore the phase structure of the model for nonzero chemical potential and map out the location of the transitions between different charge sectors with high precision.

arXiv:1812.00944•Physical review. D/Physical review. D.•Apr 1, 2019•41 citations

Quantum phase transition of (1+1)-dimensional O(3) nonlinear sigma model at finite density with tensor renormalization group

Luo Xiao, Kuramashi Yoshinobu

We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential mu at a fixed coupling of beta. We determine the transition point mu c and the critical exponent nu from the mu 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 mu.

•Nov 26, 2024•0 citations

Entanglement entropy by tensor renormalization group approach

Gota Tanaka, Takahiro Hayazaki, Daisuke Kadoh +1 more

We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a $1 + 1$-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge $c$ is obtained as $c = 0.49997(8)$ for a bond dimension $D_\text{cut}=96$, which agrees with the theoretical value $c=1/2$ within the error.

arXiv:2502.02030•International Symposium on Lattice Field Theory (LATTICE)•Feb 5, 2025•0 citations
A bstract We investigate the entanglement and Rényi entropies for the (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method. The central charge is determined from the asymptotic scaling properties of both entropies. We also examine the consistency between the entanglement entropy and the n th-order Rényi entropy with n → 1.
We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension Dcut→∞D_{\rm cut}\rightarrow \inftyDcut​→∞. At the vanishing chemical potential μ=0μ=0μ=0, we investigate the von Neumann and Rényi types of entanglement entropies. The central charge is determined to be c=1.97(9)c=1.97(9)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≠0μ\ne 0μ=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 μcμ_{\rm c}μc​ and the critical exponent of the correlation length ννν from the μμμ dependence of the number density in the thermodynamic limit. The dynamical critical exponent zzz is also extracted from the scaling behavior of the temporal correlation length as a function of μμμ. This is the first successful calculation of the dynamical critical exponent with the TRG method.
We study (1+1)-dimensional O(3) nonlinear sigma model using the tensor renormalization group method with the infinite limit of the bond dimension Dcut→∞D_{\rm cut}\rightarrow \inftyDcut​→∞. At the vanishing chemical potential μ=0\mu=0μ=0, we investigate the von Neumann and R\'enyi types of entanglement entropies. The central charge is determined to be c=1.97(9)c=1.97(9)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≠0\mu\ne 0μ=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 μc\mu_{\rm c}μc​ and the critical exponent of the correlation length ν\nuν from the μ\muμ dependence of the number density in the thermodynamic limit. The dynamical critical exponent zzz is also extracted from the scaling behavior of the temporal correlation length as a function of μ\muμ. This is the first successful calculation of the dynamical critical exponent with the TRG method.
A bstract We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential μ at a fixed coupling of β . We determine the transition point μ c and the critical exponent 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 .
We numerically study the spectral properties, the entanglement and the zero-temperature phase structure at nonvanishing chemical potential of the O(3) nonlinear sigma model. Using matrix product states, a particular kind of one-dimensional tensor network state, we show that we are able to reach the asymptotic scaling regime and to reproduce the analytical predictions for the mass gap at vanishing chemical potential. In addition, we study the scaling of the entanglement entropy towards the continuum limit obtaining a central charge consistent with 2. Moreover, our approach does not suffer from the sign problem and we also explore the phase structure of the model for nonzero chemical potential and map out the location of the transitions between different charge sectors with high precision.
We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential mu at a fixed coupling of beta. We determine the transition point mu c and the critical exponent nu from the mu 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 mu.
We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a 1+11 + 11+1-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge ccc is obtained as c=0.49997(8)c = 0.49997(8)c=0.49997(8) for a bond dimension Dcut=96D_\text{cut}=96Dcut​=96, which agrees with the theoretical value c=1/2c=1/2c=1/2 within the error.